Heat exchanger design handbook

Heat Exchanger
Design Handbook
Heat Exchanger
Design Handbook
Kuppan Thulukkanam
S e c o n d e d i t i o n

Heat Exchanger
Design Handbook
S E C O N D E D I T I O N

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Heat Exchanger
Design Handbook
Kuppan Thulukkanam
S E C O N D E D I T I O N

CRC Press
Taylor & Francis Group
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© 2013 by Taylor & Francis Group, LLC
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Dedicated to
my parents, S. Thulukkanam and T. Senthamarai,
my wife, Tamizselvi Kuppan,
and my mentor, Dr. Ramesh K. Shah

vii
Contents
Preface................................................................................................................................................li
Acknowledgments............................................................................................................................ liii
Author................................................................................................................................................lv
Chapter 1 Heat Exchangers: Introduction, Classification, and Selection.......................................1
1.1 Introduction........................................................................................................1
1.2 Construction of Heat Exchangers.......................................................................1
1.3 Classification of Heat Exchangers......................................................................1
1.3.1 Classification According to Construction.............................................2
1.3.1.1 Tubular Heat Exchanger........................................................2
1.3.1.2 Plate Heat Exchangers.........................................................10
1.3.1.3 Extended Surface Exchangers.............................................15
1.3.1.4 Regenerative Heat Exchangers............................................15
1.3.2 Classification according to Transfer Process...................................... 16
1.3.2.1 Indirect Contact Heat Exchangers....................................... 16
1.3.2.2 Direct Contact–Type Heat Exchangers................................ 17
1.3.3 Classification according to Surface Compactness.............................. 17
1.3.4 Classification According to Flow Arrangement.................................. 18
1.3.4.1 Parallelflow Exchanger........................................................ 18
1.3.4.2 Counterflow Exchanger.......................................................19
1.3.4.3 Crossflow Exchanger...........................................................19
1.3.5 Classification According to Pass Arrangements.................................20
1.3.5.1 Multipass Exchangers..........................................................20
1.3.6 Classification According to Phase of Fluids.......................................21
1.3.6.1 Gas–Liquid.......................................................................... 21
1.3.6.2 Liquid–Liquid......................................................................21
1.3.6.3 Gas–Gas..............................................................................21
1.3.7 Classification According to Heat Transfer Mechanisms..................... 21
1.3.7.1 Condensers........................................................................... 21
1.3.7.2 Evaporators.......................................................................... 21
1.3.8 Other Classifications...........................................................................22
1.3.8.1 Micro Heat Exchanger.........................................................22
1.3.8.2 Printed Circuit Heat Exchanger...........................................23
1.3.8.3 Perforated Plate Heat Exchanger as Cryocoolers................25
1.3.8.4 Scraped Surface Heat Exchanger........................................25
1.3.8.5 Graphite Heat Exchanger.....................................................27
1.4 Selection of Heat Exchangers...........................................................................28
1.4.1 Introduction.........................................................................................28
1.4.2 Selection Criteria.................................................................................29
1.4.2.1 Materials of Construction....................................................30
1.4.2.2 Operating Pressure and Temperature..................................30
1.4.2.3 Flow Rate............................................................................. 31
1.4.2.4 Flow Arrangement............................................................... 31
1.4.2.5 Performance Parameters: Thermal Effectiveness and
Pressure Drops..................................................................... 31

viii Contents
1.4.2.6 Fouling Tendencies..............................................................32
1.4.2.7 Types and Phases of Fluids..................................................32
1.4.2.8 Maintenance, Inspection, Cleaning, Repair, and
Extension Aspects................................................................32
1.4.2.9 Overall Economy.................................................................32
1.4.2.10 Fabrication Techniques........................................................33
1.4.2.11 Choice of Unit Type for Intended Applications...................33
1.5 Requirements of Heat Exchangers...................................................................34
References...................................................................................................................34
Suggested Readings.....................................................................................................35
Bibliography................................................................................................................35
Chapter 2 Heat Exchanger Thermohydraulic Fundamentals.......................................................39
2.1 Heat Exchanger Thermal Circuit and Overall Conductance Equation............39
2.2 Heat Exchanger Heat Transfer Analysis Methods............................................ 41
2.2.1 Energy Balance Equation.................................................................... 41
2.2.2 Heat Transfer....................................................................................... 41
2.2.3 Basic Methods to Calculate Thermal Effectiveness...........................42
2.2.3.1 ε-NTU Method....................................................................42
2.2.3.2 P-NTUt Method...................................................................43
2.2.3.3 Log Mean Temperature Difference Correction Factor
Method.................................................................................45
2.2.3.4 ψ-P Method.........................................................................48
2.2.4 Some Fundamental Relationships to Characterize
the Exchanger for “Subdesign” Condition..........................................49
2.3 Thermal Effectiveness Charts..........................................................................50
2.4 Symmetry Property and Flow Reversibility and Relation between
the Thermal Effectiveness of Overall Parallel and Counterflow Heat
Exchanger Geometries.....................................................................................52
2.4.1 Symmetry Property.............................................................................52
2.4.2 Flow Reversibility...............................................................................52
2.5 Temperature Approach, Temperature Meet, and Temperature Cross..............54
2.5.1 Temperature Cross for Other TEMA Shells.......................................56
2.6 Thermal Relation Formulas for Various Flow Arrangements and Pass
Arrangements...................................................................................................56
2.6.1 Parallelflow..........................................................................................57
2.6.2 Counterflow.........................................................................................57
2.6.3 Crossflow Arrangement.......................................................................57
2.6.3.1 Unmixed–Unmixed Crossflow............................................57
2.6.3.2 Unmixed–Mixed Crossflow.................................................57
2.6.3.3 Mixed–Mixed Crossflow.....................................................57
2.6.3.4 Single or Multiple Rows in Crossflow.................................57
2.6.4 Thermal Relations for Various TEMA Shells and Others..................72
2.6.4.1 E Shell.................................................................................. 74
2.6.4.2 TEMA F Shell.....................................................................79
2.6.4.3 TEMA G Shell or Split-Flow Exchanger.............................79
2.6.4.4 TEMA H Shell.....................................................................81
2.6.4.5 TEMA J Shell or Divided-Flow Shell.................................81
2.6.4.6 TEMA X Shell.....................................................................90
2.6.5 Thermal Effectiveness of Multiple Heat Exchangers..........................90

ixContents
2.6.5.1 Two-Pass Exchangers..........................................................92
2.6.5.2 N-Pass Exchangers...............................................................92
2.6.6 Multipass Crossflow Exchangers.........................................................92
2.6.6.1 Multipassing with Complete Mixing between Passes.........93
2.6.6.2 Two Passes with One Fluid Unmixed throughout,
Cross-Counterflow Arrangement.........................................94
2.6.6.3 Two Passes with Both Fluids Unmixed–Unmixed
in Each Pass and One Fluid Unmixed throughout,
Cross-Counterflow Arrangement.........................................98
2.6.6.4 Two Passes with Both Fluids Unmixed throughout,
Cross-Counterflow Arrangement....................................... 101
2.6.7 Thermal Effectiveness of Multiple-Pass Shell and
Tube Heat Exchangers.......................................................................108
Acknowledgment....................................................................................................... 113
References................................................................................................................. 113
Bibliography.............................................................................................................. 115
Chapter 3 Heat Exchanger Thermal Design.............................................................................. 117
3.1 Fundamentals of Heat Exchanger Design Methodology................................ 117
3.1.1 Process/Design Specifications.......................................................... 117
3.1.1.1 Problem Specification........................................................ 117
3.1.1.2 Exchanger Construction..................................................... 118
3.1.1.3 Surface Selection............................................................... 119
3.1.2 Thermohydraulic Design................................................................... 119
3.1.2.1 Basic Thermohydraulic Design Methods.......................... 119
3.1.2.2 Thermophysical Properties................................................ 119
3.1.2.3 Surface Geometrical Properties........................................ 119
3.1.2.4 Surface Characteristics...................................................... 119
3.2 Design Procedure...........................................................................................120
3.3 Heat Exchanger Design Problems..................................................................120
3.3.1 Rating................................................................................................120
3.3.1.1 Rating of a Compact Exchanger........................................120
3.3.1.2 Rating of a Shell and Tube Exchanger............................... 121
3.3.2 Sizing................................................................................................. 121
3.3.2.1 Size of a Heat Exchanger................................................... 121
3.3.2.2 Sensitivity Analysis...........................................................122
3.3.2.3 Sizing of a Compact Heat Exchanger................................122
3.3.2.4 Sizing of a Shell and Tube Heat Exchanger.......................122
3.3.2.5 Heat Exchanger Optimization...........................................122
3.3.3 Solution to the Rating and Sizing Problem.......................................122
3.3.3.1 Rating.................................................................................122
3.3.3.2 Solution to the Sizing Problem..........................................123
3.4 Computer-Aided Thermal Design..................................................................123
3.4.1 Overall Structure of a Thermal Design Computer Program.............123
3.4.1.1 Guidelines on Program Logic............................................124
3.4.2 Program Structure for a Shell and Tube Exchanger..........................125
3.5 Pressure-Drop Analysis, Temperature-Dependent Fluid Properties,
Performance Failures, Flow Maldistribution, Fouling, and Corrosion..........125
3.5.1 Heat Exchanger Pressure-Drop Analysis..........................................125
3.5.1.1 Pressure-Drop Evaluation for Heat Exchangers................125

x Contents
3.5.1.2 Pressure Drop through a Heat Exchanger.........................126
3.5.1.3 Shell and Tube Heat Exchangers.......................................127
3.5.1.4 Pressure Drop due to Flow Turning..................................127
3.5.1.5 Pressure Drop in the Nozzles............................................128
3.5.2 Temperature-Dependent Fluid Properties Correction.......................128
3.5.2.1 Gases..................................................................................128
3.5.2.2 Liquids...............................................................................129
3.5.3 Performance Failures........................................................................130
3.5.4 Maldistribution.................................................................................. 131
3.5.5 Fouling.............................................................................................. 131
3.5.6 Corrosion Allowance......................................................................... 132
3.6 Cooperative Research Programs on Heat Exchanger Design........................ 132
3.6.1 HTRI................................................................................................. 132
3.6.2 HTFS................................................................................................. 132
3.7 Uncertainties in Thermal Design of Heat Exchangers................................... 133
3.7.1 Uncertainties in Heat Exchanger Design.......................................... 133
3.7.1.1 Uncertainty in Process Conditions....................................134
3.7.1.2 Uncertainty in the Physical Properties of the Process
Fluids.................................................................................134
3.7.1.3 Flow Nonuniformity..........................................................134
3.7.1.4 Nonuniform Flow Passages............................................... 135
3.7.1.5 Uncertainty in the Basic Design Correlations................... 135
3.7.1.6 Uncertainty due to Thermodynamically Defined
Mixed or Unmixed Flows for Crossflow Heat
Exchangers, after Digiovanni and Webb...........................136
3.7.1.7 Nonuniform Heat Transfer Coefficient..............................136
3.7.1.8 Bypass Path on the Air Side of Compact Tube-Fin
Exchangers.........................................................................137
3.7.1.9 Uncertainty in Fouling......................................................137
3.7.1.10 Miscellaneous Effects........................................................137
3.7.2 Determination of Uncertainties......................................................... 137
3.7.2.1 Computational Procedures................................................137
3.7.3.2 Additional Surface Area Required due to Uncertainty..... 139
3.7.3.3 Additional Pressure Drop due to Uncertainty................... 139
Nomenclature............................................................................................................ 140
References................................................................................................................. 141
Bibliography.............................................................................................................. 143
Chapter 4 Compact Heat Exchangers........................................................................................ 145
4.1 Classification and Construction Details of Tube-Fin Compact Heat
Exchangers...................................................................................................... 145
4.1.1 Characteristics of Compact Heat Exchangers................................... 145
4.1.2 Construction Types of Compact Heat Exchangers............................ 146
4.1.3 Tube-Fin Heat Exchangers................................................................ 146
4.1.3.1 Specific Qualitative Considerations for Tube-Fin Surfaces......147
4.1.3.2 Applications....................................................................... 148
4.1.3.3 Individually Finned Tubes................................................. 148
4.1.4 Continuous Fins on a Tube Array..................................................... 151
4.1.4.1 Tube: Primary Surface................................................... 151
4.1.4.2 Fin: Secondary Surface.................................................. 151

xiContents
4.1.4.3 Headers........................................................................... 152
4.1.4.4 Tube-to-Header Joints.................................................... 152
4.1.4.5 Casings or Tube Frame.................................................. 152
4.1.4.6 Circuiting....................................................................... 152
4.1.4.7 Exchangers for Air Conditioning and Refrigeration...... 152
4.1.4.8 Radiators........................................................................ 153
4.1.4.9 Effect of Fin Density on Fouling................................... 153
4.1.4.10 One-Row Radiator ........................................................154
4.1.4.11 Manufacture of Continuous Finned Tube Heat
Exchangers..................................................................... 155
4.1.5 Surface Selection...............................................................................156
4.1.5.1 Qualitative Considerations.............................................156
4.1.5.2 Quantitative Considerations........................................... 157
4.2 Plate-Fin Heat Exchangers............................................................................. 157
4.2.1 PFHE: Essential Features.................................................................. 158
4.2.2 Application for Fouling Service........................................................ 158
4.2.3 Size....................................................................................................159
4.2.4 Advantages of PFHEs....................................................................... 159
4.2.5 Limitations of PFHEs.......................................................................159
4.2.6 Applications....................................................................................... 159
4.2.7 Economics.........................................................................................160
4.2.8 Flow Arrangements...........................................................................160
4.2.9 Fin Geometry Selection and Performance Factors........................... 160
4.2.9.1 Plain Fin.........................................................................160
4.2.9.2 Plain-Perforated Fin....................................................... 161
4.2.9.3 Offset Strip Fin.............................................................. 162
4.2.9.4 Serrated Fins.................................................................. 163
4.2.9.5 Herringbone or Wavy Fin.............................................. 163
4.2.9.6 Louver Fins.................................................................... 163
4.2.9.7 Pin Fins..........................................................................164
4.2.9.8 FIN Corrugation Code................................................... 165
4.2.10 Corrugation Selection........................................................................166
4.2.11 Materials of Construction.................................................................. 166
4.2.11.1 Aluminum......................................................................166
4.2.11.2 Other Metals..................................................................166
4.2.12 Mechanical Design............................................................................ 166
4.2.13 Manufacture, Inspection, and Quality Control.................................166
4.2.14 Brazed Aluminum Plate-Fin Heat Exchanger (BAHX)................... 166
4.2.14.1 ALPEMA Standard........................................................ 166
4.2.14.2 Applications................................................................... 169
4.2.14.3 Heat Exchanger Core..................................................... 169
4.2.14.4 Flow Arrangement......................................................... 169
4.2.14.5 Rough Estimation of the Core Volume.......................... 171
4.2.14.6 Provisions for Thermal Expansion and Contraction.........173
4.2.14.7 Mechanical Design of Brazed Aluminum Plate-Fin
Heat Exchangers............................................................. 173
4.2.14.8 Codes.............................................................................. 173
4.2.14.9 Materials of Construction.............................................. 173
4.2.14.10 Manufacture................................................................... 174
4.2.14.11 Quality Assurance Program and Third Party
Inspection....................................................................... 174

xii Contents
4.2.14.12 Testing of BAHX........................................................... 174
4.2.14.13 Guarantees..................................................................... 174
4.2.14.14 ALEX: Brazed ALuminum EXchanger........................ 174
4.2.15 Comparison of Salient Features of Plate-Fin Heat Exchangers
and Coil-Wound Heat Exchanger...................................................... 175
4.2.16 Heat Exchanger Specification Sheet for Plate-Fin Heat Exchanger..........175
4.3 Surface Geometrical Relations....................................................................... 175
4.3.1 Surface Geometrical Parameters: General........................................ 175
4.3.1.1 Hydraulic Diameter, Dh..................................................... 175
4.3.1.2 Surface Area Density α and σ........................................... 177
4.3.2 Tubular Heat Exchangers.................................................................. 177
4.3.2.1 Tube Inside......................................................................... 177
4.3.2.2 Tube Outside...................................................................... 178
4.3.3 Compact Plate-Fin Exchangers......................................................... 184
4.3.3.1 Heat Transfer Area............................................................ 184
4.3.3.2 Components of Pressure Loss............................................ 186
4.4 Factors Influencing Tube-Fin Heat Exchanger Performance......................... 187
4.4.1 Tube Layout....................................................................................... 187
4.4.2 Equilateral Layout versus Equivelocity Layout................................ 187
4.4.3 Number of Tube Rows....................................................................... 187
4.4.4 Tube Pitch.......................................................................................... 188
4.4.5 Tube-Fin Variables............................................................................ 188
4.4.5.1 Fin Height and Fin Pitch.................................................... 188
4.4.6 Finned Tubes with Surface Modifications........................................ 188
4.4.7 Side Leakage..................................................................................... 189
4.4.8 Boundary-Layer Disturbances and Characteristic Flow Length...... 189
4.4.9 Contact Resistance in Finned Tube Heat Exchangers.......................190
4.4.9.1 Continuous Finned Tube Exchanger..................................190
4.4.9.2 Tension-Wound Fins on Circular Tubes.............................190
4.4.9.3 Integral Finned Tube..........................................................190
4.4.10 Induced Draft versus Forced Draft................................................... 191
4.4.10.1 Induced Draft..................................................................... 191
4.4.10.2 Forced Draft...................................................................... 191
4.5 Thermohydraulic Fundamentals of Finned Tube Heat Exchangers............... 191
4.5.1 Heat Transfer and Friction Factor Correlations for Crossflow
over Staggered Finned Tube Banks................................................... 191
4.5.2 The j and f Factors.............................................................................192
4.5.2.1 Bare Tube Bank.................................................................192
4.5.2.2 Circular Tube-Fin Arrangement........................................ 193
4.5.2.3 Continuous Fin on Circular Tube......................................196
4.5.2.4 Continuous Fin on Flat Tube Array...................................198
4.6 Correlations for j and f factors of Plate-Fin Heat Exchangers.......................198
4.6.1 Offset Strip Fin Heat Exchanger....................................................... 198
4.6.2 Louvered Fin.....................................................................................200
4.6.3 Pin Fin Heat Exchangers...................................................................201
4.7 Fin Efficiency.................................................................................................202
4.7.1 Fin Length for Some Plate-Fin Heat Exchanger Fin
Configurations...................................................................................202
4.7.2 Fin Efficiency....................................................................................202
4.7.2.1 Circular Fin........................................................................202
4.7.2.2 Plain Continuous Fin on Circular Tubes...........................204

xiiiContents
4.8 Rating of a Compact Exchanger.....................................................................206
4.8.1 Rating of Single-Pass Counterflow and Crossflow Exchangers........207
4.8.2 Shah’s Method for Rating of Multipass Counterflow and
Crossflow Heat Exchangers...............................................................209
4.9 Sizing of a Compact Heat Exchanger............................................................. 210
4.9.1 Core Mass Velocity Equation............................................................ 210
4.9.2 Procedure for Sizing a Compact Heat Exchanger............................. 211
4.9.3 Optimization of Plate-Fin Exchangers and Constraints on
Weight Minimization........................................................................ 211
4.10 Effect of Longitudinal Heat Conduction on Thermal Effectiveness.............. 212
4.10.1 Longitudinal Conduction Influence on Various Flow
Arrangements.................................................................................... 213
4.10.2 Comparison of Thermal Performance of Compact Heat
Exchangers........................................................................................ 213
4.11 Air-Cooled Heat Exchanger (ACHE)............................................................. 213
4.11.1 Air versus Water Cooling.................................................................. 214
4.11.1.1 Air Cooling........................................................................ 215
4.11.2 Construction of ACHE...................................................................... 216
4.11.2.1 Tube Bundle Construction................................................. 216
4.11.3 American Petroleum Institute Standard API 661/ISO 13706...........224
4.11.4 Problems with Heat Exchangers in Low-Temperature Environments... 225
4.11.4.1 Temperature Control..........................................................225
4.11.5 Forced Draft versus Induced Draft...................................................225
4.11.5.1 Forced Draft......................................................................225
4.11.5.2 Induced Draft.....................................................................225
4.11.6 Recirculation.....................................................................................226
4.11.7 Design Aspects..................................................................................226
4.11.7.1 Design Variables................................................................226
4.11.7.2 Design Air Temperature....................................................227
4.11.8 Design Tips........................................................................................228
4.11.8.1 Air-Cooled Heat Exchanger Design Procedure.................228
4.11.8.2 Air-Cooled Heat Exchanger Data/Specification Sheet......229
4.11.8.3 Performance Control of ACHEs........................................230
Nomenclature............................................................................................................230
References.................................................................................................................232
Bibliography..............................................................................................................236
Chapter 5 Shell and Tube Heat Exchanger Design....................................................................237
5.1 Construction Details for Shell and Tube Exchangers.....................................237
5.1.1 Design Standards...............................................................................237
5.1.1.1 TEMA Standard................................................................237
5.1.1.2 ANSI/API Standard 660....................................................237
5.2 Tubes...............................................................................................................238
5.2.1 Tube Diameter...................................................................................239
5.2.2 Tube Wall Thickness.........................................................................239
5.2.3 Low-Finned Tubes.............................................................................240
5.2.4 Tube Length.......................................................................................240
5.2.5 Means of Fabricating Tubes..............................................................240
5.2.6 Duplex or Bimetallic Tubes...............................................................240
5.2.7 Number of Tubes...............................................................................241

xiv Contents
5.2.8 Tube Count........................................................................................ 241
5.2.9 U-Tube............................................................................................... 241
5.2.9.1 U-Tube U-Bend Requirements as per TEMA....................241
5.3 Tube Arrangement..........................................................................................242
5.3.1 Tube Pitch..........................................................................................242
5.3.2 Tube Layout.......................................................................................242
5.3.2.1 Triangular and Rotated Triangular Arrangements............242
5.3.2.2 Square and Rotated Square Arrangements........................243
5.4 Baffles.............................................................................................................243
5.4.1 Classification of Baffles.....................................................................243
5.4.2 Transverse Baffles.............................................................................243
5.4.2.1 Segmental Baffles..............................................................243
5.4.3 Disk and Doughnut Baffle.................................................................247
5.4.4 Orifice Baffle.....................................................................................248
5.4.5 No Tubes in Window.........................................................................248
5.4.6 Longitudinal Baffles..........................................................................249
5.4.7 Rod Baffles........................................................................................249
5.4.8 NEST Baffles and Egg-Crate Tube Support......................................249
5.4.8.1 Non-Segmental Baffles......................................................250
5.4.9 Grimmas Baffle................................................................................. 251
5.4.10 Wavy Bar Baffle................................................................................ 251
5.4.11 Baffles for Steam Generator Tube Support....................................... 251
5.5 Tubesheet and Its Connection with Shell and Channel..................................252
5.5.1 Clad and Faced Tubesheets...............................................................253
5.5.2 Tube-to-Tubesheet Attachment.........................................................253
5.5.3 Double Tubesheets.............................................................................253
5.5.3.1 Types of Double Tubesheet Designs..................................253
5.5.4 Demerits of Double Tubesheets........................................................256
5.6 Tube Bundle....................................................................................................256
5.6.1 Bundle Weight...................................................................................256
5.6.2 Spacers, Tie-Rods, and Sealing Devices...........................................256
5.6.3 Outer Tube Limit...............................................................................256
5.7 Shells..............................................................................................................258
5.8 Pass Arrangement...........................................................................................258
5.8.1 Tubeside Passes.................................................................................258
5.8.1.1 Number of Tube Passes......................................................258
5.8.1.2 End Channel and Channel Cover.......................................260
5.8.2 Shellside Passes.................................................................................262
5.8.2.1 Expansion Joint..................................................................263
5.8.2.2 Drains and Vents................................................................263
5.8.2.3 Nozzles and Impingement Protection................................263
5.9 Fluid Properties and Allocation.....................................................................266
5.10 Classification of Shell and Tube Heat Exchangers.........................................266
5.11 TEMA System for Describing Heat Exchanger Types...................................266
5.11.1 Fixed Tubesheet Exchangers.............................................................269
5.11.2 U-Tube Exchangers............................................................................270
5.11.2.1 Shortcomings of U-Tube Exchangers................................270
5.11.3 Floating Head Exchangers................................................................271
5.11.3.1 Sliding Bar/Surface............................................................ 271
5.11.3.2 Kettle-Type Reboiler..........................................................272

xvContents
5.12 Differential Thermal Expansion.....................................................................272
5.13 TEMA Classification of Heat Exchangers Based on Service Condition........272
5.14 Shell and Tube Heat Exchanger Selection......................................................272
5.14.1 Shell Types........................................................................................272
5.14.1.1 TEMA E Shell................................................................... 274
5.14.1.2 TEMA F Shell................................................................... 274
5.14.1.3 TEMA G, H Shell..............................................................275
5.14.1.4 TEMA G Shell or Split Flow Exchanger...........................275
5.14.1.5 TEMA H Shell or Double Split Flow Exchanger..............275
5.14.1.6 TEMA J Shell or Divided Flow Exchanger......................276
5.14.1.7 TEMA K Shell or Kettle Type Reboiler............................276
5.14.1.8 TEM X Shell......................................................................277
5.14.1.9 Comparison of Various TEMA Shells...............................278
5.14.2 Front and Rear Head Designs...........................................................278
5.14.2.1 Designations for Head Types.............................................278
5.14.3 TEMA Specification Sheet................................................................279
5.15 Shellside Clearances.......................................................................................279
5.15.1 Tube-to-Baffle-Hole Clearance.........................................................279
5.15.2 Shell-to-Baffle Clearance..................................................................279
5.15.3 Shell-to-Bundle Clearance................................................................279
5.15.4 Bypass Lanes.....................................................................................282
5.16 Design Methodology......................................................................................282
5.16.1 Shellside Flow Pattern.......................................................................282
5.16.1.1 Shell Fluid Bypassing and Leakage..................................282
5.16.1.2 Bypass Prevention and Sealing Devices............................282
5.16.1.3 Shellside Flow Pattern.......................................................284
5.16.1.4 Flow Fractions for Each Stream........................................285
5.16.1.5 Shellside Performance.......................................................285
5.16.2 Sizing of Shell and Tube Heat Exchangers.......................................285
5.16.3 Guidelines for STHE Design............................................................285
5.16.3.1 Heat Transfer Coefficient and Pressure Drop....................286
5.16.4 Guidelines for Shellside Design........................................................286
5.16.4.1 Specify the Right Heat Exchanger....................................287
5.16.5 Design Considerations for a Shell and Tube Heat Exchanger...........287
5.16.5.1 Thermal Design Procedure................................................288
5.16.5.2 Detailed Design Method: Bell–Delaware Method............ 291
5.16.5.3 Auxiliary Calculations, Step-by-Step Procedure..............293
5.16.6 Shellside Heat Transfer and Pressure-Drop Correction Factors.......297
5.16.6.1 Step-by-Step Procedure to Determine Heat Transfer
and Pressure-Drop Correction Factors..............................298
5.16.6.2 Shellside Heat Transfer Coefficient and Pressure Drop........301
5.16.6.3 Tubeside Heat Transfer Coefficient and Pressure Drop............304
5.16.6.4 Accuracy of the Bell–Delaware Method...........................308
5.16.6.5 Extension of the Delaware Method to Other Geometries..........308
5.17 Shell and Tube Heat Exchangers with Non-Segmental Baffles..................... 310
5.17.1 Phillips RODbaffle Heat Exchanger................................................. 310
5.17.1.1 RODbaffle Exchanger Concepts........................................ 310
5.17.1.2 Important Benefit: Elimination of Shellside
Flow- Induced Vibration..................................................... 311
5.17.1.3 Proven RODbaffle Applications........................................ 311

xvi Contents
5.17.1.4 Operational Characteristics............................................... 311
5.17.1.5 Thermal Performance........................................................ 311
5.17.1.6 Design and Rating Program Available.............................. 312
5.17.2 EMbaffle® Heat Exchanger............................................................... 312
5.17.2.1 Application of EMbaffle Technology................................ 312
5.17.2.2 Design................................................................................ 312
5.17.2.3 Benefits of EMbaffle Technology...................................... 314
5.17.3 Helixchanger® Heat Exchanger......................................................... 314
5.17.3.1 Merits of Helixchanger Heat Exchanger............................ 315
5.17.3.2 Applications....................................................................... 315
5.17.3.3 Helixchanger Heat Exchanger: Configurations................. 315
5.17.3.4 Performance....................................................................... 317
5.17.4 Twisted Tube® Heat Exchanger......................................................... 318
5.17.4.1 Applications....................................................................... 318
5.17.4.2 Advantages......................................................................... 318
5.17.4.3 Merits of Twisted Tube Heat Exchanger............................ 319
5.17.5 End Closures..................................................................................... 319
5.17.5.1 Breech-Lock™ Closure..................................................... 319
5.17.5.2 Easy Installation and Dismantling Jig...............................320
5.17.6 Taper-Lok® Closure...........................................................................320
5.17.7 High-Pressure End Closures.............................................................320
5.A Appendix A.................................................................................................... 321
5.A.1 Reference Crossflow Velocity as per Tinker..................................... 321
5.A.2 Design of Disk and Doughnut Heat Exchanger................................323
5.A.2.1 Design Method..................................................................323
5.A.2.2 Heat Transfer.....................................................................324
5.A.2.3 Shellside Pressure Drop.....................................................326
5.A.2.4 Shortcomings of Disk and Doughnut Heat Exchanger......326
5.A.3 NORAM RF™ Radial Flow Gas Heat Exchanger...........................326
5.A.3.1 Tube Layout.......................................................................327
5.A.4 Closed Feedwater Heaters.................................................................327
5.A.4.1 Low-Pressure Feedwater Heaters......................................328
5.A.4.2 High-Pressure Feedwater Heaters.....................................328
5.A.5 Steam Surface Condenser.................................................................329
5.A.5.1 Mechanical Description.....................................................330
5.A.5.2 Parts of Condenser.............................................................330
5.A.5.3 Condenser Tube Material................................................... 331
5.A.5.4 Condenser Support Systems.............................................. 332
Nomenclature............................................................................................................ 332
References................................................................................................................. 333
Suggested Readings...................................................................................................336
Chapter 6 Regenerators.............................................................................................................. 337
6.1 Introduction....................................................................................................337
6.1.1 Regeneration Principle......................................................................337
6.1.2 Regenerators in Thermodynamic Systems and Others.....................337
6.1.3 Gas Turbine Cycle with Regeneration...............................................337
6.1.4 Waste Heat Recovery Application..................................................... 338
6.1.5 Benefits of Waste Heat Recovery......................................................338
6.1.5.1 Direct Benefits...................................................................338

xviiContents
6.1.5.2 Indirect Benefits................................................................. 339
6.1.5.3 Fuel Savings due to Preheating Combustion Air...............339
6.2 Heat Exchangers Used for Regeneration........................................................339
6.2.1 Recuperator.......................................................................................339
6.2.1.1 Merits of Recuperators...................................................... 339
6.2.2 Regenerator.......................................................................................340
6.2.3 Types of Regenerators.......................................................................340
6.2.4 Fixed-Matrix or Fixed-Bed-Type Regenerator.................................. 341
6.2.4.1 Fixed-Matrix Surface Geometries.....................................342
6.2.4.2 Size....................................................................................342
6.2.4.3 Merits of Fixed-Bed Regenerators.....................................342
6.2.5 Rotary Regenerators..........................................................................343
6.2.5.1 Salient Features of Rotary Regenerators...........................343
6.2.5.2 Rotary Regenerators for Gas Turbine Applications...........345
6.2.5.3 Types of Rotary Regenerators...........................................345
6.2.5.4 Drive to Rotary Regenerators............................................345
6.2.5.5 Operating Temperature and Pressure................................345
6.2.5.6 Surface Geometries for Rotary Regenerators....................345
6.2.5.7 Influence of Hydraulic Diameter on Performance............345
6.2.5.8 Size....................................................................................346
6.2.5.9 Desirable Characteristics for a Regenerative Matrix.........346
6.2.5.10 Total Heat Regenerators.....................................................346
6.2.5.11 Merits of Regenerators.......................................................347
6.3 Rotary Regenerative Air Preheater................................................................347
6.3.1 Design Features.................................................................................348
6.3.2 Heating Element Profiles...................................................................349
6.3.3 Enameled Elements...........................................................................349
6.3.4 Corrosion and Fouling.......................................................................349
6.3.5 Heat Exchanger Baskets....................................................................349
6.3.6 Seals and Sealing System Components.............................................350
6.3.6.1 Radial Seals and Sector Plates...........................................350
6.3.6.2 Axial Seals and Sealing Plates.......................................... 351
6.3.6.3 Circumferential Seals and Circumferential Sealing
Ring...............................................................................351
6.3.7 Leakage............................................................................................. 351
6.3.8 Alstom Power Trisector Ljungström® Air Preheater......................... 351
6.4 Comparison of Recuperators and Regenerators............................................. 352
6.5 Considerations in Establishing a Heat Recovery System............................... 352
6.5.1 Compatibility with the Existing Process System.............................. 352
6.5.2 Economic Benefits............................................................................. 353
6.5.2.1 Capital Costs...................................................................... 353
6.5.3 Life of the Exchanger........................................................................ 353
6.5.4 Maintainability.................................................................................. 353
6.6 Regenerator Construction Material................................................................ 353
6.6.1 Strength and Stability at the Operating Temperature.......................354
6.6.2 Corrosion Resistance......................................................................... 355
6.6.3 Ceramic Heat Exchangers................................................................. 355
6.6.3.1 Low Gas Permeability....................................................... 355
6.6.4 Ceramic–Metallic Hybrid Recuperator............................................. 355
6.6.5 Regenerator Materials for Other than Waste Heat Recovery............ 355

xviii Contents
6.7 Thermal Design: Thermal-Hydraulic Fundamentals.....................................356
6.7.1 Surface Geometrical Properties........................................................356
6.7.2 Correlation for j and f........................................................................ 357
6.8 Thermal Design Theory................................................................................. 358
6.8.1 Regenerator Solution Techniques...................................................... 359
6.8.1.1 Open Methods: Numerical Finite-Difference Method...... 359
6.8.1.2 Closed Methods................................................................. 359
6.8.2 Basic Thermal Design Methods........................................................ 359
6.8.3 Coppage and Longon Model for a Rotary Regenerator....................360
6.8.3.1 Thermal Effectiveness.......................................................362
6.8.3.2 Heat Transfer.....................................................................364
6.8.4 Parameter Definitions........................................................................364
6.8.5 Classification of Regenerator............................................................365
6.8.6 Additional Formulas for Regenerator Effectiveness.........................365
6.8.6.1 Balanced and Symmetric Counterflow Regenerator.........366
6.8.7 Reduced Length–Reduced Period (Λ–Π) Method............................367
6.8.7.1 Counterflow Regenerator...................................................367
6.8.8 Razelos Method for Asymmetric-Unbalanced Counterflow
Regenerator.......................................................................................370
6.8.9 Influence of Longitudinal Heat Conduction in the Wall................... 371
6.8.9.1 Bahnke and Howard Method.............................................372
6.8.9.2 Romie’s Solution................................................................372
6.8.9.3 Shah’s Solution to Account for the Longitudinal
Conduction Effect..............................................................373
6.8.10 Fluid Bypass and Carryover on Thermal Effectiveness.................... 374
6.8.11 Regenerator Design Methodology..................................................... 374
6.8.12 Primary Considerations Influencing Design..................................... 374
6.8.13 Rating of Rotary Regenerators.......................................................... 374
6.8.14 Sizing of Rotary Regenerators.......................................................... 374
6.9 Mechanical Design......................................................................................... 375
6.9.1 Single-Bed and Dual-Bed Fixed Regenerators................................. 375
6.9.2 Rotary Regenerators.......................................................................... 375
6.9.2.1 Leakages............................................................................ 375
6.9.2.2 Seal Design........................................................................ 376
6.9.2.3 Drive for the Rotor............................................................. 376
6.9.2.4 Thermal Distortion and Transients....................................377
6.9.2.5 Pressure Forces..................................................................377
6.10 Industrial Regenerators and Heat Recovery Devices.....................................377
6.10.1 Fluid-Bed Regenerative Heat Exchangers.........................................377
6.10.2 Fluidized-Bed Waste Heat Recovery................................................ 378
6.10.3 Vortex-Flow Direct-Contact Heat Exchangers..................................379
6.10.4 Ceramic Bayonet Tube Heat Exchangers..........................................379
6.10.5 Regenerative Burners........................................................................379
6.10.6 Porcelain-Enameled Flat-Plate Heat Exchangers..............................380
6.10.7 Radiation Recuperators.....................................................................380
6.10.8 Heat-Pipe Heat Exchangers............................................................... 381
6.10.8.1 Merits of Heat-Pipe Heat Exchanger.................................382
6.10.8.2 Application........................................................................382
6.10.9 Economizer.......................................................................................382
6.10.10 Thermocompressor............................................................................382
6.10.11 Mueller Temp-Plate® Energy Recovery Banks.................................383

xixContents
6.11 Rotary Heat Exchangers for Space Heating...................................................383
6.11.1 Working Principle.............................................................................384
6.11.2 Construction......................................................................................385
6.11.3 Rotor Materials..................................................................................385
6.11.3.1 Construction.......................................................................385
6.11.3.2 Carryover...........................................................................385
6.11.3.3 Seals...................................................................................385
6.11.4 Drive System and Control Unit.........................................................386
6.11.5 Cleaning Devices..............................................................................386
Nomenclature............................................................................................................386
References.................................................................................................................388
Bibliography.............................................................................................................. 391
Chapter 7 Plate Heat Exchangers and Spiral Plate Heat Exchangers........................................393
7.1 Plate Heat Exchanger Construction: General.................................................393
7.1.1 Flow Patterns and Pass Arrangement...............................................394
7.1.2 Useful Data on PHE..........................................................................396
7.1.3 Standard Performance Limits...........................................................397
7.2 Benefits Offered by Plate Heat Exchangers....................................................397
7.3 Comparison between a Plate Heat Exchanger and a Shell and Tube Heat
Exchanger.......................................................................................................399
7.4 Plate Heat Exchanger: Detailed Construction Features.................................399
7.4.1 Plate...................................................................................................399
7.4.1.1 Plate Pattern.......................................................................399
7.4.1.2 Types of Plate Corrugation................................................400
7.4.1.3 Intermating Troughs Pattern..............................................400
7.4.1.4 Chevron or Herringbone Trough Pattern...........................400
7.4.1.5 Plate Materials...................................................................400
7.4.2 Gasket Selection................................................................................400
7.4.3 Bleed Port Design..............................................................................400
7.4.4 Frames...............................................................................................402
7.4.5 Nozzles..............................................................................................402
7.4.6 Tie Bolts............................................................................................402
7.4.7 Connector Plates................................................................................403
7.4.8 Connections.......................................................................................403
7.4.9 Installation.........................................................................................403
7.5 Brazed Plate Heat Exchanger.........................................................................403
7.6 Other Forms of Plate Heat Exchangers..........................................................403
7.6.1 All-Welded Plate Exchangers............................................................403
7.6.2 Supermax® and Maxchanger® Plate Heat Exchangers......................404
7.6.3 Wide-Gap Plate Heat Exchanger.......................................................406
7.6.4 GEABloc Fully Welded Plate Heat Exchanger.................................407
7.6.5 Free-Flow Plate Heat Exchanger.......................................................407
7.6.6 Flow-Flex Tubular Plate Heat Exchanger.........................................407
7.6.7 Semiwelded or Twin-Plate Heat Exchanger......................................409
7.6.8 Double-Wall Plate Heat Exchanger................................................... 411
7.6.9 Diabon F Graphite Plate Heat Exchanger......................................... 411
7.6.10 Glue-Free Gaskets (Clip-On Snap-On Gaskets)............................... 411
7.6.11 AlfaNova 100% Stainless Steel Plate Heat Exchanger..................... 412
7.6.12 Plate Heat Exchanger with Electrode Plate............................................412

xx Contents
7.6.13 Plate Heat Exchanger with Flow Rings............................................. 412
7.6.14 AlfaRex™ Gasket-Free Plate Heat Exchanger................................... 412
7.6.15 Alfa Laval Plate Evaporator.............................................................. 413
7.6.16 Sanitary Heat Exchangers................................................................. 413
7.6.17 EKasic® Silicon Carbide Plate Heat Exchangers.............................. 413
7.6.18 Deep-Set Gasket Grooves................................................................. 413
7.7 Where to Use Plate Heat Exchangers............................................................. 413
7.7.1 Applications for Which Plate Heat Exchangers Are Not
Recommended................................................................................... 413
7.8 Thermohydraulic Fundamentals of Plate Heat Exchangers........................... 414
7.8.1 High- and Low-Theta Plates.............................................................. 415
7.8.2 Thermal Mixing................................................................................ 416
7.8.2.1 Thermal Mixing Using High- and Low-Theta Plates........ 416
7.8.2.2 Thermal Mixing Using Horizontal and
Vertical Plates............................................................416
7.8.3 Flow Area.......................................................................................... 417
7.8.4 Heat Transfer and Pressure-Drop Correlations................................. 419
7.8.4.1 Heat Transfer Correlations................................................. 419
7.8.4.2 Pressure Drop....................................................................420
7.8.5 Specific Pressure Drop or Jensen Number........................................ 421
7.9 PHE Thermal Design Methods...................................................................... 421
7.9.1 LMTD Method due to Buonopane et al............................................422
7.9.2 ε-NTU Approach...............................................................................422
7.9.3 Specification Sheet for PHE..............................................................423
7.9.3.1 Design Pressure.................................................................423
7.9.3.2 Plate Hanger.......................................................................424
7.10 Corrosion of Plate Heat Exchangers...............................................................424
7.11 Fouling............................................................................................................425
7.12 Limitations of Plate Heat Exchangers............................................................425
7.13 Spiral Plate Heat Exchangers.........................................................................425
7.13.1 Flow Arrangements and Applications...............................................426
7.13.2 Construction Material.......................................................................426
7.13.3 Thermal Design of Spiral Plate Heat Exchangers.............................426
7.13.4 Mechanical Design of Spiral Plate Heat Exchangers........................427
7.13.5 Applications for Spiral Plate Heat Exchangers.................................427
7.13.6 Advantages of Spiral Plate Exchangers.............................................428
7.13.7 Limitations........................................................................................428
7.14 Platecoil® Prime Surface Plate Heat Exchangers...........................................428
Nomenclature............................................................................................................429
References.................................................................................................................430
Bibliography.............................................................................................................. 431
Chapter 8 Heat Transfer Augmentation..................................................................................... 433
8.1 Introduction.................................................................................................... 433
8.1.1 Benefits of Heat Transfer Augmentation........................................... 433
8.2 Application of Augmented Surfaces.............................................................. 433
8.3 Principle of Single-Phase Heat Transfer Enhancement..................................434
8.3.1 Increase in Convection Coefficient without an Appreciable
Area Increase....................................................................................434

xxiContents
8.3.2 Enhancement in Turbulent Flow.......................................................434
8.3.3 Enhancement in Laminar Flow......................................................... 435
8.4 Approaches and Techniques for Heat Transfer Enhancement........................ 435
8.5 Heat Transfer Mode........................................................................................ 437
8.6 Passive Techniques.........................................................................................437
8.6.1 Extended Surfaces.............................................................................437
8.6.1.1 Extended Surfaces for Gases............................................. 437
8.6.1.2 Extended Surfaces for Liquids..........................................438
8.6.2 Treated Surfaces................................................................................441
8.6.3 Rough Surfaces.................................................................................442
8.6.4 Tube Inserts and Displaced Flow Enhancement Devices.................444
8.6.4.1 Enhancement Mechanism..................................................444
8.6.4.2 Forms of Insert Device......................................................444
8.6.4.3 Displaced Flow Enhancement Devices.............................444
8.6.5 Swirl Flow Devices...........................................................................450
8.6.5.1 Twisted Tape Insert............................................................450
8.6.5.2 Corrugated Surfaces..........................................................450
8.6.5.3 Doubly Enhanced Surfaces................................................ 452
8.6.5.4 Turbulators......................................................................... 453
8.6.6 Surface Tension Devices................................................................... 453
8.6.7 Additives for Liquids......................................................................... 453
8.6.8 Additives for Gases........................................................................... 453
8.7 Active Techniques..........................................................................................454
8.8 Friction Factor................................................................................................454
8.9 Pertinent Problems.........................................................................................454
8.9.1 Testing Methods................................................................................454
8.9.2 Fouling.............................................................................................. 455
8.9.3 Performance Evaluation Criteria....................................................... 455
8.9.3.1 Webb’s PECs: Performance Comparison with
a Reference........................................................................456
8.9.3.2 Shah’s Recommendation for Surface Selection of
Compact Heat Exchanger with Gas on One Side..............456
8.9.4 Market Factors................................................................................... 457
8.9.4.1 Alternate Means of Energy Savings.................................. 457
8.9.4.2 Adoptability to Existing Heat Exchanger..........................457
8.9.4.3 Proven Field/Performance Trials....................................... 457
8.9.5 Mechanical Design and Construction Considerations...................... 458
8.10 Phase Change.................................................................................................458
8.10.1 Condensation Enhancement..............................................................458
8.10.1.1 Horizontal Orientation.......................................................459
8.10.1.2 Shellside Condensation on Vertical Tubes......................... 459
8.10.2 Evaporation Enhancement................................................................. 459
8.10.3 Heat Transfer Augmentation Devices for the Air-Conditioning
and Refrigeration Industry............................................................... 459
8.10.3.1 Shellside Evaporation of Refrigerants............................... 459
8.10.3.2 Shellside Condensation of Refrigerants.............................460
8.10.3.3 In-Tube Evaporation of Refrigerants.................................460
8.11 Major Areas of Applications..........................................................................460
Nomenclature............................................................................................................ 461
References................................................................................................................. 461
Bibliography..............................................................................................................463

xxii Contents
Chapter 9 Fouling......................................................................................................................465
9.1 Effect of Fouling on the Thermohydraulic Performance of Heat Exchangers....... 465
9.2 Costs of Heat Exchanger Fouling...................................................................467
9.2.1 Oversizing.........................................................................................467
9.2.2 Additional Energy Costs...................................................................467
9.2.3 Treatment Cost to Lessen Corrosion and Fouling.............................467
9.2.4 Lost Production due to Maintenance Schedules and Down
Time for Maintenance.......................................................................467
9.3 Fouling Curves/Modes of Fouling.................................................................467
9.4 Stages of Fouling............................................................................................468
9.5 Fouling Model................................................................................................468
9.6 Parameters That Influence Fouling Resistances............................................469
9.6.1 Properties of Fluids and Usual Propensity for Fouling.....................469
9.6.2 Temperature.......................................................................................469
9.6.3 Velocity and Hydrodynamic Effects................................................. 470
9.6.4 Tube Material.................................................................................... 470
9.6.5 Impurities.......................................................................................... 470
9.6.6 Surface Roughness............................................................................ 471
9.6.7 Suspended Solids............................................................................... 471
9.6.8 Placing More Fouling Fluid on the Tubeside.................................... 471
9.6.9 Shellside Flow................................................................................... 471
9.6.10 Type of Heat Exchanger.................................................................... 472
9.6.10.1 Low-Finned Tube Heat Exchanger.................................... 472
9.6.10.2 Heat Transfer Augmentation Devices................................472
9.6.10.3 Gasketed Plate Heat Exchangers.......................................472
9.6.10.4 Spiral Plate Exchangers.....................................................472
9.6.11 Seasonal Temperature Changes........................................................472
9.6.12 Equipment Design.............................................................................472
9.6.13 Heat Exchanger Geometry and Orientation...................................... 472
9.6.14 Heat Transfer Processes like Sensible Heating, Cooling,
Condensation, and Vaporization....................................................... 473
9.6.15 Shell and Tube Heat Exchanger with Improved Shellside
Performance...................................................................................... 473
9.6.15.1 EMbaffle® Heat Exchanger................................................ 473
9.6.15.2 Twisted Tube Heat Exchanger........................................... 473
9.6.15.3 Helixchanger Heat Exchanger........................................... 473
9.7 Mechanisms of Fouling.................................................................................. 474
9.7.1 Particulate Fouling............................................................................ 474
9.7.2 Chemical Reaction Fouling (Polymerization)................................... 475
9.7.3 Corrosion Fouling............................................................................. 475
9.7.4 Crystallization or Precipitation Fouling............................................ 476
9.7.4.1 Modeling for Scaling......................................................... 476
9.7.5 Biological Fouling............................................................................. 476
9.7.6 Solidification Fouling or Freezing Fouling.......................................477
9.8 Fouling Data...................................................................................................477
9.9 How Fouling Is Dealt while Designing Heat Exchangers..............................477
9.9.1 Specifying the Fouling Resistances..................................................477
9.9.2 Oversizing.........................................................................................477
9.10 TEMA Fouling Resistance Values................................................................. 478
9.10.1 Research in Fouling.......................................................................... 478

xxiiiContents
9.11 Fouling Monitoring........................................................................................ 478
9.11.1 Fouling Inline Analysis..................................................................... 478
9.11.2 Tube Fouling Monitors......................................................................481
9.11.3 Fouling Monitor Operation...............................................................482
9.11.3.1 Instruments for Monitoring of Fouling.............................482
9.11.3.2 Gas-Side Fouling Measuring Devices...............................482
9.12 Expert System.................................................................................................482
9.13 Fouling Prevention and Control.....................................................................483
9.13.1 Measures to Be Taken during the Design Stages..............................483
9.14 Cleaning of Heat Exchangers.........................................................................484
9.14.1 Cleaning Techniques.........................................................................484
9.14.2 Deposit Analysis................................................................................485
9.14.3 Selection of Appropriate Cleaning Methods.....................................485
9.14.3.1 Precautions to Be Taken while Undertaking
a Cleaning Operation.........................................................485
9.14.4 Off-Line Mechanical Cleaning.........................................................485
9.14.4.1 Manual Cleaning...............................................................486
9.14.4.2 Jet Cleaning.......................................................................486
9.14.4.3 Drilling and Roding of Tubes............................................487
9.14.4.4 Turbining...........................................................................487
9.14.4.5 Hydro Drilling Action.......................................................487
9.14.4.6 Passing Brushes through Exchanger Tubes.......................487
9.14.4.7 Scraper-Type Tube Cleaners..............................................487
9.14.4.8 Blast Cleaning....................................................................488
9.14.4.9 Soot Blowing.....................................................................488
9.14.4.10 Thermal Cleaning..............................................................488
9.14.5 Merits of Mechanical Cleaning.........................................................488
9.14.6 Chemical Cleaning............................................................................489
9.14.6.1 Clean-in-Place Systems.....................................................489
9.14.6.2 Choosing a Chemical Cleaning Method............................489
9.14.6.3 Chemical Cleaning Solutions............................................489
9.14.7 General Procedure for Chemical Cleaning.......................................489
9.14.8 Off-line Chemical Cleaning..............................................................490
9.14.8.1 Integrated Chemical Cleaning Apparatus......................... 491
9.14.9 Merits of Chemical Cleaning............................................................ 491
9.14.10 Disadvantages of Chemical Cleaning Methods................................ 491
9.14.11 Online Cleaning Methods................................................................. 491
9.14.12 Online Mechanical Cleaning Methods.............................................492
9.14.12.1 Upstream Filtration (Debris Filter)....................................492
9.14.12.2 Flow Excursion..................................................................492
9.14.12.3 Air Bumping......................................................................492
9.14.12.4 Reversing Flow in Heat Exchangers..................................492
9.14.12.5 Automatic Tube Cleaning Systems....................................493
9.14.12.6 Insert Technology...............................................................494
9.14.12.7 Grit Cleaning......................................................................496
9.14.12.8 Self-Cleaning Heat Exchangers.........................................497
9.14.13 Merits of Online Cleaning................................................................499
9.15 Foulant Control by Chemical Additives.........................................................499
9.16 Control of Fouling from Suspended Solids....................................................501
9.17 Cooling-Water Management for Reduced Fouling.........................................501
9.17.1 Forms of Water-Side Fouling............................................................501

xxiv Contents
9.17.2 Influence of Surface Temperature on Fouling...................................502
9.17.3 Foulant Control versus Type of Cooling-Water System....................502
9.17.3.1 Once-Through System.......................................................502
9.17.3.2 Open Recirculating System...............................................502
9.17.3.3 Closed Recirculating Systems...........................................502
9.17.3.4 Online Chemical Control of Cooling-Water Foulants.......502
9.17.4 Control of Scale Formation and Fouling Resistances for Treated
Cooling Water...................................................................................503
9.17.4.1 Chemical Means to Control Scaling..................................503
9.17.4.2 Electrostatic Scale Controller and Preventer.....................504
9.17.5 Cleaning of Scales.............................................................................504
9.17.5.1 Chemical Cleaning............................................................504
9.17.6 Iron Oxide Removal..........................................................................504
Nomenclature............................................................................................................504
References.................................................................................................................505
Bibliography..............................................................................................................507
Chapter 10 Flow-Induced Vibration of Shell and Tube Heat Exchangers...................................509
10.1 Principles of Flow-Induced Vibration............................................................509
10.1.1 Principles of Flow-Induced Vibration...............................................509
10.1.2 Possible Damaging Effects of FIV on Heat Exchangers................... 510
10.1.3 Most Probable Regions of Tube Failure............................................ 510
10.1.4 Failure Mechanisms.......................................................................... 510
10.1.5 Flow-Induced Vibration Mechanisms............................................... 511
10.1.6 Tube Response Curve........................................................................ 511
10.1.7 Dynamical Behavior of Tube Arrays in Crossflow........................... 511
10.1.8 Hydrodynamic Forces....................................................................... 512
10.1.9 FIV Mechanisms versus Flow Mediums.......................................... 512
10.1.10 Approaches to FIV Analysis............................................................. 512
10.1.11 Empirical Nature of Flow-Induced Vibration Analysis.................... 512
10.2 Discussion of Flow-Induced Vibration Mechanisms..................................... 513
10.2.1 Vortex Shedding................................................................................ 513
10.2.1.1 Single Tube........................................................................ 513
10.2.1.2 Strouhal Number............................................................... 513
10.2.1.3 Vortex Shedding for Tube Bundles.................................... 514
10.2.1.4 Avoiding Resonance.......................................................... 515
10.2.1.5 Calculation of Strouhal Number for Tube Arrays............. 515
10.2.1.6 Criteria to Avoid Vortex Shedding.................................... 516
10.2.1.7 Response due to Vortex Shedding Vibration
Prediction by Dynamic Analysis....................................... 517
10.3 Turbulence-Induced Excitation Mechanism................................................... 518
10.3.1 Turbulence......................................................................................... 518
10.3.2 Turbulent Buffeting........................................................................... 518
10.3.3 Owen’s Expression for Turbulent Buffeting Frequency.................... 518
10.3.4 Turbulent Buffeting Excitation as a Random Phenomenon.............. 519
10.4 Fluid Elastic Instability.................................................................................. 519
10.4.1 Fluid Elastic Forces...........................................................................520
10.4.2 General Characteristics of Instability...............................................520
10.4.3 Connors’ Fluid Elastic Instability Analysis......................................520
10.4.4 Analytical Model............................................................................... 521

xxvContents
10.4.5 Unsteady Model................................................................................ 521
10.4.5.1 Displacement Mechanism................................................. 521
10.4.5.2 Velocity Mechanism......................................................... 521
10.4.5.3 Unsteady Model................................................................522
10.4.6 Design Recommendations................................................................. 522
10.4.6.1 Chen’s Criterion................................................................ 522
10.4.6.2 Au-Yang et al. Criteria......................................................523
10.4.6.2 Guidelines of Pettigrew and Taylor..................................523
10.4.7 Acceptance Criteria...........................................................................523
10.4.8 Stability Diagrams............................................................................524
10.5 Acoustic Resonance........................................................................................524
10.5.1 Principle of Standing Waves.............................................................524
10.5.1.1 Effect of Tube Solidity on Sound Velocity.......................525
10.5.2 Expressions for Acoustic Resonance Frequency...............................526
10.5.2.1 Blevins Expression............................................................527
10.5.3 Excitation Mechanisms.....................................................................528
10.5.3.1 Vortex Shedding Mechanism............................................528
10.5.3.2 Turbulent Buffeting Mechanism.......................................528
10.5.4 Acceptance Criteria for Occurrence of Acoustic Resonance............ 529
10.5.4.1 Vortex Shedding...............................................................529
10.5.4.2 Turbulent Buffeting...........................................................530
10.6 Vibration Evaluation Procedure.....................................................................530
10.6.1 Steps of Vibration Evaluation............................................................530
10.6.1.1 Step 6 for Liquid Flow...................................................... 531
10.6.1.2 Step 6 for Gas Flow.......................................................... 531
10.6.2 Caution in Applying Experimentally Derived Values
for Vibration Evaluation.................................................................... 531
10.7 Design Guidelines for Vibration Prevention.................................................. 531
10.7.1 Methods to Increase Tube Natural Frequency.................................. 531
10.7.1.1 FIV of Retubed Units........................................................ 533
10.7.2 Methods to Decrease Crossflow Velocity.........................................534
10.7.3 Suppression of Standing Wave Vibration.......................................... 535
10.7.3.1 Antivibration Baffles......................................................... 535
10.7.3.2 Helmholtz Cavity Resonator............................................. 537
10.7.3.3 Concept of Fin Barrier...................................................... 537
10.7.3.4 Concept of Helical Spacers............................................... 538
10.7.3.5 Detuning........................................................................... 538
10.7.3.6 Removal of Tubes.............................................................. 538
10.7.3.7 Surface Modification........................................................ 539
10.7.3.8 Irregular Spacing of Tubes................................................ 539
10.7.3.9 Change the Mass Flow Rate............................................. 539
10.8 Baffle Damage and Collision Damage........................................................... 539
10.8.1 Empirical Checks for Vibration Severity.......................................... 539
10.9 Impact and Fretting Wear............................................................................... 539
10.9.1 Tube Wear Prediction by Experimental Techniques.........................540
10.9.2 Theoretical Model.............................................................................540
10.10 Determination of Hydrodynamic Mass, Natural Frequency,
and Damping..........................................................................................541
10.10.1 Added Mass or Hydrodynamic Mass................................................ 541
10.10.2 Determination of Added Mass Coefficient, Cm, for Single-Phase
Flow................................................................................................... 541

xxvi Contents
10.10.2.1 Blevins Correlation......................................................... 541
10.10.2.2 Experimental Data of Moretti et al.................................542
10.10.3 Natural Frequencies of Tube Bundles...............................................542
10.10.3.1 Estimation of Natural Frequencies of Straight Tubes.....543
10.10.3.2 U-Tube Natural Frequency..............................................544
10.10.4 Damping............................................................................................544
10.10.4.1 Determination of Damping.............................................545
10.10.5 Other Values......................................................................................546
10.11 New Technologies of Antivibration Tools......................................................546
10.11.1 Antivibration Tube Stakes.................................................................546
10.11.2 ExxonMobil Research and Engineering...........................................548
10.12 Software Programs for Analysis of FIV.........................................................548
10.A Appendix A: Calculation Procedure for Shellside Liquids............................549
Nomenclature............................................................................................................ 556
References................................................................................................................. 558
Suggested Readings...................................................................................................562
Chapter 11 Mechanical Design of Shell and Tube Heat Exchangers..........................................563
11.1 Standards and Codes......................................................................................563
11.1.1 Standards...........................................................................................563
11.1.1.1 Company Standards...........................................................563
11.1.1.2 Trade or Manufacturer’s Association Standards...............564
11.1.1.3 National Standards............................................................564
11.1.2 Design Standards Used for the Mechanical Design of Heat
Exchangers........................................................................................564
11.1.2.1 TEMA Standards Scope and General Requirements
(Section B-1, RCB-1.1).......................................................564
11.1.2.2 Scope of TEMA Standards................................................564
11.1.2.3 Differences among TEMA Classes R, C, and B...............565
11.1.2.4 TEMA Engineering Software...........................................565
11.1.2.5 When Do the TEMA Standards Supplement
or Override the ASME Code Specification?......................565
11.1.2.6 Heat Exchange Institute Standards....................................566
11.1.3 Codes.................................................................................................566
11.1.3.1 ASME Codes.....................................................................567
11.1.3.2 CODAP..............................................................................572
11.1.3.3 AD Merkblatter 2000–German Pressure Vessel Code..... 572
11.1.3.4 UPV: The European Standards EN 13445........................ 573
11.2 Basics of Mechanical Design.........................................................................573
11.2.1 Fundamentals of Mechanical Design................................................ 574
11.2.1.1 Information for Mechanical Design.................................. 574
11.2.1.2 Content of Mechanical Design of Shell and Tube Heat
Exchangers......................................................................... 575
11.2.1.3 Mechanical Design Procedure...........................................577
11.2.1.4 Design Loadings................................................................577
11.2.1.5 Topics Covered in the Next Sections.................................577
11.3 Stress Analysis, Classes, and Categories of Stress.........................................577
11.3.1 Stress Analysis..................................................................................577
11.3.2 Classes and Categories of Stresses....................................................577
11.3.2.1 Stress Categories................................................................ 578

xxviiContents
11.3.2.2 Stress Classification........................................................... 578
11.3.2.3 Membrane Stress............................................................... 578
11.3.2.4 Primary Stress................................................................... 578
11.3.3 Stress Classification........................................................................... 578
11.3.3.1 Primary Membrane Stress, Pm........................................... 578
11.3.3.2 Primary Bending Stress, Pb...............................................579
11.3.3.3 Local Membrane Stress, PL...............................................579
11.3.3.4 Secondary Stress................................................................579
11.3.3.5 Thermal Stresses................................................................580
11.3.3.6 Peak Stress, F....................................................................580
11.3.3.7 Discontinuity Stresses.......................................................580
11.3.4 Fatigue Analysis................................................................................580
11.3.5 Design Methods and Design Criteria................................................ 581
11.3.5.1 ASME Code Section VIII Design Criteria........................ 581
11.3.6 Allowable Stress................................................................................ 581
11.3.7 Combined-Thickness Approach for Clad Plates............................... 581
11.3.8 Welded Joints....................................................................................582
11.3.8.1 Welded Joint Efficiencies...................................................582
11.3.8.2 Joint Categories..................................................................582
11.3.8.3 Weld Joint Types................................................................583
11.3.9 Key Terms in Heat Exchanger Design..............................................583
11.3.9.1 Design Pressure.................................................................583
11.3.9.2 Design Temperature...........................................................584
11.3.9.3 Maximum Allowable Working Pressure...........................584
11.3.9.4 Operating Temperature or Working Temperature.............584
11.3.9.5 Operating Pressure or Working Pressure..........................584
11.4 Tubesheet Design............................................................................................585
11.4.1 Fundamentals....................................................................................585
11.4.1.1 Tubesheet Connection with the Shell and Channel...........585
11.4.1.2 Supported Tubesheet and Unsupported Tubesheet............585
11.4.1.3 Tubesheet Thickness..........................................................585
11.4.1.4 Tubesheet Design Procedure: Historical
Background.............................................................586
11.4.1.5 Assumptions in Tubesheet Analysis..................................587
11.4.2 Basis of Tubesheet Design.................................................................590
11.4.2.1 Analytical Treatment of Tubesheets..................................590
11.4.2.2 Design Analysis................................................................. 591
11.4.3 Tubesheet Design as per TEMA Standards......................................595
11.4.3.1 Tubesheet Formula for Bending........................................595
11.4.3.2 Parameter F.......................................................................596
11.4.3.3 Shear Formula RCB-7.133.................................................597
11.4.3.4 Stress Category Concept in TEMA Formula....................598
11.4.3.5 Determination of Effective Design Pressure, P
(RCB-7.16)...................................................................... 598
11.4.3.6 Equivalent Differential Expansion Pressure, pd
(RCB 7.161)........................................................................598
11.4.3.7 Differential Pressure Design, after Yokell........................600
11.4.3.8 Longitudinal Stress Induced in the Shell and Tube
Bundle................................................................................601
11.4.3.9 TEMA Fixed Tubesheet Design with Different
Thickness.........................................................................603

xxviii Contents
11.4.4 Tubesheet Design Method as per ASME,
CODAP and UPV:EN 13443 and Comparison
with TEMA Rules...................................................................... 603
11.4.4.1 Effect of Ligament Efficiency in Tubesheet Thickness
and Tube-to-Tubesheet Joint Strength Calculation............604
11.4.4.2 Tubesheet Design Rules.....................................................605
11.4.5 Methodology to Use ASME Rules....................................................608
11.4.6 Flanged Tubesheets: TEMA Design Procedure................................609
11.4.6.1 Fixed Tubesheet or Floating Tubesheet.............................609
11.4.6.2 U-Tube Tubesheet.............................................................. 610
11.4.7 Rectangular Tubesheet Design.......................................................... 610
11.4.7.1 Methods of Tubesheet Analysis......................................... 610
11.4.8 Curved Tubesheets............................................................................ 611
11.4.8.1 Advantages of Curved Tubesheets..................................... 611
11.4.9 Conventional Double Tubesheet Design........................................... 611
11.5 Cylindrical Shell, End Closures, and Formed Heads under Internal
Pressure.......................................................................................................... 612
11.5.1 Cylindrical Shell under Internal Pressure......................................... 612
11.5.1.1 Thin Thick Cylindrical Shells........................................... 612
11.5.1.2 Design for External Pressure and/or Internal Vacuum...... 613
11.5.2 End Closures and Formed Heads...................................................... 613
11.5.2.1 Flat Cover.......................................................................... 614
11.5.2.2 Hemispherical.................................................................... 614
11.5.2.3 Ellipsoidal.......................................................................... 614
11.5.2.4 Torispherical...................................................................... 615
11.5.2.5 Conical............................................................................... 615
11.5.3 Minimum Thickness of Heads and Closures.................................... 616
11.5.3.1 Flat Cover.......................................................................... 617
11.5.3.2 Ellipsoidal Heads............................................................... 617
11.5.3.3 Torispherical Heads........................................................... 617
11.5.3.4 Hemispherical Heads......................................................... 617
11.5.3.5 Conical Heads and Sections (without Transition
Knuckle)............................................................................. 618
11.5.4 Comparison of Various Heads.......................................................... 619
11.6 Bolted Flanged Joint Design........................................................................... 619
11.6.1 Construction and Design................................................................... 619
11.6.1.1 Flanged Joint Types........................................................... 619
11.6.1.2 Constructional Details of Bolted Flange Joints................. 619
11.6.1.3 Design of Bolted Flange Joints..........................................620
11.6.1.4 Gasket Design....................................................................623
11.6.1.5 Bolting Design...................................................................626
11.6.1.6 Flange Design....................................................................629
11.6.2 Step-by-Step Procedure for Integral/Loose/Optional Flanges
Design................................................................................................633
11.6.2.1 Data Required....................................................................633
11.6.2.2 Step-by-Step Design Procedure......................................... 633
11.6.2.3 Taper-Lok® Heat Exchanger Closure.................................637
11.6.2.4 Zero-Gap Flange................................................................638
11.6.2.5 Long Weld Neck Assembly...............................................639
11.7 Expansion Joints.............................................................................................640
11.7.1 Flexibility of Expansion Joints..........................................................640

xxixContents
11.7.2 Classification of Expansion Joints.....................................................640
11.7.2.1 Formed Head or Flanged-and-Flued Head........................640
11.7.2.2 Bellows or Formed Membrane..........................................642
11.7.2.3 Deciding between Thick- and Thin-Walled Expansion
Joints..................................................................................644
11.7.3 Design of Expansion Joints...............................................................644
11.7.3.1 Formed Head Expansion Joints.........................................644
11.7.3.2 Finite Element Analysis.....................................................645
11.7.3.3 FEA by Design Consultants..............................................645
11.7.3.4 Singh and Soler Model......................................................646
11.7.3.5 Procedure for Design of Formed Head Expansion
Joints...............................................................................647
11.7.3.6 Design Procedure as per ASME Code..............................648
11.7.4 Design of Bellows or Formed Membranes........................................649
11.7.4.1 Shapes and Cross Section..................................................649
11.7.4.2 Bellows Materials..............................................................649
11.7.4.3 Bellows Design: Circular Expansion Joints.......................649
11.7.4.4 Limitations and Means to Improve the Operational
Capability of Bellows........................................................649
11.7.4.5 Fatigue Life........................................................................652
11.8 Opening and Nozzles.....................................................................................653
11.8.1 Openings...........................................................................................653
11.8.1.1 Reinforcement Pad............................................................. 653
11.8.1.2 Reinforced Pad and Air–Soap Solution Testing................653
11.8.2 Nozzles..............................................................................................654
11.8.3 Stacked Units.....................................................................................655
11.9 Supports..........................................................................................................655
11.9.1 Design Loads.....................................................................................655
11.9.2 Horizontal Vessel Supports...............................................................656
11.9.2.1 Saddle Supports.................................................................656
11.9.2.2 Ring Supports....................................................................656
11.9.2.2 Leg Supports......................................................................657
11.9.3 Vertical Vessels.................................................................................657
11.9.3.1 Skirt Supports....................................................................657
11.9.3.2 Lug Supports......................................................................657
11.8.3.3 Ring Support......................................................................658
11.9.4 Procedure for Support Design...........................................................658
11.9.4.1 TEMA Rules for Supports Design (G-7.1).........................658
11.9.4.2 ASME Code.......................................................................659
11.9.5 Lifting Devices and Attachments.....................................................659
References.................................................................................................................659
Bibliography..............................................................................................................663
Chapter 12 Corrosion...................................................................................................................665
12.1 Basics of Corrosion.........................................................................................665
12.1.1 Reasons for Corrosion Studies..........................................................665
12.1.2 Corrosion Mechanism.......................................................................666
12.1.2.1 Basic Corrosion Mechanism of Iron in Aerated
Aqueous System................................................................667

xxx Contents
12.1.3 Forms of Electrochemical Corrosion................................................668
12.1.3.1 Bimetallic Cell...............................................................668
12.1.3.2 Concentration Cell.........................................................668
12.1.3.3 Differential Temperature Cells......................................669
12.1.4 Corrosion Potential and Corrosion Current......................................669
12.1.5 Corrosion Kinetics............................................................................669
12.1.5.1 Polarization Effects........................................................669
12.1.5.2 Passivation...................................................................... 670
12.1.6 Factors Affecting Corrosion of a Material in an Environment.........672
12.1.6.1 Environmental Factors...................................................672
12.2 Forms of Corrosion.........................................................................................673
12.2.1 Uniform Corrosion versus Localized Corrosion............................... 673
12.2.2 Factors That Favor Localized Attack................................................ 674
12.2.3 Forms of Corrosion........................................................................... 674
12.2.3.1 Uniform or General Corrosion....................................... 675
12.2.3.2 Galvanic Corrosion........................................................680
12.2.3.3 Pitting Corrosion............................................................684
12.2.3.4 Crevice Corrosion..........................................................689
12.2.3.5 Intergranular Corrosion................................................. 691
12.2.3.6 Dealloying or Selective Leaching..................................692
12.2.3.7 Erosion–Corrosion.........................................................694
12.2.3.8 Stress Corrosion Cracking............................................. 701
12.2.3.9 Hydrogen Damage..........................................................705
12.2.3.10 Fretting Corrosion..........................................................706
12.2.3.11 Corrosion Fatigue...........................................................706
12.2.3.12 Microbiologically Influenced Corrosion........................707
12.3 Corrosion of Weldments................................................................................. 711
12.4 Corrosion Prevention and Control.................................................................. 712
12.4.1 Principles of Corrosion Control........................................................ 712
12.4.2 Corrosion Control by Proper Engineering Design............................ 713
12.4.2.1 Design Details................................................................ 713
12.4.2.2 Preservation of Inbuilt Corrosion Resistance................ 713
12.4.2.3 Design to Avoid Various Forms of Corrosion................ 713
12.4.2.4 Weldments, Brazed and Soldered Joints........................ 713
12.4.2.5 Plant Location................................................................ 714
12.4.2.6 Startup and Shutdown Problems.................................... 714
12.4.2.7 Overdesign..................................................................... 714
12.4.3 Corrosion Control by Modification of the Environment
(Use of Inhibitors)............................................................................. 714
12.4.3.1 Inhibitors........................................................................ 715
12.4.4 Corrosion-Resistant Alloys............................................................... 717
12.4.5 Bimetal Concept................................................................................ 717
12.4.5.1 Cladding......................................................................... 718
12.4.5.2 Bimetallic or Duplex Tubing.......................................... 718
12.4.6 Protective Coatings........................................................................... 719
12.4.6.1 Plastic Coatings..............................................................720
12.4.6.2 Effectiveness of Coatings...............................................720
12.4.6.3 Surface Treatment..........................................................720
12.4.7 Electrochemical Protection (Cathodic and Anodic Protection)........720
12.4.7.1 Principle of Cathodic Protection....................................720
12.4.7.2 Anodic Protection.......................................................... 721

xxxiContents
12.4.8 Passivation.........................................................................................722
12.5 Corrosion Monitoring.....................................................................................722
12.5.1 Benefits..............................................................................................722
12.5.2 Approaches to Corrosion Monitoring...............................................722
12.5.3 Corrosion Monitoring Techniques....................................................723
12.5.3.1 Online Monitoring Techniques..........................................723
12.5.3.2 Corrosion Monitoring of Condensers by Systematic
Examination of the State of the Tubes...............................724
12.5.4 Limitations of Corrosion Monitoring................................................724
12.5.5 Requirements for Success of Corrosion Monitoring Systems...........724
12.6 Cooling-Water Corrosion................................................................................725
12.6.1 Corrosion Processes in Water Systems.............................................725
12.6.2 Causes of Corrosion in Cooling-Water Systems...............................725
12.6.2.1 Dissolved Solids and Water Hardness...............................726
12.6.2.2 Chloride.............................................................................728
12.6.2.3 Sulfates..............................................................................728
12.6.2.4 Silica..................................................................................728
12.6.2.5 Oil......................................................................................728
12.6.2.6 Iron and Manganese..........................................................728
12.6.2.7 Suspended Matter..............................................................729
12.6.2.8 Dry Residue.......................................................................729
12.6.2.9 Dissolved Gases.................................................................729
12.6.3 Cooling Systems................................................................................732
12.6.3.1 Once-Through System.......................................................732
12.6.3.2 Open Recirculating Systems.............................................. 733
12.6.3.3 Closed Recirculating Systems........................................... 733
12.6.4 Corrosion Control Methods for Cooling-Water Systems.................. 733
12.6.4.1 Material Selection..............................................................734
12.6.4.2 Water Treatment................................................................735
12.6.4.3 Corrosion Inhibitors........................................................... 735
12.6.4.4 Ferrous Sulfate Dosing...................................................... 735
12.6.4.5 Passivation......................................................................... 735
12.6.5 Influence of Cooling-Water Types on Corrosion...............................736
12.6.5.1 Fresh Water........................................................................736
12.6.5.2 Seawater Corrosion............................................................736
12.6.5.3 Brackish Waters.................................................................736
12.6.5.4 Boiler Feedwaters..............................................................736
12.6.6 Corrosion of Individual Metals in Cooling-Water Systems..............736
12.6.7 Forms of Corrosion in Cooling Water...............................................737
12.6.7.1 Uniform Corrosion............................................................737
12.6.7.2 Galvanic Corrosion............................................................737
12.6.7.3 Pitting Corrosion................................................................737
12.6.7.4 Crevice Corrosion..............................................................738
12.6.7.5 Stress Corrosion Cracking.................................................738
12.6.7.6 Corrosion Fatigue and Fretting Wear................................738
12.6.7.7 Erosion of Tube Inlet.........................................................738
12.6.7.8 Dezincification...................................................................738
12.6.7.9 Microbiologically Induced Corrosion................................738
12.6.8 Material Selection for Condenser Tubes...........................................738
12.6.9 Operational Maintenance of Condensers and Feedwater Heaters....739
12.6.10 Preventing Corrosion in Automotive Cooling Systems....................739

xxxii Contents
12.7 Material Selection for Hydrogen Sulfide Environments................................739
12.7.1 Effects of Hydrogen in Steel (ASTM/ASME A/SA 516 Grades
60/65/70)............................................................................................ 739
12.7.2 Sources of Hydrogen in Steel............................................................740
12.7.3 Hydrogen-Induced Cracking.............................................................740
12.7.3.1 Stress-Oriented Hydrogen-Induced Cracking...................740
12.7.3.2 Susceptibility of Steels to HIC.......................................... 741
12.7.3.3 Prevention of HIC.............................................................. 741
12.7.4 Hydrogen Embrittlement................................................................... 741
12.7.4.1 Mechanism of Hydrogen Embrittlement........................... 741
12.7.4.2 Hydrogen Embrittlement of Steel Weldments................... 742
12.7.5 Hydrogen-Assisted Cracking............................................................. 742
12.7.5.1 Prevention of HSCC.......................................................... 742
12.7.6 Hydrogen Blistering.......................................................................... 743
12.7.6.1 Susceptible Materials......................................................... 743
12.7.6.2 Prevention of Blistering..................................................... 743
12.7.6.3 Detection of Blisters in Service......................................... 743
12.7.6.4 Correction of Blistered Condition in Steel Equipment...... 743
12.7.7 Pressure Vessel Steels for Sour Environments.................................. 743
12.7.8 HIC Testing Specification................................................................. 743
References.................................................................................................................744
Bibliography..............................................................................................................748
Chapter 13 Material Selection and Fabrication........................................................................... 749
13.1 Material Selection Principles......................................................................... 749
13.1.1 Material Selection............................................................................. 750
13.1.2 Review of Operating Process............................................................ 750
13.1.3 Review of Design.............................................................................. 750
13.1.4 Selection of Material......................................................................... 750
13.1.4.1 ASME Code Material Requirements................................. 750
13.1.4.2 Functional Requirements of Materials.............................. 751
13.1.5 Evaluation of Materials.....................................................................760
13.1.5.1 Material Tests.................................................................... 761
13.1.5.2 Materials Evaluation and Selection to Resist Corrosion.......761
13.1.6 Cost.................................................................................................... 761
13.1.6.1 Cost-Effective Material Selection...................................... 761
13.1.7 Possible Failure Modes and Damage in Service............................... 762
13.2 Equipment Design Features............................................................................ 762
13.2.1 Maintenance...................................................................................... 762
13.2.2 Failsafe Features................................................................................ 762
13.2.3 Access for Inspection........................................................................ 762
13.2.4 Safety................................................................................................. 763
13.2.5 Equipment Life..................................................................................763
13.1.5.1 Component Life................................................................. 763
13.2.6 Field Trials......................................................................................... 763
13.3 Raw Material Forms Used in the Construction of Heat Exchangers.............763
13.3.1 Castings.............................................................................................764
13.3.2 Forgings.............................................................................................764
13.3.3 Rods and Bars...................................................................................764
13.3.3.1 Pipe Fittings and Flanges...................................................764

xxxiiiContents
13.3.4 Bolts and Studs..................................................................................764
13.3.4.1 Materials for Corrosion-Resistant Fasteners.....................764
13.3.5 Handling of Materials.......................................................................765
13.3.6 Material Selection for Pressure Boundary Components...................765
13.3.6.1 Shell, Channel, Covers, and Bonnets.................................765
13.3.6.2 Tubes..................................................................................765
13.3.6.3 Tubesheet...........................................................................765
13.3.6.4 Baffles................................................................................766
13.4 Materials for Heat Exchanger Construction...................................................766
13.5 Plate Steels...................................................................................................... 767
13.5.1 Classifications and Designations of Plate Steels: Carbon and
Alloy Steels....................................................................................... 767
13.5.1.1 How Do Plate Steels Gain Their Properties?.................... 767
13.5.1.2 Changes in Steel Properties due to Heat Treatment.......... 767
13.5.1.3 ASTM Specifications on Plate Steels Used for
Pressure Vessel Fabrications and Heat Exchangers...........768
13.5.2 Processing of Plate Steels..................................................................770
13.6 Pipes and Tubes.............................................................................................. 771
13.6.1 Tubing Requirements........................................................................ 771
13.6.2 Selection of Tubes for Heat Exchangers............................................772
13.6.3 Specifications for Tubes....................................................................772
13.6.4 Defect Detection................................................................................772
13.6.5 Standard Testing for Tubular Products..............................................772
13.6.5.1 Hydrostatic Pressure Testing.............................................772
13.6.5.2 Pneumatic Test...................................................................773
13.6.5.3 Corrosion Tests..................................................................773
13.6.5.4 Dimensional Tolerance Tests.............................................773
13.6.6 Mill Scale..........................................................................................773
13.6.7 ASTM Specifications for Ferrous Alloys Tubings............................773
13.7 Weldability Problems..................................................................................... 774
13.7.1 Cold Cracking................................................................................... 774
13.7.1.1 Hydrogen-Induced Cracking............................................. 775
13.7.1.2 Underbead Cracking..........................................................780
13.7.1.3 Lamellar Tearing...............................................................780
13.7.1.4 Fish-Eye Cracking.............................................................783
13.8 Hot Cracking..................................................................................................783
13.8.1 Factors Responsible for Hot Cracking...............................................784
13.8.1.1 Segregation of Low-Melting-Point Elements.....................784
13.8.1.2 Stress States That Induce Restraint...................................784
13.8.1.3 Mode of Solidification.......................................................784
13.8.2 Susceptible Alloys.............................................................................784
13.8.3 Types of Hot Cracking......................................................................784
13.8.3.1 Solidification Cracking......................................................784
13.8.3.2 Heat-Affected Zone Liquation Cracking...........................786
13.8.3.3 Reheat Cracking or Stress-Relief Cracking.......................786
13.8.3.4 Ductility Dip Cracking......................................................788
13.8.3.5 Chevron Cracking..............................................................788
13.8.3.6 Crater Cracks.....................................................................788
13.9 Laboratory Tests to Determining Susceptibility to Cracking........................788
13.9.1 Weldability Tests...............................................................................788
13.9.2 Varestraint (Variable Restraint) Test.................................................789

xxxiv Contents
13.9.3 MultiTask Varestraint Weldability Testing System.......................790
13.10 Service-Oriented Cracking.............................................................................790
13.10.1 Temper Embrittlement or Creep Embrittlement............................790
13.11 Welding-Related Failures...............................................................................790
13.12 Selection of Cast Iron and Carbon Steels....................................................... 791
13.12.1 Cast Iron........................................................................................ 791
13.12.2 Steels.............................................................................................. 791
13.12.2.1 Process Improvements.................................................792
13.12.2.2 Carbon Steels...............................................................792
13.12.2.3 Types of Steel...............................................................792
13.12.2.4 Product Forms.............................................................792
13.12.2.5 Use of Carbon Steels...................................................793
13.12.2.6 Fabrication...................................................................794
13.13 Low-Alloy Steels............................................................................................795
13.13.1 Selection of Steels for Pressure Vessel Construction....................795
13.13.2 Low-Alloy Steels for Pressure Vessel Constructions....................796
13.13.2.1 Applications of Low-Alloy Steel Plates.......................796
13.13.2.2 Carbon–Molybdenum Steels.......................................796
13.13.2.3 Carbon–Manganese Steels..........................................796
13.13.2.4 Carbon–Manganese–Molybdenum Steels...................797
13.14 Quenched and Tempered Steels.....................................................................797
13.14.1 Compositions and Properties.........................................................798
13.14.2 Weldability.....................................................................................799
13.14.3 Joint Design...................................................................................799
13.14.4 Preheat...........................................................................................799
13.14.5 Welding Processes.........................................................................799
13.14.6 Postweld Heat Treatment...............................................................799
13.14.7 Stress-Relief Cracking...................................................................800
13.15 Chromium–Molybdenum Steels....................................................................800
13.15.1 Composition and Properties..........................................................800
13.15.2 Applications...................................................................................801
13.15.3 Creep Strength...............................................................................801
13.15.4 Welding Metallurgy.......................................................................802
13.15.4.1 Joint Design.................................................................802
13.15.4.2 Joint Preparation..........................................................802
13.15.4.3 Preheating....................................................................802
13.15.4.4 Welding Processes.......................................................802
13.15.4.5 Filler Metal..................................................................802
13.15.5 Temper Embrittlement Susceptibility............................................802
13.15.6 Step-Cooling Heat Treatment........................................................803
13.15.7 CVN Impact Properties.................................................................804
13.15.8 Temper Embrittlement of Weld Metal...........................................804
13.15.8.1 Control of Temper Embrittlement of Weld Metal........804
13.15.9 Postweld Heat Treatment (Stress Relief).......................................804
13.15.9.1 Larson–Miller Tempering Parameter..........................805
13.15.10 Reheat Cracking in Cr–Mo and Cr–Mo–V Steels.........................805
13.15.11 Modified 9Cr–1Mo Steel...............................................................805
13.15.12 Advanced 3Cr–Mo–Ni Steels.......................................................805
13.16 Stainless Steels...............................................................................................805
13.16.1 Classification and Designation of Stainless Steels........................806
13.16.1.1 Designations................................................................806

xxxvContents
13.16.1.2 ASTM Specification for Stainless Steels.....................806
13.16.1.3 Guidance for Stainless Steel Selection........................806
13.16.2 Martensitic Stainless Steel............................................................806
13.16.3 Austenitic Stainless Steel Properties and Metallurgy..................807
13.16.3.1 Types of Austenitic Stainless Steel..............................807
13.16.3.2 Alloy Development......................................................807
13.16.3.3 Stainless Steel for Heat Exchanger Applications........808
13.16.3.4 Properties of Austenitic Stainless Steels.....................808
13.16.3.5 Alloying Elements and Microstructure.......................809
13.16.3.6 Alloy Types and Their Applications............................809
13.16.4 Mechanism of Corrosion Resistance............................................ 810
13.16.4.1 Sigma Phase................................................................. 811
13.16.4.2 Passive versus Active Behavior................................... 811
13.16.4.3 Resistance to Chemicals.............................................. 811
13.16.4.4 Stainless Steel in Seawater.......................................... 811
13.16.4.5 Resistance to Various Forms of Corrosion.................. 811
13.16.4.6 Galvanic Corrosion...................................................... 811
13.16.4.7 Localized Forms of Corrosion..................................... 812
13.16.4.8 Pitting Corrosion.......................................................... 812
13.16.4.9 Crevice Corrosion........................................................ 813
13.16.4.10 Stress Corrosion Cracking........................................... 814
13.16.4.11 Intergranular Corrosion............................................... 817
13.16.4.12 Knifeline Attack.......................................................... 818
13.16.5 Austenitic Stainless Steel Fabrication........................................... 819
13.16.5.1 Pickling........................................................................ 819
13.16.5.2 Passivation................................................................... 819
13.16.5.3 Mechanical Cutting Methods...................................... 819
13.16.5.4 Gas Cutting Method.................................................... 819
13.16.6 Austenitic Stainless Steel Welding...............................................820
13.16.6.1 Welding Processes.......................................................820
13.16.6.2 Welding Methods ........................................................820
13.16.6.3 Filler Metal Selection.................................................. 821
13.16.6.4 Shielding Gases...........................................................822
13.16.6.5 Weld Preparation.........................................................822
13.16.6.6 Joint Design.................................................................822
13.16.6.7 Preweld Cleaning.........................................................822
13.16.6.8 Welding Considerations...............................................823
13.16.6.9 TIG Welding Techniques to Overcome Carbide
Precipitation.................................................................830
13.16.6.10 Gas Coverage...............................................................830
13.16.6.11 Welding Practices to Improve the Weld Performance......831
13.16.6.12 Protection of Weld Metal against Oxidation
and Fluxing to Remove Chromium Oxide.................. 831
13.16.6.13 Protecting the Roots of the Welds against Oxidation.....831
13.16.6.14 Welding Processes Generate Different Weld Defects......832
13.16.6.15 Postweld Heat Treatment............................................. 832
13.16.6.16 Welding Stainless Steels to Dissimilar Metals............ 833
13.16.6.17 Postweld Cleaning.......................................................833
13.16.6.18 Corrosion Resistance of Stainless Steel Welds............834
13.17 Ferritic Stainless Steels..................................................................................834
13.17.1 Conventional Ferritic Stainless Steels..........................................834

xxxvi Contents
13.17.2 “New” and “Old” Ferritic Stainless Steels..................................... 835
13.17.2.1 Superferritic Stainless Steels, Superaustenitic
Stainless Steels, and Duplex Stainless Steels..............835
13.17.3 Superferritic Stainless Steel...........................................................835
13.17.3.1 Characteristics.............................................................. 835
13.17.3.2 Alloy Composition....................................................... 835
13.17.3.3 Applications.................................................................837
13.17.3.4 Physical Properties.......................................................837
13.17.3.5 Corrosion Resistance....................................................838
13.17.3.6 Fabricability.................................................................839
13.17.3.7 Welding........................................................................839
13.18 Duplex Stainless Steels...................................................................................840
13.18.1 Composition of Duplex Stainless Steels......................................... 841
13.18.2 Comparison with Austenitic and Ferritic Stainless Steels.............842
13.18.3 Corrosion Resistance of Duplex Stainless Steels...........................843
13.18.4 Process Applications......................................................................843
13.18.5 Welding Methods............................................................................843
13.18.5.1 Weldability...................................................................843
13.18.5.2 Postweld Stress Relief..................................................845
13.18.6 Nondestructive Testing of Duplex SS.............................................845
13.19 Superaustenitic Stainless Steels with Mo + N................................................845
13.19.1 4.5% Mo Superaustenitic Steels.....................................................846
13.19.2 6% Mo Superaustenitic Stainless Steel..........................................846
13.19.2.2 Applications.................................................................847
13.19.2.3 Welding........................................................................848
13.19.3 Corrosion Resistance of Superaustenitic Stainless Steel Welds.....849
13.20 Aluminum Alloys: Metallurgy.......................................................................850
13.20.1 Properties of Aluminum.................................................................850
13.20.1.1 Aluminum for Heat Exchanger Applications...............850
13.20.1.2 Wrought Alloy Designations........................................ 851
13.20.1.3 Temper Designation System of Aluminum and
Aluminum Alloys......................................................... 853
13.20.1.4 Product Forms and Shapes........................................... 853
13.20.2 Corrosion Resistance......................................................................853
13.20.2.1 Surface Oxide Film on Aluminum..............................853
13.20.2.2 Chemical Nature of Aluminum: Passivity...................854
13.20.2.3 Resistance to Waters....................................................854
13.20.2.4 Forms of Corrosion......................................................855
13.20.2.5 Corrosion Prevention and Control Measures...............858
13.20.3 Fabrication......................................................................................859
13.20.3.1 Parameters Affecting Aluminum Welding..................859
13.20.3.2 Surface Preparation and Surface Cleanliness.............. 861
13.20.3.3 Plate Cutting and Forming........................................... 861
13.20.3.4 Joint Design.................................................................. 861
13.20.3.5 Joint Geometry............................................................. 861
13.20.3.6 Preheating.................................................................... 861
13.20.3.7 Wire Feeding................................................................862
13.20.3.8 Push Technique............................................................862
13.20.3.9 Travel Speed.................................................................862
13.20.3.10 Shielding Gas...............................................................862

xxxviiContents
13.20.3.11 Welding Wire...............................................................862
13.20.3.12 Convex-Shaped Welds..................................................862
13.20.3.13 Corrosion Resistance: Welded, Brazed, and
Soldered Joints.............................................................862
13.20.3.14 Welding Filler Metals..................................................862
13.20.3.15 Welding Methods.........................................................863
13.21 Copper............................................................................................................864
13.21.1 Copper Alloy Designation...............................................................864
13.21.1.1 Wrought Alloys............................................................864
13.21.1.2 Heat Exchanger Applications.......................................864
13.21.1.3 Copper in Steam Generation........................................865
13.21.1.4 Wrought Copper Alloys: Properties and Applications..... 865
13.21.1.5 Product Forms..............................................................868
13.21.2 Copper Corrosion............................................................................868
13.21.2.2 Galvanic Corrosion......................................................868
13.21.2.3 Pitting Corrosion..........................................................870
13.21.2.4 Intergranular Corrosion...............................................870
13.21.2.5 Dealloying (Dezincification)........................................ 871
13.21.2.6 Erosion–Corrosion.......................................................872
13.21.2.7 Stress Corrosion Cracking...........................................872
13.21.2.8 Condensate Corrosion..................................................873
13.21.2.9 Deposit Attack..............................................................873
13.21.2.10 Hot-Spot Corrosion...................................................... 874
13.21.2.11 Snake Skin Formation.................................................. 874
13.21.2.12 Corrosion Fatigue......................................................... 874
13.21.2.13 Biofouling..................................................................... 874
13.21.2.14 Cooling-Water Applications......................................... 874
13.21.2.15 Resistance to Seawater Corrosion................................ 874
13.21.2.16 Sulfide Attack............................................................... 874
13.21.2.17 Exfoliation....................................................................875
13.21.2.18 Copper and Aquatic Life.............................................. 875
13.21.3 Copper Welding...............................................................................875
13.21.3.1 Weldability...................................................................875
13.21.3.2 Alloy Classification from Weldability Considerations....877
13.21.3.3 PWHT..........................................................................879
13.21.3.4 Dissimilar Metal Welding............................................879
13.22 Nickel and Nickel-Base Alloys Metallurgy and Properties...........................880
13.22.1 Classification of Nickel Alloys........................................................ 881
13.22.1.1 Commercially Pure Nickel........................................... 881
13.22.1.2 Nickel–Copper Alloys and Copper–Nickel Alloys......882
13.22.1.3 Inconel and Inco Alloy.................................................882
13.22.1.4 Nickel–Iron–Chromium Alloys and
Inco Nickel– Iron–Chromium Alloys for
High- Temperature Applications..................................884
13.22.1.5 Magnetic Properties and Differentiation of Nickels......... 885
13.22.2 Nickel and Nickel-Base Alloys: Corrosion Resistance....................885
13.22.2.1 Galvanic Corrosion......................................................885
13.22.2.2 Pitting Resistance.........................................................886
13.22.2.3 Intergranular Corrosion...............................................886
13.22.2.4 Stress Corrosion Cracking...........................................887

xxxviii Contents
13.22.3 Nickel and Nickel-Base Alloys: Welding........................................888
13.22.3.1 Considerations while Welding Nickel..........................888
13.22.3.2 Welding Methods......................................................... 891
13.22.3.3 Postweld Heat Treatment.............................................892
13.22.4 Hastelloy®........................................................................................892
13.23 Titanium: Properties and Metallurgy.............................................................892
13.23.1 Properties That Favor Heat Exchanger Applications......................892
13.23.2 Alloy Specification..........................................................................893
13.23.3 Titanium Grades and Alloys............................................................893
13.23.3.1 Unalloyed Grades.........................................................893
13.23.3.2 Alloy Grades................................................................894
13.23.3.3 ASTM and ASME Specifications for Mill Product
Forms...........................................................................894
13.23.4 Titanium Corrosion Resistance.......................................................895
13.23.4.1 Surface Oxide Film......................................................895
13.23.4.2 General Corrosion........................................................895
13.23.4.3 Resistance to Chemicals and Solutions........................896
13.23.4.4 Resistance to Waters....................................................896
13.23.4.6 Thermal Performance..................................................897
13.23.4.7 Fouling.........................................................................898
13.23.4.8 Applications.................................................................898
13.23.5 Titanium Fabrication.......................................................................899
13.23.5.1 Welding Titanium........................................................899
13.23.5.2 In-Process Quality Control and Weld Tests.................903
13.23.5.3 Heat Treatment.............................................................904
13.23.5.4 Forming of Titanium-Clad Steel Plate.........................904
13.24 Zirconium.......................................................................................................904
13.24.1 Properties and Metallurgy...............................................................904
13.24.1.1 Alloy Classification......................................................904
13.24.1.2 Limitations of Zirconium.............................................905
13.24.2 Corrosion Resistance.......................................................................905
13.24.2.1 Resistance to Chemicals..............................................906
13.24.3 Fabrication.......................................................................................906
13.24.3.1 Welding Method...........................................................906
13.24.3.2 Weld Metal Shielding...................................................907
13.24.3.3 Weld Preparation..........................................................907
13.24.3.4 Surface Cleaning..........................................................907
13.24.3.5 Filler Metals.................................................................907
13.24.3.6 Weld Inspection............................................................907
13.24.3.7 Welding of Dissimilar Metals......................................907
13.25 Tantalum.........................................................................................................907
13.25.1 Corrosion Resistance.......................................................................909
13.25.1.1 Hydrogen Embrittlement..............................................909
13.25.1.2 Resistance to Chemicals..............................................909
13.25.2 Product Forms and Cost..................................................................909
13.25.3 Performance versus Other Materials...............................................909
13.25.4 Heat Transfer...................................................................................909
13.25.5 Welding............................................................................................ 910
13.26 Graphite, Glass, Teflon, and Ceramics........................................................... 910

xxxixContents
13.27 Graphite.......................................................................................................... 910
13.27.1 Applications of Impervious Graphite Heat Exchangers............... 910
13.27.2 Drawbacks Associated with Graphite.......................................... 911
13.27.3 Forms of Graphite Heat Exchangers............................................ 911
13.27.4 Shell-and-Tube Heat Exchanger................................................... 911
13.27.5 Graphite Plate Exchanger............................................................. 912
13.28 Glass............................................................................................................... 912
13.28.1 Applications.................................................................................. 912
13.28.2 Mechanical Properties and Resistance to Chemicals................... 912
13.28.3 Construction Types....................................................................... 912
13.28.3.1 Shell-and-Tube Heat Exchangers.............................. 913
13.28.3.2 Coil Heat Exchangers............................................... 913
13.28.3.3 Hybrid Heat Exchangers........................................... 913
13.28.3.4 Glass-Lined Steel...................................................... 913
13.28.3.5 Drawbacks of Glass Material.................................... 913
13.29 Teflon.............................................................................................................. 913
13.29.1 Teflon as Heat Exchanger Material.............................................. 913
13.29.2 Heat Exchangers of Teflon in the Chemical Processing Industry......914
13.29.3 Design Considerations.................................................................. 914
13.29.4 Size/Construction......................................................................... 914
13.29.5 Heat Exchanger Fabrication Technology...................................... 914
13.29.6 Fluoropolymer Resin Development.............................................. 915
13.30 Ceramics......................................................................................................... 915
13.30.1 Suitability of Ceramics for Heat Exchanger Construction........... 915
13.30.2 Classification of Engineering Ceramics....................................... 915
13.30.3 Types of Ceramic Heat Exchanger Construction......................... 916
13.31 Hexoloy® Silicon Carbide Heat Exchanger Tube........................................... 916
13.32 Alloys for Subzero Temperatures................................................................... 917
13.32.1 Ductile–Brittle Transition Temperature....................................... 917
13.32.2 Crystal Structure Determines Low-Temperature Behavior.......... 917
13.32.3 Requirements of Materials for Low-Temperature Applications....... 918
13.32.4 Notch Toughness.......................................................................... 918
13.32.4.1 Notch Toughness: ASME Code Requirements......... 918
13.32.5 Selection of Material for Low-Temperature Applications............ 918
13.32.6 Materials for Low-Temperature and Cryogenic Applications...... 918
13.32.6.1 Aluminum for Cryogenic Applications.................... 919
13.32.6.2 Copper and Copper Alloys.......................................920
13.32.6.3 Titanium and Titanium Alloys..................................920
13.32.6.4 Nickel and High-Nickel Alloys.................................920
13.32.6.5 Carbon Steels and Alloy Plate Steels........................920
13.32.6.6 Products Other than Plate.........................................922
13.32.6.7 Austenitic Stainless Steel..........................................922
13.32.7 Fabrication of Cryogenic Vessels and Heat Exchangers..............922
13.32.8 9% Nickel Steel............................................................................923
13.32.8.1 Merits of 9% Nickel Steel.........................................923
13.32.8.2 Forming of 9% Nickel Steel......................................923
13.32.8.3 Surface Preparation and Scale Removal for
Welding.....................................................................923
13.32.8.4 Edge Preparation.......................................................923
13.32.8.5 Welding Procedures..................................................923
13.32.8.6 Electrodes.................................................................924

xl Contents
13.32.8.7 Guidelines for Welding of 9% Ni Steel.....................924
13.32.8.8 Welding Problems with 9% Ni Steel.........................925
13.32.8.9 Postweld Heat Treatment..........................................925
13.32.9 Welding of Austenitic Stainless Steels for Cryogenic Application...... 925
13.32.9.1 Charpy V-Notch Impact Properties..........................925
13.32.9.2 Problems in Welding.................................................926
13.32.10 Safety in Cryogenics.....................................................................926
13.32.10.1 Checklist...................................................................926
13.33 Cladding.........................................................................................................927
13.33.1 Clad Plate......................................................................................927
13.33.2 Cladding Thickness......................................................................927
13.33.3 Methods of Cladding....................................................................927
13.33.3.1 Loose Lining..............................................................928
13.33.3.2 Resistance Cladding...................................................928
13.33.3.3 Lining Using Plug Welding........................................928
13.33.3.4 Thermal Spraying......................................................928
13.33.3.5 Weld Overlaying or Weld Surfacing..........................928
13.33.3.6 Roll Cladding.............................................................932
13.33.3.7 Explosive Cladding....................................................933
13.33.4 Processing of Clad Plates.............................................................936
13.33.4.1 Forming of Clad Steel Plates.....................................936
13.33.5 Failure of Clad Material...............................................................938
13.33.6 ASME Code Requirements in Using Clad Material....................938
13.34 Postweld Heat Treatment of Welded Joints in Steel Pressure Vessels and
Heat Exchangers.............................................................................................938
13.34.1 Objectives of Heat Treatment.......................................................939
13.34.2 Types of Heat Treatment..............................................................939
13.34.3 Effects of Changes in Steel Quality and PWHT..........................940
13.34.4 ASME Code Requirements for PWHT........................................940
13.34.4.1 Charts for Heat Treatment as per ASME Code.........940
13.34.5 PWHT Cycle................................................................................940
13.34.6 Quality Control during Heat Treatment....................................... 941
13.34.7 Methods of PWHT....................................................................... 941
13.34.8 Effectiveness of Heat Treatment...................................................942
13.34.9 Defects due to Heat Treatment.....................................................942
13.34.10 Possible Welding-Related Failures...............................................942
13.34.11 NDT after PWHT.........................................................................942
References.................................................................................................................942
Bibliography..............................................................................................................953
Chapter 14 Quality Control and Quality Assurance, Inspection, and Nondestructive Testing...........955
14.1 Quality Control and Quality Assurance.........................................................955
14.1.1 Quality Management in Industry...................................................... 955
14.1.2 Quality and Quality Control.............................................................955
14.1.2.1 Aim of Quality Control.....................................................956
14.1.3 Quality Assurance.............................................................................956
14.1.3.1 Need for QA.......................................................................956
14.1.3.2 Essential Elements of Quality Assurance Program...........956
14.1.3.3 Requirements of QA Programs for Success......................956

xliContents
14.1.3.4 Quality Assurance in Fabrication of Heat Exchangers
and Pressure Vessels........................................................956
14.1.3.5 Contents of QAP for Pressure Vessels and
Heat Exchangers..............................................................957
14.1.4 Quality System..................................................................................957
14.1.4.1 ASME Code: Quality Control System.............................959
14.1.5 Quality Manual.................................................................................959
14.1.5.1 Details of QA Manuals....................................................960
14.1.6 Main Documents of the Quality System...........................................960
14.1.6.1 Quality Assurance Program............................................960
14.1.6.2 Operation Process Sheet..................................................960
14.1.6.3 Checklist.......................................................................... 961
14.1.7 Economics of Quality Assurance...................................................... 961
14.1.8 Review and Evaluation Procedures...................................................962
14.1.8.1 Auditing...........................................................................962
14.1.8.2 Auditing Procedure..........................................................962
14.1.8.3 Contents of an Audit Plan................................................962
14.1.9 Documentation..................................................................................962
14.1.10 ISO 9000...........................................................................................963
14.1.10.1 What Is the ISO 9000 Series?..........................................963
14.1.10.2 Principles of ISO 9000....................................................963
14.1.10.3 Why ISO 9000?...............................................................963
14.1.10.4 Benefits of ISO 9000.......................................................963
14.1.10.5 Listing of Selected ISO 9000 Quality Standards............963
14.1.10.6 Total Quality Management..............................................963
14.2 Inspection.......................................................................................................964
14.2.1 Definitions.........................................................................................964
14.2.2 Objectives of Inspection....................................................................964
14.2.3 Design and Inspection.......................................................................964
14.2.4 Inspection Guidelines........................................................................964
14.2.5 Scope of Inspection of Heat Exchangers...........................................964
14.2.5.1 Material Control and Raw Material Inspection...............965
14.2.5.2 Positive Material Identification........................................965
14.2.6 Detailed Checklist for Components..................................................966
14.2.6.1 Checklist for Tubesheet...................................................966
14.2.7 TEMA Standard for Inspection.........................................................966
14.2.8 Master Traveler..................................................................................966
14.2.9 Scope of Third-Party Inspection.......................................................967
14.2.9.1 Hold Points and Witness Points.......................................967
14.3 Welding Design..............................................................................................968
14.3.1 Parameters Affecting Welding Quality.............................................968
14.3.2 Welding Quality Design....................................................................968
14.3.2.1 Variables Affecting Welding Quality..............................969
14.3.3 Scheme of Symbols for Welding.......................................................970
14.3.4 Standard for Welding and Welding Design.......................................970
14.3.4.1 ASME Code Section IX..................................................970
14.3.5 Selection of Consumables.................................................................970
14.3.6 P Numbers.........................................................................................970
14.3.7 Filler Metals......................................................................................970
14.3.7.1 F Numbers.......................................................................971
14.3.7.2 A Numbers.......................................................................971

xlii Contents
14.3.8 Welding Procedure Qualification: Welding Procedure
Specification and Procedure Qualification Record...........................971
14.3.8.1 Welding Procedure Specification....................................971
14.3.8.2 Procedure Qualification Record......................................972
14.3.8.3 Welder’s Performance Qualification................................972
14.3.8.4 Welder Requalification....................................................972
14.3.8.5 Welding Positions and Qualifications..............................972
14.3.9 Weld Defects and Inspection of Weld Quality..................................973
14.3.9.1 Weld Defects (Discontinuities)........................................973
14.3.9.2 Causes of Discontinuities................................................973
14.3.9.3 General Types of Defects and Their Significance...........973
14.3.9.4 Approach to Weld Defect Acceptance Levels.................975
14.4 Nondestructive Testing Methods....................................................................976
14.4.1 Selection of NDT Methods...............................................................976
14.4.1.1 Capabilities and Limitations of Nondestructive
Testing Methods...............................................................976
14.4.1.2 Acceptance Criteria.........................................................976
14.4.1.3 Cost..................................................................................976
14.4.1.4 Personnel..........................................................................979
14.4.2 Inspection Equipment........................................................................980
14.4.3 Reference Codes and Standards........................................................980
14.4.3.1 ASME Code Section V: Nondestructive
Examination.............................................................980
14.4.4 NDT Symbols....................................................................................980
14.4.5 Written Procedures............................................................................980
14.4.5.1 Content of NDT Procedures............................................ 981
14.4.5.2 General Details of Requirements in the NDT
Procedure Document....................................................... 981
14.4.5.3 Deficiencies in NDT Procedures.....................................982
14.4.6 Visual Examination...........................................................................982
14.4.6.1 Principle of VT................................................................982
14.4.6.2 Merits of Visual Examination.........................................983
14.4.6.3 VT Written Procedure.....................................................983
14.4.6.4 Reference Document........................................................983
14.4.6.5 Visual Examination: Prerequisites..................................983
14.4.6.6 Visual Examination Equipment.......................................983
14.4.6.7 NDT of Raw Materials....................................................983
14.4.6.8 Visual Examination during Various Stages of
Fabrication by Welding....................................................984
14.4.6.9 Developments in Visual Examination Optical
Instruments......................................................................984
14.4.7 Liquid Penetrant Inspection..............................................................986
14.4.7.1 Principle...........................................................................986
14.4.7.2 Applications.....................................................................987
14.4.7.3 Merits of PT.....................................................................987
14.4.7.4 Limitations.......................................................................987
14.4.7.5 Written Procedure............................................................987
14.4.7.6 Standards.........................................................................988
14.4.7.7 Test Procedure.................................................................988
14.4.7.8 Penetrants.........................................................................988
14.4.7.9 Method.............................................................................989

xliiiContents
14.4.7.10 Selection of Developer.....................................................989
14.4.7.11 Penetrant Application......................................................989
14.4.7.12 Surface Preparation.........................................................989
14.4.7.13 Excess Penetrant Removal...............................................989
14.4.7.14 Standardization of Light Levels for Penetrant and
Magnetic Inspection........................................................990
14.4.7.15 Evaluation of Indications.................................................990
14.4.7.16 Acceptance Standards.....................................................990
14.4.7.17 Postcleaning.....................................................................990
14.4.7.18 Recent Developments in PT............................................990
14.4.8 Magnetic Particle Inspection.............................................................990
14.4.8.1 Principle........................................................................... 991
14.4.8.2 Applications..................................................................... 991
14.4.8.3 Reference Documents......................................................991
14.4.8.4 Test Procedure.................................................................991
14.4.8.5 Factors Affecting the Formation and Appearance
of the Magnetic Particles Pattern..................................... 991
14.4.8.6 Merits of Magnetic Particle Inspection...........................992
14.4.8.7 Limitations of the Method...............................................992
14.4.8.8 Written Procedure............................................................992
14.4.8.9 Magnetizing Current.......................................................992
14.4.8.10 Equipment for Magnetic Particle Inspection...................993
14.4.8.11 Magnetizing Technique...................................................993
14.4.8.12 Inspection Medium (Magnetic Particles)........................994
14.4.8.13 Inspection Method...........................................................995
14.4.8.15 Evaluation of Indications.................................................996
14.4.8.16 Demagnetization..............................................................996
14.4.8.17 Record of Test Data.........................................................996
14.4.8.18 Interpretation...................................................................996
14.4.8.19 Acceptance Standards.....................................................996
14.4.8.20 MT Accessories...............................................................996
14.4.9 Radiographic Testing.........................................................................996
14.4.9.1 Principle of Radiography.................................................997
14.4.9.2 Application......................................................................997
14.4.9.3 Radiation Sources (X-Rays and Gamma Rays)...............997
14.4.9.4 Merits and Limitations....................................................998
14.4.9.5 Radiographic Test Written Procedure.............................998
14.4.9.6 Requirements of Radiography.........................................999
14.4.9.7 General Procedure in Radiography.................................999
14.4.9.8 Reference Documents......................................................999
14.4.9.9 Safety...............................................................................999
14.4.9.10 Identification Marks.........................................................999
14.4.9.11 Location Markers.............................................................999
14.4.9.12 Processing of X-Ray Films..............................................999
14.4.9.14 Radiographic Techniques for Weldments
of Pressure Vessels........................................................1000
14.4.9.15 Full Radiography........................................................... 1001
14.4.9.16 Radiographic Quality....................................................1002
14.4.9.17 Recent Developments in Radiography...........................1004

xliv Contents
14.4.10 Ultrasonic Testing...........................................................................1007
14.4.10.1 Test Method................................................................1008
14.4.10.2 Application of Ultrasonic Technique in Pressure
Vessel Industry...........................................................1008
14.4.10.3 Written Procedure......................................................1009
14.4.10.4 Code Coverage............................................................1009
14.4.10.5 Advantages of Ultrasonic Inspection.........................1009
14.4.10.6 Limitations of Ultrasonic Inspection...........................1010
14.4.10.7 Examination Procedure...............................................1010
14.4.10.8 Surface Preparation.................................................... 1012
14.4.10.9 Probes......................................................................... 1012
14.4.10.10 Couplant..................................................................... 1012
14.4.10.11 Ultrasonic Testing of Welds....................................... 1012
14.4.10.12 Examination Coverage................................................1014
14.4.10.13 UT Calculators............................................................1014
14.4.10.14 Acceptance Criteria.....................................................1014
14.4.10.15 Reference Blocks.........................................................1014
14.4.10.16 Calibration.................................................................. 1015
14.4.10.17 Phased Array Ultrasonic Testing................................ 1015
14.4.10.18 Fracture Mechanics.................................................... 1019
14.4.10.19 What Is New in UT?...................................................1020
14.4.11 Acoustical Holography.................................................................... 1021
14.4.11.1 Merits and Comparison of Acoustical Holography
with Radiography and Ultrasonic Testing.................. 1021
14.4.11.2 Holographic and Speckle Interferometry................... 1021
14.4.12 Acoustic Emission Testing.............................................................. 1021
14.4.12.1 Principle of Acoustic Emission.................................. 1021
14.4.12.2 Emission Types and Characteristics........................... 1022
14.4.12.3 Kaiser Effect...............................................................1022
14.4.12.4 Reference Code........................................................... 1023
14.4.12.5 Written Procedure...................................................... 1023
14.4.12.6 AE Testing Instrument............................................... 1023
14.4.12.7 Signal Analysis...........................................................1023
14.4.12.8 Factors Influencing AE Data...................................... 1023
14.4.12.9 Applications: Role of AE in Inspection and Quality
Control of Pressure Vessels and Heat Exchangers.....1023
14.4.12.10 Merits of Acoustic Emission Testing..........................1024
14.4.13 Eddy Current Testing......................................................................1024
14.4.13.1 Principles of Eddy Current Testing............................1025
14.4.13.2 Written Procedure......................................................1026
14.4.13.3 ASTM Specifications.................................................1026
14.4.13.4 Probes.........................................................................1026
14.4.13.5 Eddy Current Test Equipment....................................1027
14.4.13.6 Signal Processing....................................................... 1027
14.4.13.7 Inspection or Test Frequency and Its Effect on
Flaw Detectability......................................................1028
14.4.13.8 Operating Variables....................................................1028
14.4.13.9 Inspection Method for Tube Interior..........................1029
14.4.13.10 Tube Inspection with Magnetic Flux Leakage........... 1030
14.4.13.11 Remote Field Eddy Current Testing........................... 1030
14.4.13.12 Tube Inspection with Near Field Testing.................... 1030

xlvContents
14.4.13.13 Tube Inspection with Internal Rotating Inspection
System for Ferrous and Nonferrous Materials........... 1033
14.4.13.14 Instrumentation.......................................................... 1033
14.4.13.15 Testing of Weldments................................................. 1033
14.4.13.16 Calibration.................................................................. 1033
14.4.13.17 Merits of ET and Comparison with Other Methods........1034
14.4.13.18 Limitations of Eddy Current Testing..........................1034
14.4.13.19 Recent Advances in Eddy Current Testing................1034
14.4.13.20 Tubesheet Diagram for Windows............................... 1035
14.4.14 Leak Testing.................................................................................... 1035
14.4.14.1 Written Procedure...................................................... 1036
14.4.14.2 Methods of Leak Testing............................................ 1036
References............................................................................................................... 1041
Bibliography............................................................................................................1044
Chapter 15 Heat Exchanger Fabrication....................................................................................1045
15.1 Introduction to Fabrication of the Shell and Tube Heat Exchanger............. 1045
15.2 Details of Manufacturing Drawing.............................................................. 1045
15.2.1 Additional Necessary Entries..........................................................1046
15.3 Stages of Heat Exchanger Fabrication..........................................................1046
15.3.1 Identification of Materials...............................................................1046
15.3.2 Edge Preparation and Rolling of Shell Sections, Tack Welding,
and Alignment for Welding of Longitudinal Seams....................... 1047
15.3.2.1 General Discussion on Forming of Plates....................... 1047
15.3.2.2 Fabrication of Shell..........................................................1049
15.3.3 Plate Bending Machines, PWHT, and Manipulative
Equipment.............................................................................. 1051
15.3.3.1 Roll Bending Machine..................................................... 1051
15.3.3.2 Vertical Plate Bending Machine...................................... 1051
15.3.3.3 PWHT of Shells............................................................... 1051
15.3.3.4 Manipulative Equipment................................................. 1051
15.3.4 Welding of Shells, Checking the Dimensions, and Subjecting
Pieces to Radiography..................................................................... 1051
15.3.5 Checking the Circularity of the Shell and the Assembly
Fit, Including Nozzles and Expansion Joints.................................. 1052
15.3.5.1 Welding of Nozzles.......................................................... 1053
15.3.5.2 Supports........................................................................... 1053
15.3.5.3 Attachment of Expansion Joints...................................... 1053
15.3.6 Tubesheet and Baffle Drilling.........................................................1054
15.3.6.1 Tubesheet Drilling...........................................................1054
15.3.6.2 Tube Hole Finish.............................................................. 1054
15.3.6.3 Drilling of Baffles............................................................ 1055
15.3.7 Tube Bundle Assembly.................................................................... 1056
15.3.7.1 Assembly of Tube Bundle outside
the Exchanger Shell....................................................1056
15.3.7.2 Assembly of Tube Bundle inside the Shell...................... 1058
15.3.7.3 Tube Nest Assembly of Large Steam Condensers........... 1059
15.3.7.4 Cautions to Exercise while Inserting Tubes.................... 1059
15.3.7.5 Assembly of U-Tube Bundle............................................ 1059
15.3.8 Tubesheet to Shell Welding.............................................................1060

xlvi Contents
15.3.9 Tube-to-Tubesheet Joint Fabrication............................................... 1061
15.3.9.1 Quality Assurance Program for Tube-to-Tubesheet
Joint............................................................................ 1062
15.3.9.2 Mock-Up Test............................................................. 1062
15.3.9.3 Tube Expansion.......................................................... 1063
15.3.9.4 Requirements for Expanded Tube-to-Tubesheet Joints.....1063
15.3.9.5 Tube-to-Tubesheet Expansion Methods..................... 1063
15.3.9.6 Rolling Equipment.....................................................1064
15.3.9.7 Basic Rolling Process.................................................1064
15.3.9.8 Optimum Degree of Expansion.................................1065
15.3.9.9 Methods to Check the Degree of Expansion..............1066
15.3.9.10 Criterion for Rolling-in Adequacy.............................1066
15.3.9.11 Length of Tube Expansion......................................... 1074
15.3.9.12 Full-Depth Rolling..................................................... 1075
15.3.9.13 Size of Tube Holes..................................................... 1076
15.3.9.14 Factors Affecting Rolling Process............................. 1079
15.3.9.15 Strength and Leak Tightness of Rolled Joints........... 1079
15.3.9.16 Expanding in Double Tubesheets............................... 1081
15.3.9.17 Leak Testing............................................................... 1081
15.3.9.18 Residual Stresses in Tube-to-Tubesheet Joints........... 1081
15.3.10 Tube-to-Tubesheet Joint Welding.................................................... 1082
15.3.10.1 Various Methods of Tube-to-Tubesheet Joint Welding.....1083
15.3.10.2 Tube-to-Tubesheet Joint Configuration...................... 1083
15.3.10.3 Welding of Sections of Unequal Thickness...............1092
15.3.10.4 Seal-Welded and Strength-Welded Joints..................1093
15.3.10.5 Considerations in Tube-to-Tubesheet Welding..........1094
15.3.10.6 Welding of Titanium Tubes to Tubesheet..................1096
15.3.10.7 Merits of Sequence of Completion of Expanded
and Welded Joints......................................................1096
15.3.10.8 Full-Depth, Full-Strength Expanding after Welding........1099
15.3.10.9 Ductility of Welded Joint in Feedwater Heaters........1099
15.3.10.10 Welded Mock-Ups...................................................... 1100
15.3.10.11 Inspection of Tube-to-Tubesheet Joint Weld.............. 1100
15.3.10.12 Leak Testing of Tube-to-Tubesheet Joint................... 1102
15.3.10.13 Brazing Method for Tube-to-Tubesheet Joints........... 1102
15.3.11 Heat Treatment................................................................................ 1103
15.3.11.1 With Tubes Welded in One Tubesheet and Left
Free in the Other Tubesheet....................................... 1103
15.3.11.2 Both Ends of the Tubes Welded with Tubesheets...... 1103
15.3.11.3 Heat Treatment: General Requirements..................... 1103
15.3.12 Assembly of Channels/End Closures.............................................. 1104
15.3.12.1 Bolt Tightening.......................................................... 1104
15.3.13 Hydrostatic Testing.......................................................................... 1104
15.3.13.1 ASME CODE Requirement....................................... 1104
15.3.13.2 TEMA Standard Requirement................................... 1105
15.3.13.3 Hydrostatic Testing: Prerequisites.............................. 1105
15.3.13.4 Improved Method for Hydrostatic Testing of
Welded Tube-to-Tubesheet Joint of Feedwater
Heaters....................................................................... 1106
15.3.13.5 HydroProof™............................................................. 1106
15.3.13.6 Plate-Fin Heat Exchanger.............................................. 1107

xlviiContents
15.3.14 Preparation of Heat Exchangers for Shipment................................ 1108
15.3.14.1 Painting.......................................................................... 1108
15.3.14.2 Nitrogen Filling.............................................................. 1108
15.3.15 Making Up Certificates................................................................... 1108
15.3.15.1 Foundation Loading Diagrams/Drawings..................... 1109
15.3.15.2 Schematics or Flow Diagrams....................................... 1109
15.3.15.3 Installation, Maintenance, and Operating
Instructions...............................................................1109
15.4 Forming of Heads and Closures................................................................... 1109
15.4.1 Forming Methods............................................................................ 1109
15.4.2 Spinning.......................................................................................... 1109
15.4.3 Pressing............................................................................................1110
15.4.4 Crown-and-Segment (C and S) Technique.......................................1112
15.4.5 PWHT of Dished Ends.....................................................................1112
15.4.6 Dimensional Check of Heads...........................................................1114
15.4.7 Purchased End Closures...................................................................1114
15.5 Brazing..........................................................................................................1114
15.5.1 Definition and General Description of Brazing...............................1114
15.5.2 Brazing Advantages.........................................................................1114
15.5.3 Disadvantages of Brazing.................................................................1115
15.6 Elements of Brazing......................................................................................1115
15.6.1 Joint Design......................................................................................1115
15.6.1.1 Joint Types.......................................................................1116
15.6.2 Brazing Filler Metals.......................................................................1116
15.6.2.1 Composition of Filler Metals...........................................1116
15.6.2.2 Aluminum Filler Metals..................................................1116
15.6.2.3 Copper Fillers..................................................................1117
15.6.2.4 Nickel-Based Filler Metals..............................................1117
15.6.2.5 Silver-Based Filler Metals...............................................1117
15.6.2.6 Gold-Based Fillers...........................................................1117
15.6.2.7 Forms of Filler Metal......................................................1118
15.6.2.8 Placement of Filler Metal................................................1118
15.6.2.9 ASME Code Specification for Filler Metals...................1118
15.6.3 Precleaning and Surface Preparation...............................................1118
15.6.3.1 Precleaning......................................................................1118
15.6.3.2 Scale and Oxide Removal...............................................1118
15.6.3.3 Protection of Precleaned Parts........................................1119
15.6.4 Fluxing.............................................................................................1119
15.6.4.1 Selection of a Flux...........................................................1119
15.6.4.2 Composition of the Flux..................................................1119
15.6.4.3 Demerits of Brazing Using Corrosive Fluxes..................1119
15.6.5 Fixturing...........................................................................................1119
15.6.6 Brazing Methods............................................................................. 1120
15.6.6.1 Torch Brazing................................................................. 1120
15.6.6.2 Dip Brazing.................................................................... 1120
15.6.6.3 Furnace Brazing............................................................. 1122
15.6.6.4 Vacuum Brazing............................................................. 1124
15.6.7 Postbraze Cleaning.......................................................................... 1125
15.6.7.1 Braze Stopoffs................................................................ 1125
15.7 Fundamentals of Brazing Process Control................................................... 1125
15.7.1 Heating Rate.................................................................................... 1125

xlviii Contents
15.7.2 Brazing Temperature....................................................................... 1125
15.7.3 Brazing Time................................................................................... 1125
15.7.4 Temperature Uniformity................................................................. 1126
15.7.5 Control of Distortion during the Furnace Cycle............................. 1126
15.8 Brazing of Aluminum.................................................................................. 1126
15.8.1 Need for Closer Temperature Control............................................. 1126
15.8.2 Aluminum Alloys That Can Be Brazed.......................................... 1127
15.8.3 Elements of Aluminum Brazing..................................................... 1127
15.8.3.1 Joint Clearance.............................................................. 1127
15.8.3.2 Precleaning.................................................................... 1127
15.8.3.3 Surface Oxide Removal................................................ 1127
15.8.3.4 Aluminum Filler Metals................................................ 1127
15.8.3.5 Fluxing.......................................................................... 1127
15.8.4 Brazing Methods............................................................................. 1128
15.8.4.1 Aluminum Dip Brazing................................................. 1128
15.8.4.2 Furnace Brazing............................................................ 1128
15.8.4.3 Brazing Process............................................................. 1130
15.8.4.4 Vacuum Brazing of Aluminum..................................... 1132
15.9 Brazing of Heat-Resistant Alloys and Stainless Steel.................................. 1135
15.9.1 Brazing of Nickel-Based Alloys...................................................... 1135
15.9.1.1 Brazing Filler Metals.................................................... 1135
15.9.2 Brazing of Cobalt-Based Alloys...................................................... 1136
15.9.3 Brazing of Stainless Steel............................................................... 1136
15.9.3.1 Brazeability of Stainless Steel....................................... 1136
15.10 Quality Control, Inspection, and NDT of Brazed Heat Exchangers............ 1137
15.10.1 Quality of the Brazed Joints............................................................ 1138
15.10.1.1 Discontinuities............................................................... 1138
15.10.2 Inspection........................................................................................ 1139
15.10.2.1 Visual Examination....................................................... 1139
15.10.2.2 Leak Testing.................................................................. 1139
15.10.3 Brazing Codes and Standards......................................................... 1139
15.11 Soldering of Heat Exchangers...................................................................... 1139
15.11.1 Elements of Soldering..................................................................... 1139
15.11.1.1 Joint Design................................................................... 1140
15.11.1.2 Tube Joints..................................................................... 1140
15.11.1.3 Tube-to-Header Solder Joints........................................ 1140
15.11.1.4 Solders........................................................................... 1140
15.11.1.5 Cleaning and Descaling.................................................1141
15.11.1.6 Soldering Fluxes.............................................................1141
15.11.1.7 Soldering Processes........................................................1141
15.11.1.8 Flux Residue Removal....................................................1142
15.11.2 Ultrasonic Soldering of Aluminum Heat Exchangers......................1142
15.11.2.1 Material That Can Be Ultrasonically Soldered............. 1143
15.11.2.2 Basic Processes for Soldering All-Aluminum Coils......... 1143
15.11.3 Quality Control, Inspection, and Testing........................................ 1146
15.11.4 Nondestructive Testing.................................................................... 1146
15.11.4.1 Visual Inspection........................................................... 1146
15.11.4.2 Discontinuities............................................................... 1146
15.11.4.3 Removal of Residual Flux............................................. 1146
15.11.4.4 Pressure and Leak Testing.............................................1147
15.11.4.5 Destructive Testing.........................................................1147

xlixContents
15.12 Corrosion of Brazed and Soldered Joints......................................................1147
15.12.1 Factors Affecting Corrosion of Brazed Joints..................................1147
15.12.2 Corrosion of the Aluminum Brazed Joint........................................1147
15.12.2.1 Galvanic Corrosion Resistance...................................1147
15.12.2.2 Influence of Brazing Process..................................... 1148
15.12.3 Corrosion of Soldered Joints............................................................1149
15.12.3.1 Solder Bloom Corrosion..............................................1149
15.12.3.2 Manufacturing Procedures to Control Solder
Bloom Corrosion.........................................................1149
15.13 Evaluation of Design and Materials of Automotive Radiators......................1149
15.13.1 Mechanical Durability Tests........................................................... 1150
15.13.2 Tests for Corrosion Resistance........................................................ 1150
15.13.2.1 External Corrosion Tests............................................ 1150
15.13.2.2 Internal Corrosion Tests............................................. 1150
15.14 CuproBraze Heat Exchanger.........................................................................1151
15.14.1 Round Tube versus Flat Tube...........................................................1151
15.14.1.1 Tube Fabrication..........................................................1151
15.14.1.2 High-Performance Coatings.......................................1151
15.A Appendix.......................................................................................................1151
References................................................................................................................1162
Suggested Reading.................................................................................................. 1165
Chapter 16 Heat Exchanger Installation, Operation, and Maintenance.....................................1167
16.1 Storage.......................................................................................................... 1168
16.2 Installation.................................................................................................... 1168
16.3 Operation...................................................................................................... 1168
16.4 Maintenance................................................................................................. 1169
16.5 Periodical Inspection of Unit........................................................................ 1169
16.6 Indications of Fouling.................................................................................. 1169
16.7 Deterioration of Heat Exchanger Performance.............................................1170
16.7.1 Air-Cooled Heat Exchangers...........................................................1170
16.7.1.1 Determine the Original Design Performance Data of
the ACHE..........................................................................1170
16.7.1.2 Inspect the Heat Exchanger Unit......................................1170
16.7.1.3 Determine the Current ACHE Performance and Set
Baseline............................................................................1170
16.7.1.4 Install Upgrades................................................................1170
16.7.1.5 Tube Bundle......................................................................1171
16.7.2 Shell and Tube Heat Exchanger.......................................................1171
16.7.2.1 Quality Auditing of Existing Heat Exchanger..................1171
16.7.2.2 Leak Detection: Weep-Hole Inspection...........................1171
16.7.2.3 Tube Bundle Removal and Handling................................1172
16.7.3 Brazed Aluminum Plate-Fin Heat Exchanger..................................1181
16.7.3.1 Leak Detection.................................................................1181
16.7.3.2 Repair of Leaks................................................................1181
16.8 NDT Methods to Inspect and Assess the Condition of Heat Exchanger
and Pressure Vessel Components..................................................................1182
16.8.1 Ultrasonic Internal Rotary Inspection System.................................1182
16.8.2 Remote Field Eddy Current Testing.................................................1182

l Contents
16.8.3 Eddy Current Testing.......................................................................1182
16.8.4 Tubes................................................................................................1183
16.9 Residual Life Assessment of Heat Exchangers by NDT Techniques............1183
16.9.1 Creep Waves.................................................................................... 1184
16.9.2 Ultrasonic Method Based on Backscatter and Velocity Ratio
Measurement................................................................................... 1184
16.9.3 Pulsed Eddy Currents...................................................................... 1184
16.9.4 Flash Radiography.......................................................................... 1184
16.9.5 Low-Frequency Electromagnetic Test............................................. 1184
16.9.6 Photon-Induced Positron Annihilation and Distributed Source
Positron Annihilation.......................................................................1185
16.9.6.1 Replication Techniques.....................................................1185
16.9.6.2 Creep Determinations by Nondestructive Testing
Method..............................................................................1185
16.10 Pressure Vessel Failure..................................................................................1185
16.10.1 Failure Modes...................................................................................1185
16.11 Professional Service Providers for Heat Exchangers....................................1185
References............................................................................................................... 1186

li
Preface
INTRODUCTION
The advances in heat exchanger technology since the publication of the first edition and the topics
that had been missed have necessitated a second edition of this book. This edition showcases recent
advances in the selection, design, construction, operation, and maintenance of heat exchangers.
The errors in the previous edition have been corrected, and the quality of figures including
thermal effectiveness charts has been improved. This book provides up-to-date information on
the single-phase heat transfer problems encountered by engineers in their daily work. It will con-
tinue to be a centerpiece of information for practicing engineers, research engineers, academicians,
designers, and manufacturers involved in heat exchange between two or more fluids. Permission
was sought from leading heat exchanger manufacturers and research organizations to include
figures of practical importance, and these have been added in this edition. Care has been taken to
minimize errors.
COVERAGE
In the chapter on the classification of heat exchangers, topics such as scrapped surface heat exchanger,
graphite heat exchanger, coil wound heat exchanger, microscale heat exchanger, and printed circuit
heat exchanger have been included. The construction and performance features of various types of
heat exchangers have been compared.
Concepts like ALEX core for PFHE, radial flow heat exchanger for waste heat recovery, and
rotary regenerator for HVAC applications have been added. Breach-LockTM and Taper-LokTM end
closures have also been included.
Construction details and performance features of nonsegmental baffles heat exchangers such as
EMbaffle®, Helixchanger®, and Twisted Tube® heat exchangers have been added. Design features of
feedwater heater, steam surface condenser, and tantalum heat exchanger for pharmaceutical appli-
cations have also been included.
Information on pressure vessel codes, manufacturer’s association standards, and ASME codes
has been updated. ALPEMA standards for PFHE have been dealt with in depth.
Performance features of coil wound heat exchangers have been compared with brazed aluminum
heat exchangers. The construction, selection, design, and concepts of manufacture of ACHE have
been updated.
Recent advances in PHE concepts such as all welded, shell type, wide gap, free flow, semi-welded,
and double-wall have been discussed and their construction and performance features compared.
The chapter on heat transfer augmentation has been thoroughly revised. Underlying the principle
of heat transfer enhancement, devices such as hiTRAN thermal system and wire matrix turbulators
have been described.
Fouling control concepts, such as back flushing, heat exchangers, such as self-cleaning, and liq-
uid fluidized bed technology, fluidized bed units, and fouling control devices, such as Spirelf®,
Fixotal®, and Turbotal®, have been added.
A new chapter on heat exchanger installation, operation, and maintenance covers the commis-
sioning of new units, operation, their maintenance, repair practices, tube bundle removal, handling
and cleaning, leak testing and plugging of tubes, condition monitoring, quality audit, and residual
life assessment by NDT methods.
The tubesheet design procedure as per the latest ASME code, CODAP, PD 5000, and UPV has
been discussed and compared with TEMA standards. The software program structure for design

lii Preface
of ACHE and STHE has been updated. Recent trends in NDT methods such as ECT, UT, and leak
testing have been included.
The chapter on fabrication of heat exchangers has now been revised, covering the recent advances
in tube expansion and tube-to-tubesheet welding practices, rolling equipment, accessories, adequacy
of rolling, cold working principle, configuration of tube-to-tubesheet joints for welding, modern
equipment for tube hole preparation, and internal bore welding tubes. The section on heat exchanger
heads has now been updated by incorporating various hot/cold working methods, and manufactur-
ing procedures and PWHT have been discussed. New topics like CAB brazing of compact heat
exchanger, cupro-braze radiators, and flat tube versus round tube concept for radiator tubings have
also been added.
Due to their content and coverage, chapters 2, 5, 13 and 15 can be treated as individually
self-contained units, as they do not require other chapters to be understood. This edition is abun-
dantly illustrated with over 600 drawings, diagrams, photos, and tables. The Heat Exchanger Design
Handbook, Second Edition is an excellent resource for mechanical, chemical, and petrochemical
engineers; process equipment and pressure vessel designers, consultants, and heat exchanger manu-
facturers; and upper-level undergraduate and graduate students in these disciplines.

liii
Acknowledgments
A large number of my colleagues from Indian Railways, well-wishers, and family members had
contributed immensely toward the preparation of the book. Though I could not acknowledge them
individually in the first edition, I mention a few of them here, as follows: Jothimani Gunasekaran,
V. R. Ventakaraman, P. Subramani, Rajasri Anandan, and P. Gajapathy of ICF; Amitab Chakraborty
(ADG), O. P. Agarwal (ED), M. Vijayakumar (Director), R. S. Madhukar, Suresh Prakash, Ashok
Krishan, P. A. Rehman, and V. P. Gupta of RDSO, Lucknow; S. Bangaru Lakshman (then MOSR) and
S. Dasarathy (then member mechanical, Railway Board, Ministry of Railways); Lilly Ravi, Renuka
Devi Balasubramanian, Sukanya Balakrishnan, Sardha Balasubramaniam, and T. Adikesavan of
Southern Railway; Amarnath, GM (retd.), and Radhey Shyam, GM, CLW; Cittaranjan, Ministry of
Railways; Shanka Sinha of CLW; K. Kamaraj of IIT-Madras Library; M. Krishnasamy, Member
of Parliament; my sisters, Anjala Manoharan, Maya Pannerselvam, and Indira Mari; my family
members, Dr. K. Kalai (alias Vasanth), Dr. K. Kumudhini, and Er. K. Praveen; and Arunkumar
Aranganathan, project manager, and Anithajohny Mariasusai, assistant director at SPi Global,
Puducherry, India, who oversaw the production of the second edition on behalf of Taylor Francis
Group. I have immensely benefited from the contributions of scholars such as Dr. K. P. Singh,
Dr. J. P. Gupta, and Dr. Ramesh K. Shah, the Donald Q. Kern awardee for the year 2005 by the
American Society of Mechanical Engineers and the American Institute of Chemical Engineers. I also
acknowledge the computer facilities of the Engine Development Directorate of RDSO, Lucknow,
Ministry of Railways, and the library facilities of IIT-M, IIT-K, IIT-D, and RDSO, Lucknow. A
large number of heat exchanger manufacturers and research organizations had spared photos and
figures, and their names are acknowledged in the respective figure captions.

lv
Author
Thulukkanam Kuppan, Indian Railway Service of Mechanical Engineers (IRSME), Ministry of
Railways, is the chief mechanical engineer (senior administrative grade) in a rolling stock produc-
tion unit. He has authored an article in the ASME Journal of Pressure Vessel Technology. His
various roles have included being an experienced administrator, staff recruitment board chairman
for a zonal railway, and joint director of the Engine Development Directorate of RDSO, Lucknow.
He was also involved in design and performance evaluation of various types of heat exchangers
used in diesel electric locomotives and has served as chief workshop engineer for the production
of rolling stocks and as Director of Public Grievances (DPG) to the Minister of State for Railways,
Railway Board, Government of India. Kuppan received his BE (hons) in 1980 from the PSG College
of Technology, Coimbatore, Madras University, and his MTech in production engineering in 1982
from the Indian Institute of Technology, Madras, India.

1
1 Heat Exchangers
Introduction, Classification,
and Selection
1.1 INTRODUCTION
A heat exchanger is a heat transfer device that is used for transfer of internal thermal energy
between two or more fluids available at different temperatures. In most heat exchangers, the fluids
are separated by a heat transfer surface, and ideally they do not mix. Heat exchangers are used in
the process, power, petroleum, transportation, air-conditioning, refrigeration, cryogenic, heat recov-
ery, alternate fuels, and other industries. Common examples of heat exchangers familiar to us in
day-to-day use are automobile radiators, condensers, evaporators, air preheaters, and oil coolers.
Heat exchangers can be classified into many different ways.
1.2 CONSTRUCTION OF HEAT EXCHANGERS
A heat exchanger consists of heat-exchanging elements such as a core or matrix containing the heat
transfer surface, and fluid distribution elements such as headers or tanks, inlet and outlet nozzles
or pipes, etc. Usually, there are no moving parts in the heat exchanger; however, there are excep-
tions, such as a rotary regenerator in which the matrix is driven to rotate at some design speed and
a scraped surface heat exchanger in which a rotary element with scraper blades continuously rotates
inside the heat transfer tube. The heat transfer surface is in direct contact with fluids through which
heat is transferred by conduction. The portion of the surface that separates the fluids is referred to
as the primary or direct contact surface. To increase heat transfer area, secondary surfaces known
as fins may be attached to the primary surface. Figure 1.1 shows a collection of few types of heat
exchangers.
1.3 CLASSIFICATION OF HEAT EXCHANGERS
In general, industrial heat exchangers have been classified according to (1) construction, (2) trans-
fer processes, (3) degrees of surface compactness, (4) flow arrangements, (5) pass arrangements,
(6) phase of the process fluids, and (7) heat transfer mechanisms. These classifications are briefly
discussed here. For more details on heat exchanger classification and construction, refer to Shah
[1,2], Gupta [3], and Graham Walker [4]. For classification and systematic procedure for selection
of heat exchangers, refer to Larowski et al. [5a,5b]. Table 1.1 shows some types of heat exchangers,
their construction details, and performance parameters.

2 Heat Exchanger Design Handbook
1.3.1 Classification According to Construction
According to constructional details, heat exchangers are classified as [1] follows:
Tubular heat exchangers—double pipe, shell and tube, coiled tube
Plate heat exchangers (PHEs)—gasketed, brazed, welded, spiral, panel coil, lamella
Extended surface heat exchangers—tube-fin, plate-fin
Regenerators—fixed matrix, rotary matrix
1.3.1.1 Tubular Heat Exchanger
1.3.1.1.1 Double-Pipe Exchangers
A double-pipe heat exchanger has two concentric pipes, usually in the form of a U-bend design. Double-
pipe heat changers with U-bend design are known as hairpin heat exchangers. The flow arrangement is
pure countercurrent. A number of double-pipe heat exchangers can be connected in series or parallel
as necessary. Their usual application is for small duties requiring, typically, less than 300 ft2 and they
are suitable for high pressures and temperatures and thermally long duties [5]. This has the advantage
of flexibility since units can be added or removed as required, and the design is easy to service and
requires low inventory of spares because of its standardization. Either longitudinal fins or circumfer-
ential fins within the annulus on the inner pipe wall are required to enhance the heat transfer from the
inner pipe fluid to the annulus fluid. Design pressures and temperatures are broadly similar to shell
and tube heat exchangers (STHEs). The design is straightforward and is carried out using the method
of Kern [6] or proprietary programs. The Koch Heat Transfer Company LP, USA, is the pioneer in the
design of hairpin heat exchangers. Figures 1.2 through 1.4 show double-pipe heat exchangers.
1.3.1.1.1.1 Application When the process calls for a temperature cross (when the hot fluid
outlet temperature is below the cold fluid outlet temperature), a hairpin heat exchanger is the
most efficient design and will result in fewer sections and less surface area. Also, they are com-
monly used for high-fouling services such as slurries and for smaller heat duties. Multitube heat
FIGURE 1.1 Collection of few types of heat exchangers. (Courtesy of ITT STANDARD, Cheektowaga, NY.)

3Heat Exchangers
TABLE 1.1
Heat Exchanger Types: Construction and Performance Features
Type of Heat
Exchanger Constructional Features Performance Features
Double
pipe(hair
pin) heat
exchanger
A double pipe heat exchanger has two concentric
pipes, usually in the form of a U-bend design.
U-bend design is known as hairpin heat
exchangers. The flow arrangement is pure
countercurrent. The surface area ranges from
300 to 6000 ft2 (finned tubes). Pressure
capabilities are full vacuum to over 14,000 psi
(limited by size, material, and design condition)
and temperature from −100°C to 600°C (−150°F
to 1100°F).
Applicable services: The process results in a
temperature cross, high-pressure stream on
tubeside, a low allowable pressure drop is
required on one side, when the exchanger is
subject to thermal shocks, when flow-induced
vibration may be a problem.
Shell and
tube heat
exchanger
(STHE)
The most commonly used heat exchanger. It is the
“workhorse” of industrial process heat transfer.
They are used as oil cooler, surface condenser,
feed water heater, etc.
The major components of a shell and tube
exchanger are tubes, baffles, shell, front head, rear
head, and nozzles.
Shell diameter: 60 up to 2000 mm. Operating
temperature: −20°C up to 500°C. Operating
pressure max. 600 bar.
Advantages: Extremely flexible and robust design,
easy to maintain and repair.
Disadvantages
1. Require large site (footprint) area for
installation and often need extra space to
remove the bundle.
2. Construction is heavy.
3. PHE may be cheaper for pressure below 16 bar
(230 psi) and temperature below 200°C
(392°F).
Coiled tube
heat
exchanger
(CTHE)
Construction of these heat exchangers involves
winding a large number of small-bore ductile
tubes in helix fashion around a central core tube,
with each exchanger containing many layers of
tubes along both the principal and radial axes.
Different fluids may be passed in counterflow to
the single shellside fluid.
Advantages, especially when dealing with
low-temperature applications where
simultaneous heat transfer between more
than two streams is desired. Because of small
bore tubes on both sides, CTHEs do not
permit mechanical cleaning and therefore are
used to handle clean, solid-free fluids or fluids
whose fouling deposits can be cleaned by
chemicals. Materials are usually aluminum
alloys for cryogenics, and stainless
steels for high-temperature applications.
Finned-tube
heat
exchanger
Construction
1. Normal fins on individual tubes referred to as
individually finned tubes.
2. Longitudinal fins on individual tubes, which
are generally used in condensing applications
and for viscous fluids in double-pipe heat
exchangers.
3. Flat or continuous (plain, wavy, or interrupted)
external fins on an array of tubes (either circular
or flat tube).
4. The tube layout pattern is mostly staggered.
Merits: small inventory, low weight, easier
transport, less foundation, better temperature
control
Applications
Condensers and evaporators of air conditioners,
radiators for internal combustion engines, charge
air coolers and intercoolers for cooling
supercharged engine intake air of diesel
engines, etc.
(continued)

TABLE 1.1 (continued)
Type of Heat
Air cooled
heat
exchanger
(ACHE)
Construction
1. Individually finned tube bundle. The tube
bundle consists of a series of finned tubes set
between side frames, passing between header
boxes at either end.
2. An air-pumping device (such as an axial flow
fan or blower) across the tube bundle which may
be either forced draft or induced draft.
3. A support structure high enough to allow air to
enter beneath the ACHE.
Merits: Design of ACHE is simpler compared to
STHE, since the airside pressure and temperature
pertain to ambient conditions. Tubeside design is
same as STHE. Maintenance cost is normally
less than that for water-cooled systems. The
fouling on the air side can be cleaned easily.
Disadvantages of ACHEs
ACHEs require large heat transfer surfaces
because of the low heat transfer coefficient on
the air side and the low specific heat of air. Noise
is a factor with ACHEs.
Plate-fin heat
exchanger
(PFHE)
Plate fin heat exchangers (PFHEs) are a form of
compact heat exchanger consisting of a stack of
alternate flat plates called “parting sheets” and fin
corrugations, brazed together as a block. Different
fins (such as the plain triangular, louver,
perforated, or wavy fin) can be used between
plates for different applications.
Plate-fin surfaces are commonly used in gas-to-gas
exchanger applications. They offer high area
densities (up to about 6000 m2/m3 or 1800 ft2/ft3).
Designed for low-pressure applications, with
operating pressures limited to about 1000 kPa g
(150 psig) and operating temperature from
cryogenic to 150°C (all-aluminum PFHE) and
about 700°C–800°C (1300°F–1500°F) (made of
heat-resistant alloys).
1. PFHE offers superior in thermal performance
compared to extended surface heat exchangers.
2. PFHE can achieve temperature approaches as
low as 1°C between single-phase streams and
3°C between multiphase streams.
3. With their high surface compactness, ability to
handle multiple streams, and with aluminum’s
highly desirable low-temperature properties,
brazed aluminum plate fins are an obvious
choice for cryogenic applications.
4. Very high thermal effectiveness can be achieved;
for cryogenic applications, effectiveness of the
order of 95% and above is common.
Limitations:
1. Narrow passages in plate-fin exchangers make
them susceptible for fouling and they cannot be
cleaned by mechanical means. This limits their
use to clean applications like handling air, light
hydrocarbons, and refrigerants.
Regenerator The heat exchanger used to preheat combustion air
is called either a recuperator or a regenerator.
A recuperator is a convective heat transfer type heat
exchanger like tubular, plate-fin and extended
surface heat exchangers. The regenerator is classified
as (1) fixed matrix or fixed bed and (2) rotary
regenerators. The matrix is alternatively heated by
hot fluid and cooled by the cold fluid. Features:
1. A more compact size (β = 8800 m2/m3 for
rotating type and 1600 m2/m3 for fixed
matrix type).
2. Application to both high temperatures
(800°C–1100°C) for metal matrix, and 2000°C
for ceramic regenerators for services like gas
turbine applications, melting furnaces or steam
power plant heat recovery, and low-temperature
applications like space heating (HVAC).
Usage
1. Reheating process feedstock.
2. Waste heat boiler and feed water heating for
generating steam (low-temperature recovery
system).
3. Air preheater—preheating the combustion air
(high temperature heat recovery system).
4. Space heating—rotary heat exchanger (wheel)
is mainly used in building ventilation or in the
air supply/discharge system of air conditioning
equipment.

5Heat Exchangers
Type of Heat
3. Operating pressure of 5–7 bar for gas turbine
applications and low pressure of 1–1.5 bar for
air dehumidifier and waste heat recovery
applications.
4. The absence of a separate flow path like tubes
or plate walls but the presence of seals to
separate the gas stream in order to avoid mixing
due to pressure differential.
Plate heat
exchanger
(PHE)
A plate heat exchanger is usually comprised of a
stack of corrugated or embossed metal plates in
mutual contact, each plate having four apertures
serving as inlet and outlet ports, and seals
designed so as to direct the fluids in alternate flow
passages.
Standard performance limits
Maximum operating pressure 25 bar (360 psi)
Maximum temperature 160°C (320°F)
With special gaskets 200°C (390°F)
Maximum flow rate 3600 m3/h (950,000
USG/min)
Temperature approach As low as 1°C
Heat recovery As high as 93%
Heat transfer coefficient 3000–7000 W/m2·°C
(water–water duties with
normal fouling resistance)
Merits: True counterflow, high turbulence and
high heat transfer performance. Close approach
temperature.
Reduced fouling: Cross-contamination eliminated.
Multiple duties with a single unit. Expandable.
Easy to inspect and clean, and less maintenance.
Low liquid volume and quick process control.
Lower cost.
Disadvantages
1. The maximum operating temperature and
pressure are limited by gasket materials. The
gaskets cannot handle corrosive or
aggressive media.
2. Gasketed plate heat exchangers cannot handle
particulates that are larger than 0.5 mm.
3. Gaskets always increase the leakage risk.
Exchanger
Other varieties include, brazed plate heat exchanger
(BPHE), shell and plate heat exchanger, welded
plate heat exchanger, wide-gap plate heat
exchanger, free-flow plate heat exchanger,
semi-welded or twin-plate heat exchanger,
double-wall plate heat exchanger, biabon F
graphite plate heat exchanger, etc.
Spiral plate
heat
exchanger
(SPHE)
SPHE is fabricated by rolling a pair of relatively
long strips of plate to form a pair of spiral
passages. Channel spacing is maintained
uniformly along the length of the spiral passages
by means of spacer studs welded to the plate strips
prior to rolling.
Advantages: To handle slurries and liquids with
suspended fibers, and mineral ore treatment
where the solid content is up to 50%. The SPHE
is the first choice for extremely high viscosities,
say up to 500,000 cp, especially in cooling
duties.
Applications: SPHEs are finding applications in
reboiling, condensing, heating or cooling of
viscous fluids, slurries, and sludge.
Printed
circuit heat
exchangers
(PCHEs)
HEATRIC printed circuit heat exchangers consist
of diffusion-bonded heat exchanger core that are
constructed from flat metal plates into which
fluid flow channels are either chemically etched
or pressed. They can withstand pressure of
600 bar (9000 psi) with extreme temperatures,
ranging from cryogenic to 700°C (1650°F).
Merits: fluid flow can be parallelflow,
counterflow, crossflow, or a combination of these
to suit the process requirements. Thermal
effectiveness is of the order of 98% in a single
unit. They can incorporate more than two
process streams into a single unit.
(continued)

Type of Heat
Lamella heat
exchanger
(LHE)
A lamella heat exchanger normally consists of a
cylindrical shell surrounding a number of heat
transferring lamellas. The design can be
compared to a tube heat exchanger but with the
circular tubes replaced by thin and wide
channels, lamellas. The lamella heat exchanger
works with the media in full counter current
flow. The absence of baffle plates minimizes the
pressure drop and makes handling of most
media possible.
Merits: Since the lamella bundle can be easily
dismantled from the shell, inspection and
cleaning is easy.
Applications
Cooking fluid heating in pulp mills.
Liquor preheaters.
Coolers and condensers of flue gas.
Oil coolers.
Heat pipe
heat
exchanger
The heat-pipe heat exchanger used for gas–gas
heat recovery is essentially bundle of finned
tubes assembled like a conventional air-cooled
heat exchanger. The heat pipe consists of three
elements: (1) a working fluid inside the tubes,
(2) a wick lining inside the wall, and
(3) vacuum sealed finned tube. The heat-pipe
heat exchanger consists of an evaporative
section through which the hot exhaust gas flows
and a condensation section through which the
cold air flows. These two sections are separated
by a separating wall.
Application: The heat pipes are used for (i) heat
recovery from process fluid to preheating of air
for space heating, (ii) HVAC application-waste
heat recovery from the exhaust air to heat the
incoming process air
It virtually does not need mechanical
maintenance, as there are no moving parts. The
heat pipe heat recovery systems are capable of
operating at a temperature of 300°C–315°C with
60%–80% heat recovery capability.
Plate coil
heat
exchanger
(PCHE)
Fabricated from two metal sheets, one or both of
which are embossed. When welded together, the
embossings form a series of well-defined passages
through which the heat transfer media flows.
A variety of standard PLATECOIL® fabrications,
such as pipe coil, half pipe, jacketed tanks and
vessels, clamp-on upgrades, immersion heaters
and coolers, heat recovery banks, storage tank
heaters, etc., are available. Easy access to panels
and robust cleaning surfaces reduce maintenance
burdens.
Scraped
surface heat
exchanger
Scraped surface heat exchangers are essentially
double pipe construction with the process fluid
in the inner pipe and the cooling (water) or
heating medium (steam) in the annulus. A
rotating element is contained within the tube
and is equipped with spring-loaded blades. In
operation the rotating shaft scraper blades
continuously scrape product film from the heat
transfer tube wall, thereby enhancing heat
transfer and agitating the product to produce a
homogenous mixture.
Scraped surface heat exchangers are used for
processes likely to result in the substantial
deposition of suspended solids on the heat
transfer surface. Scraped surface heat
exchangers can be employed in the
continuous, closed processing of virtually
any pumpable fluid or slurry involving
cooking, slush freezing, cooling,
crystallizing, mixing, plasticizing, gelling,
polymerizing, heating, aseptic processing,
etc. Use of a scraped surface exchanger
prevents the accumulation of significant
buildup of solid deposits.

7Heat Exchangers
Outer tube
Inner tube
(i) (ii) (iii) (iv)
(a)
(b)
FIGURE 1.2 Double pipe/twin pipe hairpin heat exchanger. (a) Schematic of the unit, (b): (i) double pipe
with bare internal tube, (ii) double pipe with finned internal tube, (iii) double pipe with multibare inter-
nal tubes, and (iv) double pipe with multifinned internal tubes. (Courtesy of Peerless Mfg. Co., Dallas, TX,
Makers of Alco and Bos-Hatten brands of heat exchangers.)
(a)
(b)
FIGURE 1.3 Double pipe/hairpin heat exchanger. (a) 3-D view and (b) tube bundle with longitudinal fins.
(Courtesy of Peerless Mfg. Co., Dallas, TX, Makers of Alco and Bos-Hatten brands of heat exchangers.)

exchangers are used for larger heat duties. A hairpin heat exchanger should be considered when
one or more of the following conditions exist:
• The process results in a temperature cross
• High pressure on tubeside application
• A low allowable pressure drop is required on one side
• When an augmentation device to enhance the heat transfer coefficient is desired
• When the exchanger is subject to thermal shocks
• When flow-induced vibration may be a problem
• When solid particulates or slurries are present in the process stream
1.3.1.1.2 Shell and Tube Heat Exchanger
In process industries, shell and tube heat exchangers are used in great numbers, far more than any
other type of exchanger. More than 90% of heat exchangers used in industry are of the shell and
tube type [7]. STHEs are the “workhorses” of industrial process heat transfer [8]. They are the first
choice because of well-established procedures for design and manufacture from a wide variety of
materials, many years of satisfactory service, and availability of codes and standards for design and
fabrication. They are produced in the widest variety of sizes and styles. There is virtually no limit
on the operating temperature and pressure. Figure 1.5 shows STHEs.
1.3.1.1.3 Coiled Tube Heat Exchanger
Construction of these heat exchangers involves winding a large number of small-bore ductile tubes
in helix fashion around a central core tube, with each exchanger containing many layers of tubes
(a) (b)
(c)
FIGURE 1.4 Hairpin heat exchanger. (a) Separated head closure using separate bolting on shellside and tube-
side and (b) Hairpin exchangers for high-pressure and high-temperature applications and (c) multitubes (bare)
bundle. (Photo courtesy of Heat Exchanger Design, Inc., Indianapolis, IN.)

9Heat Exchangers
along both the principal and radial axes. The tubes in individual layers or groups of layers may
be brought together into one or more tube plates through which different fluids may be passed in
counterflow to the single shellside fluid. The construction details have been explained in Refs. [5,9].
The high-pressure stream flows through the small-diameter tubes, while the low-pressure return
stream flows across outside of the small-diameter tubes in the annular space between the inner
central core tube and the outer shell. Pressure drops in the coiled tubes are equalized for each
high-pressure stream by using tubes of equal length and varying the spacing of these in the different
layers. Because of small-bore tubes on both sides, CTHEs do not permit mechanical cleaning and
therefore are used to handle clean, solid-free fluids or fluids whose fouling deposits can be cleaned
by chemicals. The materials used are usually aluminum alloys for cryogenics and stainless steel for
high-temperature applications.
CTHE offers unique advantages, especially when dealing with low-temperature applications for
the following cases [9]:
• Simultaneous heat transfer between more than two streams is desired. One of the three
classical heat exchangers used today for large-scale liquefaction systems is CTHE.
• A large number of heat transfer units are required.
• High-operating pressures are involved.
CTHE is not cheap because of the material costs, high labor input in winding the tubes, and the
central mandrel, which is not useful for heat transfer but increases the shell diameter [5].
1.3.1.1.3.1 Linde Coil-Wound Heat Exchangers Linde coil-wound heat exchangers are com-
pact and reliable with a broad temperature and pressure range and suitable for both single- and two-
phase streams. Multiple streams can be accommodated in one exchanger. They are known for their
(a)
(b)
FIGURE 1.5 Shell and tube heat exchanger. (a) Components and (b) heat exchanger. (Courtesy of Allegheny
Bradford Corporation, Bradford, PA.)

robustness in particularly during start-up and shut-down or plant-trip conditions. Both the brazed
aluminum PFHEs and CTHEs find application in liquefication processes. A comparison of salient
features of these two types of heat exchangers is shown in Chapter 4. Figure 1.6 shows Linde coil-
wound heat exchangers.
Glass coil heat exchangers: Two basic types of glass coil heat exchangers are (i) coil type and
(ii) STHE with glass or MS shells in combination with glass tube as standard material for tube.
Glass coil exchangers have a coil fused to the shell to make a one-piece unit. This prohibits leak-
age between the coil and shellside fluids [10]. The reduced heat transfer coefficient of boro silicate
glass equipment compares favorably with many alternate tube materials. This is due to the smooth
surface of the glass that improves the film coefficient and reduces the tendency for fouling. More
details on glass heat exchangers are furnished in Chapter 13.
1.3.1.2 Plate Heat Exchangers
PHEs are less widely used than tubular heat exchangers but offer certain important advantages.
PHEs can be classified into three principal groups:
1. Plate and frame or gasketed PHEs used as an alternative to tube and shell exchangers for
low- and medium-pressure liquid–liquid heat transfer applications
2. Spiral heat exchanger used as an alternative to shell and tube exchangers where low main-
tenance is required, particularly with fluids tending to sludge or containing slurries or
solids in suspension
3. Panel heat exchangers made from embossed plates to form a conduit or coil for liquids
coupled with fins
(a) (b)
(c)
FIGURE 1.6 Coiled tube heat exchanger. (a) End section of a tube bundle, (b) tube bundle under fabrication,
and (c) construction details. (From Linde AG, Engineering Division. With permission.)

11Heat Exchangers
1.3.1.2.1 Plate and Frame or Gasketed Plate Heat Exchangers
A PHE essentially consists of a number of corrugated metal plates in mutual contact, each plate hav-
ing four apertures serving as inlet and outlet ports, and seals designed to direct the fluids in alternate
flow passages. The plates are clamped together in a frame that includes connections for the fluids.
Since each plate is generally provided with peripheral gaskets to provide sealing arrangements, PHEs
are called gasketed PHEs. PHEs are shown in Figure 1.7 and are covered in detail in Chapter 7.
1.3.1.2.2 Spiral Plate Heat Exchanger
SPHEs have been used since the 1930s, when they were originally developed in Sweden for heat
recovery in pulp mills. They are classified as a type of welded PHE. An SPHE is fabricated by roll-
ing a pair of relatively long strips of plate around a split mandrel to form a pair of spiral passages.
Channel spacing is maintained uniformly along the length of the spiral passages by means of spacer
studs welded to the plate strips prior to rolling. Figure 1.8 shows an SPHE. For most applications,
both flow channels are closed by alternate channels welded at both sides of the spiral plate. In some
services, one of the channels is left open, whereas the other closed at both sides of the plate. These
two types of construction prevent the fluids from mixing.
The SPHE is intended especially for the following applications [5]:
To handle slurries and liquids with suspended fibers and mineral ore treatment where the solid
content is up to 50%.
SPHE is the first choice for extremely high viscosities, say up to 500,000 cp, especially in
cooling duties, because of maldistribution, and hence partial blockage by local overcooling
is less likely to occur in a single-channel exchanger.
SPHEs are finding applications in reboiling, condensing, heating, or cooling of viscous fluids,
slurries, and sludge [11].
More details on SPHE are furnished in Chapter 7.
(a) (b)
2
1
7
8
3
5
6
4
FIGURE 1.7 Plate heat exchanger. (a) Construction details—schematic (Parts details: 1, Fixed frame plate; 2, Top
carrying bar; 3, Plate pack; 4, Bottom carrying bar; 5, Movable pressure plate; 6, Support column; 7, Fluids port; and
8, Tightening bolts.) and (b) closer view of assembled plates. (Courtesy of ITT STANDARD, Cheektowaga, NY.)

1.3.1.2.3 Plate or Panel Coil Heat Exchanger
These exchangers are called panel coils, plate coils, or embossed panel or jacketing. The panel coil
serves as a heat sink or a heat source, depending upon whether the fluid within the coil is being
cooled or heated. Panel coil heat exchangers are relatively inexpensive and can be made into any
desired shape and thickness for heat sinks and heat sources under varied operating conditions.
Hence, they have been used in many industrial applications such as cryogenics, chemicals, fibers,
food, paints, pharmaceuticals, and solar absorbers.
Construction details of a panel coil: A few types of panel coil designs are shown in Figure 1.9.
The panel coil is used in such industries as plating, metal finishing, chemical, textile, brewery,
pharmaceutical, dairy, pulp and paper, food, nuclear, beverage, waste treatment, and many others.
Construction details of panel coils are discussed next. M/s Paul Muller Company, Springfield, MO,
and Tranter, Inc., TX, are the leading manufacturers of panel coil/plate coil heat exchangers.
Single embossed surface: The single embossed heat transfer surface is an economical type to utilize
for interior tank walls, conveyor beds, and when a flat side is required. The single embossed design
uses two sheets of material of different thickness and is available in stainless steel, other alloys,
carbon steel, and in many material gages and working pressures.
Double embossed surface: Inflated on both sides using two sheets of material and the same thick-
ness, the double embossed construction maximizes the heating and cooling process by utilizing
both sides of the heat transfer plate. The double embossed design is commonly used in immersion
applications and is available in stainless steel, other alloys, carbon steel, and in many material gages
and working pressures.
FIGURE 1.8 Spiral plate heat exchanger. (Courtesy of Tranter, Inc., Wichita Falls, TX.)

13Heat Exchangers
Dimpled surface: This surface is machine punched and swaged, prior to welding, to increase
the flow area in the passages. It is available in stainless steel, other alloys, carbon steel, in
many material gages and working pressures, and in both MIG plug-welded and resistance spot-
welded forms.
Methods of manufacture of panel coils: Basically, three different methods have been used to
manufacture the panel coils: (1) they are usually welded by the resistance spot-welding or seam-
welding process. An alternate method now available offers the ability to resistance spot-weld the
dimpled jacket-style panel coil with a perimeter weldment made with the GMAW or resistance
welding. Figure 1.10 shows a vessel jacket welded by GMAW and resistance-welding process. Other
methods are (2) the die-stamping process and (3) the roll-bond process. In the die-stamping process,
flow channels are die-stamped on either one or two metal sheets. When one sheet is embossed and
joined to a flat (unembossed sheet), it forms a single-sided embossed panel coil. When both sheets
are stamped, it forms a double-sided embossed panel coil.
Types of jackets: Jacketing of process vessels is usually accomplished by using one of the three
main available types: conventional jackets, dimple jackets, and half-pipe coil jackets [12].
Advantages of panel coils: Panel coils provide the optimum method of heating and cooling pro-
cess vessels in terms of control, efficiency, and product quality. Using a panel as a means of heat
transfer offers the following advantages [12]:
• All liquids can be handled, as well as steam and other high-temperature vapors.
• Circulation, temperature, and velocity of heat transfer media can be accurately controlled.
• Panels may often be fabricated from a much less expensive metal than the vessel itself.
• Contamination, cleaning, and maintenance problems are eliminated.
FIGURE 1.9 Temp-Plate® heat transfer surface. (Courtesy of Mueller, Heat Transfer Products, Springfield, MO.)
(a)
(b)
FIGURE 1.10 Welded dimpled jacket template. (a) Gas metal arc welded and (b) resistance welded.

• Maximum efficiency, economy, and flexibility are achieved.
• In designing reactors for specific process, this variety gives chemical engineers a great
deal of flexibility in the choice of heat transfer medium.
1.3.1.2.4 Lamella Heat Exchanger
The lamella heat exchanger is an efficient, and compact, heat exchanger. The principle was
originally developed around 1930 by Ramens Patenter. Later Ramens Patenter was acquired by
Rosenblads Patenter and the lamella heat exchanger was marketed under the Rosenblad name. In
1988, Berglunds acquired the product and continued to develop it. A lamella heat exchanger nor-
mally consists of a cylindrical shell surrounding a number of heat-transferring lamellas. The design
can be compared to a tube heat exchanger but with the circular tubes replaced by thin and wide
channels, lamellas. Sondex Tapiro Oy Ab Pikkupurontie 11, FIN-00810 Helsinki, Finland, markets
lamella heat exchangers worldwide.
The lamella is a form of welded heat exchanger that combines the construction of a PHE with
that of a shell and tube exchanger without baffles. In this design, tubes are replaced by pairs of thin
flat parallel metal plates, which are edge welded to provide long narrow channels, and banks of
these elements of varying width are packed together to form a circular bundle and fitted within a
shell. The cross section of a lamella heat exchanger is shown schematically in Figure 1.11. With this
design, the flow area on the shellside is a minimum and similar in magnitude to that of the inside
of the bank of elements; due to this, the velocities of the two liquid media are comparable [13]. The
flow is essentially longitudinal countercurrent “tubeside” flow of both tube and shell fluids [4]. Due
to this, the velocities of the two liquid media are comparable. Also, the absence of baffles minimizes
the pressure drop. One end of the element pack is fixed and the other is floating to allow for thermal
expansion and contraction. The connections fitted at either end of the shell, as in the normal shell
and tube design, allow the bank of elements to be withdrawn, making the outside surface accessible
for inspection and cleaning. Opposed from an STHE, where the whole exchanger has to be replaced
in case of damage, it is possible just to replace the lamella battery and preserve the existing shell.
Lamella heat exchangers can be fabricated from carbon steel, stainless steel, titanium, Incolly, and
Hastelloy. They can handle most fluids, with large volume ratios between fluids. The floating nature
of the bundle usually limits the working pressure to 300 psi. Lamella heat exchangers are generally
used only in special cases. Design is usually done by the vendors.
Merits of lamella heat exchanger are as follows:
1. Strong turbulence in the fluid
2. High operation pressure
(a) (b)
FIGURE 1.11 Lamella heat exchanger. (a) Counterflow concept and (b) lamella tube bundle.

15Heat Exchangers
Applications
Cooking fluid heating in pulp mills
Liquor preheaters
Coolers and condensers of flue gas
Oils coolers
1.3.1.3 Extended Surface Exchangers
In a heat exchanger with gases or some liquids, if the heat transfer coefficient is quite low, a large
heat transfer surface area is required to increase the heat transfer rate. This requirement is served
by fins attached to the primary surface. Tube-fin heat exchangers (Figure 1.12) and plate-fin heat
exchangers (Figure 1.13) are the most common examples of extended surface heat exchangers. Their
design is covered in Chapter 4.
1.3.1.4 Regenerative Heat Exchangers
Regeneration is an old technology dating back to the first open hearths and blast furnace stoves.
Manufacturing and process industries such as glass, cement, and primary and secondary metals
account for a significant fraction of all energy consumed. Much of this energy is discarded in the
form of high-temperature exhaust gas. Recovery of waste heat from the exhaust gas by means of
heat exchangers known as regenerators can improve the overall plant efficiency [14].
Types of regenerators: Regenerators are generally classified as fixed-matrix and rotary regenera-
tors. Further classifications of fixed and rotary regenerators are shown in Figure 1.14. In the former,
FIGURE 1.12 Air-cooled condenser. (Courtesy of GEA Iberica S.A., Vizcaya, Spain.)
(a) (b)
FIGURE 1.13 Plate-fin heat exchanger. (a) Schematic of exchanger and (b) brazed aluminum plate-fin heat
exchanger. (From Linde AG, Engineering Division. With permission.)

regeneration is achieved with periodic and alternate blowing of hot and the cold stream through a
fixed matrix. During the hot flow period, the matrix receives thermal energy from the hot gas and
transfers it to the cold stream during the cold stream flow. In the latter, the matrix revolves slowly
with respect to two fluid streams. The rotary regenerator is commonly employed in gas turbine
power plants where the waste heat in the hot exhaust gases is utilized for raising the temperature
of compressed air before it is supplied to the combustion chamber. A rotary regenerator (rotary
wheel for HVAC application) working principle is shown in Figure 1.15, and Figure 1.16 shows the
Rothemuhle regenerative air preheater of Babcock and Wilcox Company. Rotary regenerators fall
in the category of compact heat exchangers since the heat transfer surface area to regenerator vol-
ume ratio is very high. Regenerators are further discussed in detail in Chapter 6.
1.3.2 Classification according to Transfer Process
These classifications are as follows:
Indirect contact type—direct transfer type, storage type, fluidized bed
Direct contact type—cooling towers
1.3.2.1 Indirect Contact Heat Exchangers
In an indirect contact–type heat exchanger, the fluid streams remain separate and the heat transfer
takes place continuously through a dividing impervious wall. This type of heat exchanger can be
further classified into direct transfer type, storage type, and fluidized bed exchangers. Direct transfer
type is dealt with next, whereas the storage type and the fluidized bed type are discussed in Chapter 6.
Regenerator
Rotary
regenerator
Rotary
matrix
Fixed matrix—
rotating hoods
Fixed
matrix
Dual bed
valved
Single bed
FIGURE 1.14 Classification of regenerators.
Rotating regenerator
Atmospheric
cold air
Cooled
exhaust air
Direction of
rotation
Warm room
exhaust air
Warm air
to room
FIGURE 1.15 Rotary regenerator: working principle.

17Heat Exchangers
1.3.2.1.1 Direct Transfer–Type Exchangers
In this type, there is a continuous flow of heat from the hot fluid to the cold fluid through a separat-
ing wall. There is no direct mixing of the fluids because each fluid flows in separate fluid passages.
There are no moving parts. This type of exchanger is designated as a recuperator. Some examples
of direct transfer–type heat exchangers are tubular exchangers, PHEs, and extended surface exchangers.
Recuperators are further subclassified as prime surface exchangers, which do not employ fins or
extended surfaces on the prime surface. Plain tubular exchangers, shell and tube exchangers with
plain tubes, and PHEs are examples of prime surface exchangers.
1.3.2.2 Direct Contact–Type Heat Exchangers
In direct contact–type heat exchangers, the two fluids are not separated by a wall and come into
direct contact, exchange heat, and are then separated.
Owing to the absence of a wall, closer temperature approaches are attained. Very often, in the
direct contact type, the process of heat transfer is also accompanied by mass transfer. Various types
of direct contact heat exchangers include (a) immiscible fluid exchanger, (b) gas–liquid exchanger,
and (c) liquid–vapor exchanger. The cooling towers and scrubbers are examples of a direct contact–
type heat exchanger.
1.3.3 Classification according to Surface Compactness
Compact heat exchangers are important when there are restrictions on the size and weight of
exchangers. A compact heat exchanger incorporates a heat transfer surface having a high area den-
sity, β, somewhat arbitrarily 700 m2/m3 (200 ft2/ft3) and higher [1]. The area density, β, is the ratio
of heat transfer area A to its volume V. A compact heat exchanger employs a compact surface on one
or more sides of a two-fluid or a multifluid heat exchanger. They can often achieve higher thermal
effectiveness than shell and tube exchangers (95% vs. the 60%–80% typical for STHEs), which
2
1
2
FIGURE 1.16 Rothemuhle regenerative air preheater of Babcock and Wilcox Company—stationary matrix
(part 1) and revolving hoods (part 2). (Adapted from Mondt, J.R., Regenerative heat exchangers: The elements
of their design, selection and use, Research Publication GMR-3396, General Motors Research Laboratories,
Warren, MI, 1980.)

makes them particularly useful in energy-intensive industries [15]. For least capital cost, the size
of the unit should be minimal. There are some additional advantages to small volume as follows:
Small inventory, making them good for handling expensive or hazardous materials [15]
Low weight
Easier transport
Less foundation
Better temperature control
Some barriers to the use of compact heat exchangers include [15] the following:
The lack of standards similar to pressure vessel codes and standards, although this is now
being redressed in the areas of plate-fin exchangers [16] and air-cooled exchangers [17].
Narrow passages in plate-fin exchangers make them susceptible for fouling and they cannot
be cleaned by mechanical means. This limits their use to clean applications like handling
air, light hydrocarbons, and refrigerants.
1.3.4 Classification According to Flow Arrangement
The basic flow arrangements of the fluids in a heat exchanger are as follows:
Parallelflow
Counterflow
Crossflow
The choice of a particular flow arrangement is dependent upon the required exchanger effective-
ness, fluid flow paths, packaging envelope, allowable thermal stresses, temperature levels, and other
design criteria. These basic flow arrangements are discussed next.
1.3.4.1 Parallelflow Exchanger
In this type, both the fluid streams enter at the same end, flow parallel to each other in the same direc-
tion, and leave at the other end (Figure 1.17). (For fluid temperature variations, idealized as one-dimen-
sional, refer Figure 2.2 of Chapter 2.) This arrangement has the lowest exchanger effectiveness among
the single-pass exchangers for the same flow rates, capacity rate (mass × specific heat) ratio, and surface
area. Moreover, the existence of large temperature differences at the inlet end may induce high thermal
stresses in the exchanger wall at inlet. Parallelflows are advantageous. (a) In heating very viscous fluids,
parallelflow provides for rapid heating. The quick change in viscosity results in reduced pumping power
requirements through the heat exchanger, (b) where the more moderate mean metal temperatures of the
tube walls are required, and (c) where the improvements in heat transfer rates compensate for the lower
LMTD. Although this flow arrangement is not used widely, it is preferred for the following reasons [2]:
1. When there is a possibility that the temperature of the warmer fluid may reach its freezing point.
2. It provides early initiation of nucleate boiling for boiling applications.
3. For a balanced exchanger (i.e., heat capacity rate ratio C* = 1), the desired exchanger effec-
tiveness is low and is to be maintained approximately constant over a range of NTU values.
4. The application allows piping only suited to parallelflow.
1
2
FIGURE 1.17 Parallelflow arrangement.

19Heat Exchangers
5. Temperature-sensitive fluids such as food products, pharmaceuticals, and biological prod-
ucts are less likely to be “thermally damaged” in a parallelflow heat exchanger.
6. Certain types of fouling such as chemical reaction fouling, scaling, corrosion fouling, and
freezing fouling are sensitive to temperature. Where control of temperature-sensitive foul-
ing is a major concern, it is advantageous to use parallelflow.
1.3.4.2 Counterflow Exchanger
In this type, as shown in Figure 1.18a, the two fluids flow parallel to each other but in opposite
directions, and its temperature distribution may be idealized as shown in Figure 1.18b. Ideally,
this is the most efficient of all flow arrangements for single-pass arrangements under the same
parameters. Since the temperature difference across the exchanger wall at a given cross section
is the lowest, it produces minimum thermal stresses in the wall for equivalent performance com-
pared to other flow arrangements. In certain types of heat exchangers, counterflow arrangement
cannot be achieved easily, due to manufacturing difficulties associated with the separation of the
fluids at each end, and the design of inlet and outlet header design is complex and difficult [2].
1.3.4.3 Crossflow Exchanger
In this type, as shown in Figure 1.19, the two fluids flow normal to each other. Important types of
flow arrangement combinations for a single-pass crossflow exchanger include the following:
• Both fluids unmixed
• One fluid unmixed and the other fluid mixed
• Both fluids mixed
2
1
(a)
th,i
ChCc
Hot fluid Hot fluid
Hot fluid
Cold fluid Cold fluid
Cold fluid
Flow length Flow length Flow length
Ch CcCh=Cc
tc,o
th,i
th,o tc,o
tc,i
th,i
th,o
tc,o
tc,i
th,o
tc,i
(b)
FIGURE 1.18 (a) Counterflow arrangement (schematic) and (b) temperature distribution (schematic). (Note:
Ch and Cc are the heat capacity rate of hot fluid and cold fluid respectively, i refers to inlet, o refers to outlet
conditions and t refers to fluid temperature.)
1
2(a)
1
2(b)
1
2
1
2 (c)
FIGURE 1.19 Crossflow arrangement: (a) unmixed–unmixed, (b) unmixed–mixed, and (c) mixed–mixed.

A fluid stream is considered “unmixed” when it passes through individual flow passage without any
fluid mixing between adjacent flow passages. Mixing implies that a thermal averaging process takes
place at each cross section across the full width of the flow passage. A tube-fin exchanger with flat
(continuous) fins and a plate-fin exchanger wherein the two fluids flow in separate passages (e.g.,
wavy fin, plain continuous rectangular or triangular flow passages) represent the unmixed–unmixed
case. A crossflow tubular exchanger with bare tubes on the outside would be treated as the unmixed–
mixed case, that is, unmixed on the tubeside and mixed on the outside. The both fluid mixed case
is practically a less important case and represents a limiting case of some multipass shell and tube
exchangers (TEMA E and J shell).
For the unmixed–unmixed case, fluid temperature variations are idealized as two-dimensional
only for the inlet and outlet sections; this is shown in Figure 1.20. The thermal effectiveness for
the crossflow exchanger falls in between those of the parallelflow and counterflow arrangements.
This is the most common flow arrangement used for extended surface heat exchangers because it
greatly simplifies the header design. If the desired heat exchanger effectiveness is generally more
than 80%, the size penalty for crossflow may become excessive. In such a case, a counterflow unit
is preferred [2]. In shell and tube exchangers, crossflow arrangement is used in the TEMA X shell
having a single tube pass.
1.3.5 Classification According to Pass Arrangements
These are either single pass or multipass. A fluid is considered to have made one pass if it flows
through a section of the heat exchanger through its full length once. In a multipass arrangement, a
fluid is reversed and flows through the flow length two or more times.
1.3.5.1 Multipass Exchangers
When the design of a heat exchanger results in either extreme length, significantly low veloci-
ties, or low effectiveness, or due to other design criteria, a multipass heat exchanger or several
single-pass exchangers in series or a combination of both is employed. Specifically, multipassing
is resorted to increase the exchanger thermal effectiveness over the individual pass effectiveness.
As the number of passes increases, the overall direction of the two fluids approaches that of a pure
counterflow exchanger. The multipass arrangements are possible with compact, shell and tube, and
plate exchangers.
tc,i
tc,o
Hot fluid outlet
temperature
distribution
th,i th,o
Cold fluid outlet
temperature
distribution
FIGURE 1.20 Temperature distribution for unmixed–unmixed crossflow arrangement.

21Heat Exchangers
1.3.6 Classification According to Phase of Fluids
1.3.6.1 Gas–Liquid
Gas–liquid heat exchangers are mostly tube-fin-type compact heat exchangers with the liquid on the
tubeside. The radiator is by far the major type of liquid–gas heat exchanger, typically cooling the
engine jacket water by air. Similar units are necessary for all the other water-cooled engines used in
trucks, locomotives, diesel-powered equipment, and stationery diesel power plants. Other examples
are air coolers, oil coolers for aircraft, intercoolers and aftercoolers in compressors, and condensers
and evaporators of room air-conditioners. Normally, the liquid is pumped through the tubes, which
have a very high convective heat transfer coefficient. The air flows in crossflow over the tubes. The
heat transfer coefficient on the air side will be lower than that on the liquid side. Fins will be gener-
ally used on the outside of the tubes to enhance the heat transfer rate.
1.3.6.2 Liquid–Liquid
Most of the liquid–liquid heat exchangers are shell and tube type, and PHEs to a lesser extent. Both
fluids are pumped through the exchanger, so the principal mode of heat transfer is forced convec-
tion. The relatively high density of liquids results in very high heat transfer rate, so normally fins
or other devices are not used to enhance the heat transfer [4]. In certain applications, low-finned
tubes, microfin tubes, and heat transfer augmentation devices are used to enhance the heat transfer.
1.3.6.3 Gas–Gas
This type of exchanger is found in exhaust gas–air preheating recuperators, rotary regenerators,
intercoolers, and/or aftercoolers to cool supercharged engine intake air of some land-based die-
sel power packs and diesel locomotives, and cryogenic gas liquefaction systems. In many cases,
one gas is compressed so that the density is high while the other is at low pressure and low den-
sity. Compared to liquid–liquid exchangers, the size of the gas–gas exchanger will be much larger,
because the convective heat transfer coefficient on the gas side is low compared to the liquid side.
Therefore, secondary surfaces are mostly employed to enhance the heat transfer rate.
1.3.7 Classification According to Heat Transfer Mechanisms
The basic heat transfer mechanisms employed for heat transfer from one fluid to the other are
(1) single-phase convection, forced or free, (2) two-phase convection (condensation or evaporation)
by forced or free convection, and (3) combined convection and radiation. Any of these mechanisms
individually or in combination could be active on each side of the exchanger. Based on the phase
change mechanisms, the heat exchangers are classified as (1) condensers and (2) evaporators.
1.3.7.1 Condensers
Condensers may be liquid (water) or gas (air) cooled. The heat from condensing streams may be used
for heating fluid. Normally, the condensing fluid is routed (1) outside the tubes with a water-cooled
steam condenser or (2) inside the tubes with gas cooling, that is, air-cooled condensers of refrigera-
tors and air-conditioners. Fins are normally provided to enhance heat transfer on the gas side.
1.3.7.2 Evaporators
This important group of tubular heat exchangers can be subdivided into two classes: fired systems
and unfired systems.
Fired systems: These involve the products of combustion of fossil fuels at very high temperatures
but at ambient pressure (and hence low density) and generate steam under pressure. Fired systems
are called boilers. A system may be a fire tube boiler (for small low-pressure applications) or a water
tube boiler.

Unfired systems: These embrace a great variety of steam generators extending over a broad
temperature range from high-temperature nuclear steam generators to very-low-temperature cryo-
genic gasifiers for liquid natural gas evaporation. Many chemical and food processing applications
involve the use of steam to evaporate solvents, concentrate solutions, distill liquors, or dehydrate
compounds.
1.3.8 Other Classifications
1.3.8.1 Micro Heat Exchanger
Micro- or microscale heat exchangers are heat exchangers in which at least one fluid flows in lateral
confinements with typical dimensions below 1 mm and are fabricated via silicon micromachin-
ing, deep x-ray lithography, or nonlithographic micromachining [18]. The plates are stacked forming
“sandwich” structures, as in the “large” plate exchangers. All flow configurations (cocurrent, coun-
tercurrent, and crossflow) are possible.
Typically, the fluid flows through a cavity called a microchannel. Microheat exchangers have
been demonstrated with high convective heat transfer coefficient. Investigation of microscale
thermal devices is motivated by the single-phase internal flow correlation for convective heat
transfer:

h
k
D
=
Nu
h
where
h is the heat transfer coefficient
Nu is the Nusselt number
k is the thermal conductivity of the fluid
Dh is the hydraulic diameter of the channel or duct
In internal laminar flows, the Nusselt number becomes a constant. As the Reynolds number is
proportional to hydraulic diameter, fluid flow in channels of small hydraulic diameter will predomi-
nantly be laminar. This correlation therefore indicates that the heat transfer coefficient increases as
the channel diameter decreases. Heat transfer enhancement in laminar flow is further discussed in
Chapter 8 Section 8.3.3.
1.3.8.1.1 Advantages over Macroscale Heat Exchangers
• Substantially better performance
• Enhanced heat transfer coefficient with a large number of smaller channels
• Smaller size that allows for an increase in mobility and uses
• Light weight reduces the structural and support requirements
• Lower cost due to less material being used in fabrication
1.3.8.1.2 Applications of Microscale Heat Exchangers
Microscale heat exchangers are being used in the development of fuel cells. They are currently used
in automotive industries, HVAC applications, aircraft, manufacturing industries, and electronics
cooling.
1.3.8.1.3 Demerits of Microscale Heat Exchangers
One of the main disadvantages of microchannel heat exchangers is the high-pressure loss that is
associated with a small hydraulic diameter.

23Heat Exchangers
1.3.8.2 Printed Circuit Heat Exchanger
PCHE, developed by Heatric Division of Meggitt (UK) Ltd., is a promising heat exchanger because
it is able to withstand pressures up to 50 MPa and temperatures from cryogenic to 700°C. It is
extremely compact (the most common design feature to achieve compactness has been small chan-
nel size) and has high efficiency, of the order of 98%. It can handle a wide variety of clean fluids. The
flow configuration can be either crossflow or counterflow. It will maintain parent material strength
and can be made from stainless steel, nickel alloys, copper alloys, and titanium. Fluid flow channels
are etched chemically on metal plates. It has a typical plate thickness of 1.6 mm, width 600 mm, and
length 1200 mm. The channels are semicircular with 1–2 mm diameter. Etched plates are stacked
and diffusion bonded together to fabricate as a block. The blocks are then welded together to form
the complete heat exchanger core, as shown in Figure 1.21a.
HEATRIC PCHEs consist of diffusion-bonded heat exchanger core that are constructed
from flat metal plates into which fluid flow channels are either chemically etched or pressed.
The required configuration of the channels on the plates for each fluid is governed by the
operating temperature and pressure-drop constraints for the heat exchange duty and the chan-
nels can be of unlimited variety and complexity. Fluid flow can be parallelflow, counterflow,
crossflow, or a combination of these to suit the process requirements. Figure 1.21b through f
shows HEATRIC PCHE.
The etched plates are then stacked and diffusion-bonded together to form strong, compact, all
metal heat exchanger core. Diffusion bonding is a “solid-state joining” process entailing pressing
metal surfaces together at temperatures below the melting point, thereby promoting grain growth
between the surfaces. Under carefully controlled conditions, diffusion-bonded joints reach parent
metal strength and stacks of plates are converted into solid blocks containing the fluid flow pas-
sages. The blocks are then welded together to form the complete heat exchange core. Finally, head-
ers and nozzles are welded to the core in order to direct the fluids to the appropriate sets of passages.
Welded and diffusion-bonded PCHEs employ no gaskets or braze material, resulting in superior
integrity compared to other technologies that may use gaskets or brazing as part of their construc-
tion. (Gaskets or braze material can be potential sources of leakage, fluid incompatibility, and tem-
perature limitations.) The mechanical design is normally of ASME VIII Division 1. Other design
codes can be employed as required.
(a)
FIGURE 1.21 Printed circuit heat exchanger. (a) Heat exchanger block with flow channel.
(continued)

1.3.8.2.1 Materials of Construction
The majority of diffusion-bonded heat exchangers are constructed from 300 series austenitic
stainless steel. Various other metals that are compatible with the diffusion-bonded process
and have been qualified for use include 22 chromeduplex, copper–nickel, nickel alloys, and
titanium.
(b) (c)
(d) (e)
(f)
FIGURE 1.21 (continued) Printed circuit heat exchanger. (b) Flow channel, (c) and (d) section through flow
channel, (e) diffusion bonded core, (f) comparison of size of PCHE shell and tube heat exchanger (smaller
size) with a conventional exchanger (bigger size) for similar duty. (Courtesy of Heatric UK, Dorset, U.K.)

25Heat Exchangers
1.3.8.2.2 Features of PCHE
Diffusion-bonded heat exchangers are highly compact and robust that are well established in the
upstream hydrocarbon processing, petrochemical and refining industries. Various salient construc-
tional and performance features are given next:
1. Compactness: Diffusion-bonded heat exchangers are 1/4–1/6th the conventional STHEs of
the equivalent heat duty. This design feature has space and weight advantages, reducing
exchanger size together with piping and valve requirements. The diffusion-bonded heat
exchanger in the foreground of Figure 1.21e undertakes the same thermal duty, at the same
pressure drop, as the stack of three shell and tube exchangers behind. PCHE might be
judged as a promising compact heat exchanger for the high efficiency recuperator [19].
2. Process capability: They can withstand pressures of 600 bar (9000 psi) or excess and can
cope with extreme temperatures, ranging from cryogenic to 900°C (1650°F).
3. Thermal effectiveness: Diffusion-bonded exchangers can achieve high thermal effective-
ness of the order of 98% in a single unit.
4. They can incorporate more than two process streams into a single unit.
5. The compatibility of the chemical etching and diffusion-bonding process with a wide range
of materials ensure that they are suitable for a range of corrosive and high purity streams.
1.3.8.3 Perforated Plate Heat Exchanger as Cryocoolers
High-efficiency compact heat exchangers are needed in cryocoolers to achieve very low temperatures.
One approach to meet the requirements for compact and efficient cooling systems is the perforated
PHE. Such heat exchangers are made up of a large number of parallel, perforated plates of high-
thermal conductivity metal in a stacked array, with gaps between plates being provided by spacers.
Gas flows longitudinally through the plates in one direction and other stream flows in the opposite
direction through separated portions of the plates. Heat transfer takes place laterally across the plates
from one stream to the other. The operating principles of this type of heat exchanger are described by
Fleming [20]. The device employs plates of 0.81 mm thickness with holes of 1.14 mm in diameter and a
resulting length-to-diameter ratio in the range of 0.5–1.0. The device is designed to operate from room
temperature to 80 K. In order to improve operation of a compact cryocooler, much smaller holes, in the
low-micron-diameter range, and thinner plates with high length-to-diameter ratio are needed. As per
US Patent 5101894 [21], uniform, tubular perforations having diameters down to the low-micron-size
range can be obtained. Various types of heat exchange devices including recuperative and regenera-
tive heat exchangers may be constructed in accordance with the invention for use in cooling systems
based on a number of refrigeration cycles such as the Linde–Hampson, Brayton, and Stirling cycles.
1.3.8.4 Scraped Surface Heat Exchanger
Scraped surface heat exchangers are used for processes likely to result in the substantial deposi-
tion of suspended solids on the heat transfer surface. Scraped surface heat exchangers can be
employed in the continuous, closed processing of virtually any pumpable fluid or slurry involv-
ing cooking, slush freezing, cooling, crystallizing, mixing, plasticizing, gelling, polymerizing,
heating, aseptic processing, etc. Use of a scraped surface exchanger prevents the accumulation of
significant buildup of solid deposits. The construction details of scraped surface heat exchangers
are explained in Ref. [4]. Scraped surface heat exchangers are essentially double pipe construc-
tion with the process fluid in the inner pipe and the cooling (water) or heating medium (steam) in
the annulus. A rotating element is contained within the tube and is equipped with spring-loaded
blades. In operation, the rotating shaft scraper blades continuously scrape product film from the
heat transfer tube wall, thereby enhancing heat transfer and agitating the product to produce a
homogenous mixture. For most applications, the shaft is mounted in the center of the heat transfer
tube. An off-centered shaft mount or eccentric design is recommended for viscous and sticky

products. This shaft arrangement increases product mixing and reduces the mechanical heat load.
Oval tubes are used to process extremely viscous products. All pressure elements are designed in
accordance with the latest ASME code requirements. The principle of working of scraped surface
heat exchangers is shown in Figure 1.22. For scraped surface exchangers, operating costs are high
and applications are highly specific [5]. Design is mostly done by vendors. The leading manufac-
tures include HRS Heat Exchangers, Ltd., UK, and Waukesha Cherry-Burrell, USA.
1.3.8.4.1 Unicus Scraped Surface Heat Exchanger
Unicus™ is the trade name for scraped surface heat exchanger of HRS Heat Exchangers Ltd., UK,
for high-fouling and viscous fluid applications. The design is based on STHE with scraping ele-
ments inside each interior tube. The scrapers are moved back and forth by hydraulic action. The
scraping action has two very important advantages: any fouling on the tube wall is removed and the
scraping movement introduces turbulence in the fluid increasing heat transfer.
1.3.8.4.1.1 Elements of the Unicus Unicus consists of three parts: a hydraulic cylinder that
moves the scraper bars, the STHE part, and a chamber that separates both the elements. The hydrau-
lic cylinder is connected to a hydraulic power pack. The smaller models of the Unicus range can be
supplied with a pneumatic cylinder. The scraping system consists of a stainless steel rod to which
the scraping elements are fitted, as shown in Figure 1.23, and Figure 1.24 shows Unicus scraped
surface heat exchangers. The pictures show the various types of scrapers that can be applied. For
each application, the optimal scraper is selected and fitted.
Service fluid
Service fluid
Heat transfer
Scraper
Tube wall
Scraper bar
Extra
turbulence
Product
FIGURE 1.23 Principle of Unicus scraped surface heat exchanger working. (Courtesy of HRS Heat
Exchangers Ltd, Herts, U.K.)
Heating and cooling medium
Product
Shaft
+
Heat transfer tube
Scraper blade
FIGURE 1.22 Scraped surface heat exchanger: principle.

27Heat Exchangers
1.3.8.5 Graphite Heat Exchanger
Impervious graphite as a heat exchanger material is used for the construction of various types of
heat exchangers such as STHE, cubic block heat exchanger, and plate and frame or gasketed heat
exchangers (PHEs). Graphite tubes are used in STHE (refer to Chapter 13) and plates are used in
PHEs (refer to Chapter 7) for special purpose applications. It resists a wide variety of inorganic and
organic chemicals. Graphite heat exchangers are employed as boilers and condensers in the distilla-
tion by evaporation of hydrochloric acid and in the concentration of weak sulfuric acid and of rare
earth chloride solutions. Since cubic heat exchanger cannot be treated in categorization of extended
surface heat exchanger, the same is covered next.
Cubic heat exchanger: It is similar to the compact crossflow heat exchanger, consisting of
drilled holes in two perpendicular planes. They are suitable when both the process streams are
corrosive. With a cubic exchanger, a multipass arrangement is possible. It is manufactured by
assembling of accurately machined and drilled graphite plates bonded together by synthetic res-
ins, oven cured and sintered. Gasketed headers with nozzles are assembled on both sides to the
block to form a block heat exchanger and are clamped together, as shown in Figure 1.25.
Modular-block cylindrical exchanger: In this arrangement, solid impervious graphite blocks
have holes drilled in them. These blocks can be multistacked in a cylindrical steel shell that has
(a) (b)
(c) (d)
FIGURE 1.24 Unicus dynamic scraped surface heat exchanger. (a) 3-D model, (b) hydraulic cylinder head,
(c) a unit of Unicus, and (d) multiple Unicus units. (Courtesy of HRS Heat Exchangers Ltd, Herts, U.K.)

gland fittings. The process holes are axial and the service holes are transverse. The units are designed
as evaporators and reboilers. A modular block Graphilor® exchanger is shown in Figure 1.26.
1.4 SELECTION OF HEAT EXCHANGERS
1.4.1 Introduction
Selection is the process in which the designer selects a particular type of heat exchanger for a given
application from a variety of heat exchangers. There are a number of alternatives for selecting heat
transfer equipment, but only one among them is the best for a given set of conditions. The heat
exchanger selection criteria are discussed next.
(c) Three pass Four pass
Multipass process
return head
Graphite
core
Multipass
inlet/outlet
service head
Process graphite
head liner in/out
Multipass process
inlet/outlet
head(a)
Clamping
plate
Return
service head
Process graphite
return liner
Clamping bolts
Typical flow pattern
(b)
FIGURE 1.25 NK series multipass cubic graphite heat exchanger. (a) Construction details, (b) cut section,
and (c) multipass flow pattern. (Courtesy of MERSEN, Paris La Défense, France.)

29Heat Exchangers
1.4.2 Selection Criteria
Selection criteria are many, but primary criteria are type of fluids to be handled, operating pres-
sures and temperatures, heat duty, and cost (see Table 1.1). The fluids involved in heat transfer
can be characterized by temperature, pressure, phase, physical properties, toxicity, corrosivity,
and fouling tendency. Operating conditions for heat exchangers vary over a very wide range, and
a broad spectrum of demands is imposed for their design and performance. All of these must be
Coil springs maintain
axial force on heat
exchanger assembly
during operational
temperature changes
Floating end compen-
sates for differential
expansion between
graphite core and
steel shell
Drilled axial process
holes (3 diameters
available)
Drilled transverse
service holes
Fixed end
Vertical service fluid drain
(vent and drain are on shell
for horizontal operation)
Stainless steel
longitudinal guide bars
and service baffle
Service fluid gaskets
Steel shell
Elastomeric service
baffles
Graphilor
heat transfer core
(4 diameters available)
Service fluid seal:
TFE packing
Armored floating head
assembly (1 piece
graphite and steel)
FIGURE 1.26 GRAPHILOR® cylindrical tubes (in block) heat exchanger. (Courtesy of MERSEN, Paris La
Défense, France.)

considered when assessing the type of unit to be used [22]. When selecting a heat exchanger for a
given duty, the following points must be considered:
• Materials of construction
• Operating pressure and temperature, temperature program, and temperature driving force
• Flow rates
• Flow arrangements
• Performance parameters—thermal effectiveness and pressure drops
• Fouling tendencies
• Types and phases of fluids
• Maintenance, inspection, cleaning, extension, and repair possibilities
• Overall economy
• Fabrication techniques
• Mounting arrangements: horizontal or vertical
• Intended applications
1.4.2.1 Materials of Construction
For reliable and continuous use, the construction materials for pressure vessels and heat exchangers
should have a well-defined corrosion rate in the service environments. Furthermore, the material should
exhibit strength to withstand the operating temperature and pressure. STHEs can be manufactured in vir-
tually any material that may be required for corrosion resistance, for example, from nonmetals like glass,
Teflon, and graphite to exotic metals like titanium, zirconium, tantalum, etc. Compact heat exchangers
with extended surfaces are mostly manufactured from any metal that has drawability, formability, and
malleability. Heat exchanger types like PHEs normally require a material that can be pressed or welded.
1.4.2.2 Operating Pressure and Temperature
1.4.2.2.1 Pressure
The design pressure is important to determine the thickness of the pressure-retaining components.
The higher the pressure, the greater will be the required thickness of the pressure-retaining mem-
branes and the more advantage there is to placing the high-pressure fluid on the tubeside. The pres-
sure level of the fluids has a significant effect on the type of unit selected [22].
At low pressures, the vapor-phase volumetric flow rate is high and the low-allowable pressure
drops may require a design that maximizes the area available for flow, such as crossflow or
split flow with multiple nozzles.
At high pressures, the vapor-phase volumetric flow rates are lower and allowable pressure
drops are greater. These lead to more compact units.
In general, higher heat transfer rates are obtained by placing the low-pressure gas on the out-
side of tubular surfaces.
Operating pressures of the gasketed PHEs and SPHEs are limited because of the difficulty in pressing
the required plate thickness, and by the gasket materials in the case of PHEs. The floating nature of
floating-head shell and tube heat exchangers and lamella heat exchangers limits the operating pressure.
1.4.2.2.2 Temperature
Design temperature: This parameter is important as it indicates whether a material at the design
temperature can withstand the operating pressure and various loads imposed on the component.
For low-temperature and cryogenic applications, toughness is a prime requirement, and for high-
temperature applications the material has to exhibit creep resistance.
Temperature program: Temperature program in both a single-pass and multipass STHE decides
(1) the mean metal temperatures of various components like shell, tube bundle, and tubesheet, and

31Heat Exchangers
(2) the possibility of temperature cross. The mean metal temperatures affect the integrity and capa-
bility of heat exchangers and thermal stresses induced in various components.
Temperature driving force: The effective temperature driving force is a measure of the actual
potential for heat transfer that exists at the design conditions. With a counterflow arrangement, the
effective temperature difference is defined by the log mean temperature difference (LMTD). For
flow arrangements other than counterflow arrangement, LMTD must be corrected by a correction
factor, F. The F factor can be determined analytically for each flow arrangement but is usually
presented graphically in terms of the thermal effectiveness P and the heat capacity ratio R for each
flow arrangement.
Influence of operating pressure and temperature on selection of some types of heat exchangers:
The influence of operating pressure and temperature on selection of STHE, compact heat exchanger,
gasketed PHE, and spiral exchanger is discussed next.
Shell and tube heat exchanger: STHE units can be designed for almost any combination of
pressure and temperature. In extreme cases, high pressure may impose limitations by fabrication
problems associated with material thickness, and by the weight of the finished unit. Differential
thermal expansion under steady conditions can induce severe thermal stresses either in the tube
bundle or in the shell. Damage due to flow-induced vibration on the shellside is well known. In
heat-exchanger applications where high heat transfer effectiveness (close approach temperature) is
required, the standard shell and tube design may require a very large amount of heat transfer sur-
face [23]. Depending on the fluids and operating conditions, other types of heat-exchanger design
should be investigated.
Compact heat exchanger: Compact heat exchangers are constructed from thinner materials; they
are manufactured by mechanical bonding, soldering, brazing, welding, etc. Therefore, they are lim-
ited in operating pressures and temperatures.
Gasketed plate heat exchangers and spiral exchangers: Gasketed PHEs and spiral exchangers
are limited by pressure and temperature, wherein the limitations are imposed by the capability of the
gaskets.
1.4.2.3 Flow Rate
Flow rate determines the flow area: the higher the flow rate, the higher will be the crossflow
area. Higher flow area is required to limit the flow velocity through the conduits and flow
passages, and the higher velocity is limited by pressure drop, impingement, erosion, and, in
the case of shell and tube exchanger, by shellside flow-induced vibration. Sometimes, a mini-
mum flow velocity is necessary to improve heat transfer to eliminate stagnant areas and to
minimize fouling.
1.4.2.4 Flow Arrangement
As defined earlier, the choice of a particular flow arrangement is dependent upon the required
exchanger effectiveness, exchanger construction type, upstream and downstream ducting, packag-
ing envelope, and other design criteria.
1.4.2.5 Performance Parameters: Thermal Effectiveness and Pressure Drops
Thermal effectiveness: For high-performance service requiring high thermal effectiveness, use
brazed plate-fin exchangers (e.g., cryogenic service) and regenerators (e.g., gas turbine applica-
tions), use tube-fin exchangers for slightly less thermal effectiveness in applications, and use
shell and tube units for low-thermal effectiveness service.
Pressure drop: Pressure drop is an important parameter in heat exchanger design. Limitations
may be imposed either by pumping cost or by process limitations or both. The heat exchanger
should be designed in such a way that unproductive pressure drop is avoided to the maximum extent

in areas like inlet and outlet bends, nozzles, and manifolds. At the same time, any pressure-drop
limitation that is imposed must be utilized as nearly as possible for an economic design.
1.4.2.6 Fouling Tendencies
Fouling is defined as the formation on heat exchanger surfaces of undesirable deposits that impede the
heat transfer and increase the resistance to fluid flow, resulting in higher pressure drop. The growth of
these deposits causes the thermohydraulic performance of heat exchanger to decline with time. Fouling
affects the energy consumption of industrial processes, and it also decides the amount of extra mate-
rial required to provide extra heat transfer surface to compensate for the effects of fouling. Compact
heat exchangers are generally preferred for nonfouling applications. In a shell and tube unit, the fluid
with more fouling tendencies should be put on the tubeside for ease of cleaning. On the shellside with
cross baffles, it is sometimes difficult to achieve a good flow distribution if the baffle cut is either too
high or too low. Stagnation in any regions of low velocity behind the baffles is difficult to avoid if the
baffles are cut more than about 20%–25%. PHEs and spiral plate exchangers are better chosen for
fouling services. The flow pattern in PHE induces turbulence even at comparable low velocities; in the
spiral units, the scrubbing action of the fluids on the curved surfaces minimizes fouling. Also consider
Philips RODbaffle heat exchanger, TWISTED TUBE® heat exchanger, Helixchanger® heat exchanger
or EMbaffle® heat exchanger to improve flow velocity on shellside, enhance heat transfer performance
and reduce fouling tendencies on shellside.
1.4.2.7 Types and Phases of Fluids
The phase of the fluids within a unit is an important consideration in the selection of the heat
exchanger type. Various combinations of fluid phases dealt in heat exchangers are liquid–liquid,
liquid–gas, and gas–gas. Liquid-phase fluids are generally the simplest to deal with. The high den-
sity and the favorable values of many transport properties allow high heat transfer coefficients to be
obtained at relatively low-pressure drops [4].
1.4.2.8 Maintenance, Inspection, Cleaning, Repair, and Extension Aspects
Consider the suitability of various heat exchangers as regards maintenance, inspection, cleaning, repair,
and extension. For example, the pharmaceutical, dairy, and food industries require quick access to internal
components for frequent cleaning. Since some of the heat exchanger types offer great variations in design,
this must be kept in mind when designing for a certain application. For instance, consider inspection and
manual cleaning. Spiral plate exchangers can be made with both sides open at one edge, or with one side
open and one closed. They can be made with channels between 5 and 25 mm wide, with or without studs.
STHE can be made with fixed tubesheets or with a removable tube bundle, with small- or large-diameter
tubes, or small or wide pitch. A lamella heat exchanger bundle is removable and thus fairly easy to clean on
the shellside. Inside, the lamella, however, cannot be drilled to remove the hard fouling deposits. Gasketed
PHEs are easy to open, especially when all nozzles are located on the stationary end-plate side. The plate
arrangement can be changed for other duties within the frame and nozzle capacity.
Repair of some of the shell and tube exchanger components is possible, but the repair of expansion
joint is very difficult. Tubes can be renewed or plugged. Repair of compact heat exchangers of tube-
fin type is very difficult except by plugging of the tube. Repair of the plate-fin exchanger is generally
very difficult. For these two types of heat exchangers, extension of units for higher thermal duties is
generally not possible. All these drawbacks are easily overcome in a PHE. It can be easily repaired,
and plates and other parts can be easily replaced. Due to modular construction, PHEs possess the
flexibility of enhancing or reducing the heat transfer surface area, modifying the pass arrangement,
and addition of more than one duty according to the heat transfer requirements at a future date.
1.4.2.9 Overall Economy
There are two major costs to consider in designing a heat exchanger: the manufacturing cost and the
operating costs, including maintenance costs. In general, the less the heat transfer surface area and less

33Heat Exchangers
the complexity of the design, the lower is the manufacturing cost. The operating cost is the pumping cost
due to pumping devices such as fans, blowers, and pumps. The maintenance costs include costs of spares
that require frequent renewal due to corrosion, and costs due to corrosion/fouling prevention and control.
Therefore, the heat exchanger design requires a proper balance between thermal sizing and pressure drop.
1.4.2.10 Fabrication Techniques
Fabrication techniques are likely to be the determining factor in the selection of a heat transfer
surface matrix or core. They are the major factors in the initial cost and to a large extent influence
the integrity, service life, and ease of maintenance of the finished heat exchanger [24]. For example,
shell and tube units are mostly fabricated by welding, plate-fin heat exchangers and automobile
aluminum radiators by brazing, copper–brass radiators by soldering, most of the circular tube-fin
exchangers by mechanical assembling, etc.
1.4.2.11 Choice of Unit Type for Intended Applications
According to the intended applications, the selection of heat exchangers will follow the guidelines
given in Table 1.2.
TABLE 1.2
Choice of Heat Exchanger Type for Intended Applications
Application Remarks
Low-viscosity fluids For high temperature/pressures, use STHE or double-pipe heat exchanger. Use
PHE or LHE for low temperature/pressure applications.
Low-viscosity liquid to steam Use STHE in carbon steel.
Medium-viscosity fluids Use PHE or with high solids content, use SPHE.
High-viscosity fluids PHE offers the advantages of good flow distribution. For extreme viscosities,
the SPHE is preferred.
Fouling liquids Use STHE with removable tube bundle. SPHE or PHE is preferred due to
good flow distribution. Use PHE if easy access is of importance. Also
consider Philips RODbaffle heat exchanger, TWISTED TUBE® heat
exchanger and Helixchanger® heat exchanger, and EMbaffle® heat exchanger
to improve flow velocity on the shellside, enhance heat transfer performance,
and reduce fouling tendencies on shellside.
Slurries, suspensions, and pulps SPHE offers the best characteristics. Also consider free flow PHE or wide gap
PHE, or scraped surface heat exchanger.
Heat-sensitive liquids PHE fulfills the requirements best. Also consider SPHE.
Cooling with air Extended surface types like tube-fin heat exchanger or PFHE.
Gas or air under pressure Use STHE with extended surface on the gas side or brazed plate-fin exchanger
made of stainless steel or nickel alloys.
Cryogenic applications Brazed aluminum plate-fin exchanger, coiled tube heat exchangers, or PCHE.
Vapor condensation Surface condensers of STHE in carbon steel are preferred. Also consider
SPHE or brazed plate heat exchanger.
Vapor/gas partial condensation Choose SPHE.
Refrigeration and air conditioning
applications
Finned tube heat exchangers, special types of PHEs, brazed PHE up to 200°C.
Air–air or gas–gas applications Regenerators and plate-fin heat exchangers. Also consider STHE.
Viscous products, aseptic products, jam,
food and meat processing, heat sensitive
products and particulate laden products
Scraped surface heat exchanger.
Note: STHE, shell and tube heat exchanger; PHE, gasketed plate heat exchanger; SPHE, spiral plate heat exchanger; LHE, lamella
heat exchanger; PCHE, printed circuit heat exchangers; CTHE, coiled tube heat exchanger; PFHE, plate-fin heat exchanger.

1.5 REQUIREMENTS OF HEAT EXCHANGERS
Heat exchangers have to fulfill the following requirements:
• High thermal effectiveness
• Pressure drop as low as possible
• Reliability and life expectancy
• High-quality product and safe operation
• Material compatibility with process fluids
• Convenient size, easy for installation, reliable in use
• Easy for maintenance and servicing
• Light in weight but strong in construction to withstand the operational pressures and vibra-
tions especially heat exchangers for military applications
• Simplicity of manufacture
• Low cost
• Possibility of effecting repair to maintenance problems
The heat exchanger must meet normal process requirements specified through problem specification
and service conditions for combinations of the clean and fouled conditions, and uncorroded and cor-
roded conditions. The exchanger must be maintainable, which usually means choosing a configura-
tion that permits cleaning as required and replacement of tubes, gaskets, and any other components
that are damaged by corrosion, erosion, vibration, or aging. This requirement may also place limita-
tions on space for tube bundle pulling, to carry out maintenance around it, lifting requirements for
heat exchanger components, and adaptability for in-service inspection and monitoring.
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35Heat Exchangers
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eds.), Hemisphere/McGraw-Hill, New York, 1986, pp. 3–14.
Shah, R. K., Classification of heat exchangers, in Low Reynolds Number Flow Heat Exchangers (S. Kakac,
R. K. Shah, and A. E. Bergles, eds.), Hemisphere, Washington, DC, 1983, pp. 9–19.
Shah, R. K., What’s new in heat exchanger design, ASME, Mech. Eng., 106, 50–59 (1984).
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Design (R. K. Shah, E. C. Subbarao, and R. A. Mashelikar, eds.), Hemisphere, Washington, DC,
1988, pp. 7–16.
Thome, R. T., Wolverine Heat Transfer Engineering Data Book III, Wolverine Division of UOP Inc., Decatur,
AL, 2004.
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Bhatia, M. V. and Cheremisinoff, N. P., Heat Transfer Equipment, Process equipment series, Vol. 2, Technomic,
Westport, CT, 1980.
Bryers, R. W. (ed.), Fouling of Heat Exchanger Surfaces, Engineering Foundation, New York, 1983.
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37Heat Exchangers
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39
2 Heat Exchanger
Thermohydraulic
Fundamentals
2.1 HEAT EXCHANGER THERMAL CIRCUIT AND OVERALL
CONDUCTANCE EQUATION
In order to develop relationships between the heat transfer rate q, surface area A, fluid terminal
temperatures, and flow rates in a heat exchanger, the basic equations used for analysis are the energy
conservation and heat transfer rate equations [1]. The energy conservation equation for an exchanger
having an arbitrary flow arrangement is

q C t t C t t= − = −h h,i h,o c c,o c,i( ) ( )

(2.1)
and the heat transfer rate equation is

q UA t
t
R
= =∆
∆
m
m
o
(2.2)
where
∆tm is the true mean temperature difference (MTD), which depends upon the exchanger flow
arrangement and the degree of fluid mixing within each fluid stream
Cc is the capacity rate of the cold fluid, (Mcp)c
Ch is the capacity rate of the hot fluid, (Mcp)h
tc,i and tc,o are cold fluid terminal temperatures (inlet and outlet)
th,i and th,o are hot fluid terminal temperatures (inlet and outlet)
The heat exchanger thermal circuit variables and overall conduction described here are based on
Refs. [1,2].
The inverse of the overall thermal conductance UA is referred to as the overall thermal resistance
Ro, and it is made up of component resistances in series as shown in Figure 2.1:
R R R R R Ro h 1 w 2 c= + + + + (2.3)
where the parameters of the right-hand side of Equation 2.3 are Rh, hot side film convection resis-
tance, 1/(ηohA)h; R1, thermal resistance due to fouling on the hot side given in terms of fouling
resistance Rf,h (i.e., values tabulated in standards or textbooks), Rf,h/(ηoA)h; Rw, thermal resistance of
the separating wall, expressed for a flat wall by

R
A k
w
w w
=
δ

(2.4a)

and for a circular wall by

R
d d
k LN
w
i
w t
ln
=
( )
2π
(2.4b)
where
δ is the wall thickness
Aw is the total wall area for heat conduction
kw is the thermal conductivity of the wall material
d is the tube outside diameter
di is the tube inside diameter
L is the tube length
Nt is the number of tubes, and total wall area for heat conduction is given by

A L L Lw p= 1 2

(2.5)
where
L1, L2, and Np are the length, width, and total number of separating plates, respectively
R2 is the thermal resistance due to fouling on the cold side, given in terms of cold side fouling
resistance Rf,c by Rf,c/(ηoA)c
Rc is the cold side film convection resistance, 1/(ηohA)c
In these definitions, h is the heat transfer coefficient on the side under consideration, A represents
the total of the primary surface area, Ap, and the secondary (finned) surface area, Af, on the fluid side
under consideration, ηo is the overall surface effectiveness of an extended surface, and the subscripts
h and c refer to the hot and cold fluid sides, respectively. The overall surface effectiveness ηo is related
to the fin efficiency ηf and the ratio of fin surface area Af to total surface area A as follows:

η ηo
f
f= − −1 1
A
A
( )

(2.6)
Note that ηo is the unity for an all prime surface exchanger without fins. Equation 2.3 can be alternately
expressed as

1 1 1
UA hA
R
A
R
hA
R
A
= + + + +
( ) ( )η η η ηo h
f,h
o h
w
o c
f,c
o c( ) ( )
(2.7)
Laminar sublayer
qqh, Ch, Th
Tc, Cc, qc
Laminar sublayer
Fouling layer
Fouling layer
Heat transfer surface
RhR1RwR2Rc
FIGURE 2.1 Elements of thermal resistance of a heat exchanger.

41Heat Exchanger Thermohydraulic Fundamentals
Since UA = UhAh = UcAc, the overall heat transfer coefficient U as per Equation 2.7 may be defined
optionally in terms of either hot fluid surface area or cold fluid surface area. Thus, the option of Ah or
Ac must be specified in evaluating U from the product, UA. For plain tubular exchangers, Uo based
on tube outside surface is given by

1 1
2U h
R
d d d
k
R d
d
d
h do o
f,o
i
w
f,i
i i i
/
= + + + +
ln( )

(2.8)
The knowledge of wall temperature in a heat exchanger is essential to determine the localized hot
spots, freeze points, thermal stresses, local fouling characteristics, or boiling and condensing coef-
ficients. Based on the thermal circuit of Figure 2.1, when Rw is negligible, Tw,h = Tw,c = Tw is computed
from [1,2] as

T
T T R R R R
R R R R
w
h c h 1 c
h c 2
/
/
=
+ + +[ ]
+ + +[ ]
( ) ( )
( ) ( )
2
11

(2.9)
When R1 = R2 = 0, Equation 2.9 further simplifies to

T
T R T R
R R
hA T hA T
hA hA
w
h h c c
h c
o h h o c c
o h o c
/ /
/ /
=
+
+
=
+
+1 1
( ) ( )
( ) ( )
η η
η η
(2.10)
2.2 HEAT EXCHANGER HEAT TRANSFER ANALYSIS METHODS
2.2.1 Energy Balance Equation
The first law of thermodynamics must be satisfied in any heat exchanger design procedure at
both the macro and microlevels. The overall energy balance for any two-fluid heat exchanger
is given by

m c t t m c t th p,h h,i h,o c p,c c,o c,i( ) ( )− = −

(2.11)
Equation 2.11 satisfies the “macro” energy balance under the usual idealizations made for the basic
design theory of heat exchangers [3].
2.2.2 Heat Transfer
For any flow arrangement, heat transfer for two fluid streams is given by

q C t t C t t= − = −h h,i h,o c c,o c,i( ) ( )

(2.12)
and the expression for maximum possible heat transfer rate qmax is

q C t tmax min( )= −h,i c,i

(2.13)
The maximum possible heat transfer rate would be obtained in a counterflow heat exchanger with
very large surface area and zero longitudinal wall heat conduction, and the actual operating condi-
tions are the same as the theoretical conditions.

2.2.3 Basic Methods to Calculate Thermal Effectiveness
There are four design methods to calculate the thermal effectiveness of heat exchangers:
1. ε-NTU method
2. P-NTUt method
3. LMTD method
4. ψ-P method
The basics of these methods are discussed next. For more details on these methods, refer to
Refs. [1,2].
2.2.3.1 ε-NTU Method
The formal introduction of the ε-NTU method for the heat exchanger analysis was in 1942 by
London and Seban [4]. In this method, the total heat transfer rate from the hot fluid to the cold fluid
in the exchanger is expressed as
q C t t= −ε min( )h,i c,i (2.14)
where ε is the heat exchanger effectiveness. It is nondimensional and for a direct transfer type heat
exchanger, in general, it is dependent on NTU, C*, and the flow arrangement:

ε = φ ( , *, )NTU flowarrangementC

(2.15)
These three nondimensional parameters, C*, NTU, and ε, are defined next.
Heat capacity rate ratio, C*: This is simply the ratio of the smaller to larger heat capacity rate
for the two fluid streams so that C* ≤ 1.

C
C
C
mc
mc
*
( )
( )
min
max
min
max
= = p
p

(2.16)
where
C refers to the product of mass and specific heat of the fluid
the subscripts min and max refer to the Cmin and Cmax sides, respectively
In a two-fluid heat exchanger, one of the streams will usually undergo a greater temperature change
than the other. The first stream is said to be the “weak” stream, having a lower thermal capacity rate
(Cmin), and the other with higher thermal capacity rate (Cmax) is the “strong” stream.
Number of transfer units, NTU: NTU designates the nondimensional “heat transfer size” or
“thermal size” of the exchanger. It is defined as a ratio of the overall conductance to the smaller
heat capacity rate:

NTU = =
∫
UA
C C
UdA
A
min min
1

(2.17)
If U is not a constant, the definition of the second equality applies. For constant U, substitution of
the expression for UA results in [1,2]

NTU
/ /o h w o c
=
+ + + +






1 1
1 11 2C hA R R R hAmin ( ) ( )η η

(2.18)

where R1 and R2 are the thermal resistances due to fouling on the hot side and the cold side, respec-
tively, as defined in Equation 2.7. In the absence of the fouling resistances, NTU can be given by
the expression

1 1 1
NTU NTU / NTU /h h
w
c c
= + +
( ) ( )min
min
minC C
R C
C C
(2.19)
and the number of heat transfer units on the hot and cold sides of the exchanger may be defined as
follows:

NUT NTUh
o h
h
c
o c
c
= =
( ) ( )η ηhA
C
hA
C
(2.20)
Heat exchanger effectiveness, ε: Heat exchanger effectiveness, ε, is defined as the ratio of the actual
heat transfer rate, q, to the thermodynamically possible maximum heat transfer rate (qmax) by the
second law of thermodynamics:

ε =
q
qmax
(2.21)
The value of ε ranges between 0 and 1. Using the value of actual heat transfer rate q from Equation
2.12 and qmax from Equation 2.13, the exchanger effectiveness ε of Equation 2.21 is given by

ε =
−
−
=
−
−
C t t
C t t
C t t
C t t
h h,i h,o
h,i c,i
c c,o c,i
h,i c,i
( )
( )
( )
(min min ))
For * , h cC = =1 ε ε
(2.22)
Dependence of ε on NTU: At low NTU, the exchanger effectiveness is generally low. With increas-
ing values of NTU, the exchanger effectiveness generally increases, and in the limit it approaches
the maximum asymptotic value. However, there are exceptions such that after reaching a maximum
value, the effectiveness decreases with increasing NTU.
2.2.3.2 P-NTUt Method
This method represents a variant of the ε-NTU method. The origin of this method is related to shell
and tube exchangers. In the ε-NTU method, one has to keep track of the Cmin fluid. In order to avoid
possible errors, an alternative is to present the temperature effectiveness, P, of the fluid side under
consideration as a function of NTU and heat capacity rate of that side to that of the other side, R.
Somewhat arbitrarily, the side chosen is the tubeside regardless of whether it is the hot side or the
cold side.
General P-NUTt functional relationship: Similar to the exchanger effectiveness ε, the thermal
effectiveness P is a function of NTUt, R, and flow arrangement:

P R= φ ( , , )NTU flowarrangementt

(2.23)
where P, NTUt, and R are defined consistently based on the tubeside fluid variables. In this method,
the total heat transfer rate from the hot fluid to the cold fluid is expressed by

q PC T t= −t 1 1( )

(2.24)

Thermal effectiveness, P: For a shell and tube heat exchanger, the temperature effectiveness of
the tubeside fluid, P, is referred to as the “thermal effectiveness.” It is defined as the ratio of the
temperature rise (drop) of the tubeside fluid (regardless of whether it is hot or cold fluid) to the dif-
ference of inlet temperature of the two fluids. According to this definition, P is given by

P
t t
T t
P=
−
−
2 1
1
is referred to tubeside
1
( )

(2.25)
where
t1 and t2 refer to tubeside inlet and outlet temperatures, respectively
T1 and T2 refer to shellside inlet and outlet temperatures, respectively
Comparing Equations 2.25 and 2.22, it is found that the thermal effectiveness P and the exchanger
effectiveness ε are related as

P
C
C
C C
C C C
= = =
= =
min
min
max
t
t
t
for
* for
ε ε
ε

(2.26)
Note that P is always less than or equal to ε. The thermal effectiveness of the shellside fluid can be
determined from the tubeside values by the relationship given by

P P
C
C
PR
R P P
t
s
s
(tubeside)
= =
= =For * , s1

(2.27)
(For TEMA shell types, the thermal effectiveness charts given in this chapter 2, depicts thermal
effectiveness referred to tubeside only)
Heat capacity ratio, R: For a shell and tube exchanger, R is the ratio of the capacity rate of the tube
fluid to the shell fluid. This definition gives rise to the following relation in terms of temperature
drop (rise) of the shell fluid to the temperature rise (drop) of the tube fluid:

R
C
C
T T
t t
= =
−
−
t
s
1 2
2 1
(2.28)
where the right-hand-side expressions come from an energy balance and indicate the temperature drop/
rise ratios. The value of R ranges from zero to infinity, zero being for pure vapor condensation and infin-
ity being for pure liquid evaporation. Comparing Equations 2.28 and 2.16, R and C* are related by

R
C
C
C C C
C
C C
= = =
= =
t
s
t
t
for
for
*
*
min
max
1

(2.29)
Thus R is always greater than or equal to C*.
Number of transfer units, NTUt: For a shell and tube exchanger, the number of transfer units
NTUt is defined as a ratio of the overall conductance to the tubeside fluid heat capacity rate:

NTUt
t
=
UA
C
(2.30)

Thus, NTUt is related to NTU based on Cmin by

NTU NTU NTU for
NTU for
t
t
t
t
= = =
= =
C
C
C C
C C C
min
min
max*

(2.31)
Thus NTUt is always less than or equal to NTU.
2.2.3.3 Log Mean Temperature Difference Correction Factor Method
The maximum driving force for heat transfer is always the log mean temperature difference
(LMTD) when two fluid streams are in countercurrent flow. However, the overriding importance
of other design factors causes most heat exchangers to be designed in flow patterns different
from true countercurrent flow. The true MTD of such flow arrangements will differ from the
logarithmic MTD by a certain factor dependent on the flow pattern and the terminal tempera-
tures. This factor is usually designated as the log MTD correction factor, F. The factor F may
be defined as the ratio of the true MTD to the logarithmic MTD. The heat transfer rate equation
incorporating F is given by

q UA t UAF t= =∆ ∆m lm

(2.32)
where
∆tm is the true MTD
∆tlm is the LMTD
The expression for LMTD for a counterflow exchanger is given by

LMTD
ln
lm= ∆ =
∆ − ∆
∆ ∆
t
t t
t t
1 2
1 2( )
(2.33a)
where ∆t1 = th,i − tc,o = T1 − t2 and ∆t2 = th,o − tc,i = T2 − t1 for all flow arrangements except for paral-
lelflow; for parallelflow ∆t1 = th,i − tc,i(=T1 − t1) and ∆t2 = th,o − tc,o(=T2 − t2). Therefore, LMTD can be
represented in terms of the terminal temperatures, that is, greater terminal temperature difference
(GTTD or GTD) and smaller terminal temperature difference (STTD or STD) for both pure paral-
lel- and counterflow arrangements. Accordingly, LMTD is given by

LMTD
GTTD STTD
ln GTTD/STTD
lm= ∆ =
−
t
( )
(2.33b)
The terminal temperature distribution to calculate LMTD is shown in Figure 2.2a.
2.2.3.3.1 LMTD Correction Factor, F
Charts to determine LMTD from the terminal temperature differences are shown in Figure 2.2b.
(Note: While referring the nomogram of Figure 2.2b, use GTD in place of GTTD and STD in place
of STTD.)
From its definition, F is expressed by

F
t
t
=
∆
∆
m
lm
(2.34)

t1
∆t2
∆t2
∆t1
∆t1
t1
1. Parallelflow(a) 2. Counterflow
Temperature distribution along
the length of heat exchanger
Temperature distribution along
the length of heat exchanger
Temperature
Temperature
t1
t2
t2 t2
T2
T2
T2
T1
t2
t1
T2T1
T1
T1
400
400
350
300
250
150
100
90
80
70
60
50
40
30
20
∆t1
GTD
∆t1Greatesttemperaturedifference(GTD)°F
∆tmLogmeantemperaturedifference(LMTD)°F
∆t2Leasttemperaturedifference(LTD)°F
100
90
80
70
60
50
40
30
20
100
90
80
70
60
50
40
30
20
10
(b)
∆t2
LTDLMTD
10
9
8
7
6
10
9
8
7
6
5
4
200
300
250
150
200
300
250
150
200
FIGURE 2.2 (a) Terminal temperature to calculate LMTD; (b) nomogram to find LMTD. (Courtesy of
Paul-Muller Company, Springfield, MO.)

In situations where the heat release curves are nonlinear, the approach just described is not appli-
cable and a “weighted” temperature difference must be determined.
It can be shown that, in general, F is dependent upon the thermal effectiveness P, the heat capac-
ity rate ratio R, and the flow arrangement. Therefore, F is represented by

F P R= φ ( , , , )NTU flow arrangementt

(2.35)
and the expression for F in terms of P, R, and NTU is given by

F
R
P
PR
R
P
P
R
=
−
−
−





 ≠
=
−
=
1
1
1
1
1
1
1
( )
( )
NTU
ln for
NTU
for

(2.36a)

F
C
C
C
C
=
−
−
−





 ≠
=
−
=
1
1
1
1
1
1
1
( *)
*
*
(
*
NTU
ln for
)NTU
for
ε
ε
ε
ε
(2.36b)
The factor F is dimensionless.
The value of F is unity for a true counterflow exchanger, and thus independent of P and R.
For other arrangements, F is generally less than unity, and can be explicitly presented as a func-
tion of P, R, and NTUt by Equation 2.36. The value of F close to unity does not mean a highly
efficient heat exchanger, but it means a close approach to the counterflow behavior for the com-
parable operating conditions of flow rates and inlet fluid temperatures. Because of a large capital
cost involved with a shell and tube exchanger, generally it is designed in the steep region of the
P-NTUt curve (ε-NTU relation for the compact heat exchanger) (ε or P 60%), and as a rule of
thumb, the F value selected is 0.80 and higher. However, a better guideline for Fmin is provided
in the next section. For more details on heat exchanger thermal design methods, refer to Shah
and Sekulic [5] and Ref. [6].
2.2.3.3.2 Approximate F Value for Heat Exchanger Sizing Purpose
This correction factor accounts for the two streams not in counterflow. At the estimation stage, we do
not know the detailed flow and pass arrangement so we can assume the following for preliminary sizing:
• F = 1.0 for true counterflow, e.g., double-pipe heat exchanger in counterflow arrangement,
F shell type of shell and tube heat exchanger
• F = 0.7 for crossflow heat exchanger
• F = 0.7 for TEMA E shell with single pass on both shellside and tubeside
• F = 0.80 for E1–2 shell and tube heat exchanger (refer Figure 2.28)
• F = 0.95 for G1–2 (refer Figure 2.34), H1–2 shell and tube heat exchanger (refer Figure 2.36)
• F = 0.79 for J1–2 shell and tube heat exchanger (refer Figure 2.38)
• F = 0.9 for multi-pass compact heat exchanger and multiple passes on both shellside and
tubeside of TEMA E shell
• F = 1.0 if one stream is isothermal, C* = 0, R = 0 or ∞ (typically boiling or condensation)
Applicability of ε-NTU and LMTD methods: Generally, the ε-NTU method is used for the design
of compact heat exchangers. The LMTD method is used for the design of shell and tube heat
exchangers. It should be emphasized that either method will yield the identical results within the
convergence tolerances specified.

2.2.3.4 ψ-P Method
The ψ-P method was originally proposed by Smith [7] and modified by Mueller [8]. In this method,
a new term ψ is introduced, which is expressed as the ratio of the true MTD to the inlet temperature
difference of the two fluids:

ψ =
∆
−
=
∆
−
t
t t
t
T t
m
h,i c,i
m
1 1

(2.37)
and ψ is related to ε and NTU and P and NTUt as

ψ
ε
= =
NTU NTUt
P

(2.38)
and the heat transfer rate is given by

q UA t t= −ψ( )h,i c,i

(2.39a)

= −UA T tψ( )1 1

(2.39b)
Since ψ represents the nondimensional ∆tm, there is no need to compute ∆tlm in this method.
Functional relationship between the various thermal design methods: The general functional
relationship for the ε-NTU, P-NTUt, LMTD, and ψ-P methods is shown in Table 2.1, which has
been adapted and modified from Ref. [1], and the relationship between the dimensionless groups of
these methods is given in Table 2.2.
Thermal design methods for the design of shell and tube heat exchangers: Any of the four meth-
ods (ε-NTU, P-NTUt, LMTD, and ψ-P) can be used for shell and tube exchangers.
TABLE 2.1
General Functional Relationship between Dimensionless Groups of the ε-NTU, P-NTUt,
and LMTD
Heat Transfer
Parameters ε-NTU Method P-NTUt Method LMTD Method
Heat capacity rate
ratio
C
C
C
mc
mc
*
( )
( )
min
max
min
max
= =
p
p
R
C
C
T T
t t
= =
−
−
t
s
1 2
2 1
LMTD =
−






∆ ∆
∆
∆
t t
t
t
1 2
1
2
ln
NTU NTU
A
= =
∫
UA
C C
UdA
min min
1
NTUt
t
=
UA
C
LMTD = ∆tlm
F = ϕ (P, R, NTUt, flow arrangement)
Thermal
effectiveness
ε = ϕ(NTU, C*, flow
arrangement)
P = ϕ(NTUt, R, flow
arrangement)
F
t
t
=
∆
∆
m
lm
F
R
P
PR
R
P
P
R
=
−
−
−





 ≠
=
−
=
1
1
1
1
1
1
1
( )
( )
NTU
ln for
NTU
for
q UA t UAF t= =∆ ∆m lm
ε = h h,i h,o
h,i c,i
c c,o c,i
h,i c,i
C t t
C t t
C t t
C t t
( )
( )
( )
(min min
−
−
=
−
− ))
P
t t
T t
=
−
−
2 1
11
P P
C
C
PRs
t
s
= =
Heat transfer q C t t C t t= − = −h h,i h,o c c,o c,i( ) ( ) q PC T t= −t 1 1( )

2.2.4 Some Fundamental Relationships to Characterize
the Exchanger for “Subdesign” Condition
The partial derivatives of the temperature efficiency P with respect to NTU and R enable complete
characterization of the exchanger performance around an operating point. Thus, the exchanger per-
formance can be readily predicted for the “subdesign” conditions [9]. Singh [9] developed deriva-
tives of P, F, and NTU. Derivatives for P and F are discussed next.
Dependence of thermal effectiveness: Thermal performance P and thermal effectiveness ε can
be represented through R by [9]

ε

= ≤
=
P R
PR R
1
1
(2.40)

P f R= ( , )NTU
(2.41)

ε φ( )= NTU R, *

(2.42)
Thus,

d d d
R
dRε φ
φ φ
= =
∂
∂
+
∂
∂NTU
NTU

(2.43)

d dP
P
d
P
R
dR Rε = =
∂
∂
+
∂
∂
≤
NTU
NTU for 1

(2.44)
d PdR RdPε = + (2.45)

= +
∂
∂
+
∂
∂



PdR R
P
d
P
R
dR
NTU
NTU

(2.46)
TABLE 2.2
Relationship between Dimensionless Groups
of the ε-NTU, P-NTUt, and LMTD Methods
R
C
C
C C C
C
C C
= = =
= =
t
s
t
t
for*
*
for
min
max
1
NTU NTU NTU for
NTU for
t t
t
= = =
= =
C
C
C C
C C C
min
t
min
max*
F
R
P
PR
R
P
P
R
P
=
−
−
−





 ≠
=
−
=
= =
1
1
1
1
1
1
1
( )
ln
( )
NTU
for
NTU
for
NTU NT
ψ
ε
UUt

or

d P R
P
R
dR R
P
d Rε ≥= +
∂
∂



 +
∂
∂NTU
NTU for 1

(2.47)
Dependence of LMTD correction factor, F: The derivatives of F with respect to ε, P, and R are
given by [9]

∂
∂
= −
−
−
−





 =
−F
R
P
PR
F
NTU NTU
ln
NTU
1
1
1
12
( )
(2.48)

∂
∂
=
− −
F
P P PR
1
1 1NTU( )( )
(2.49)

∂
∂
=
−
−
+
− −
F
R
F
R R PR( ) ( )( )1
1
1 1NTU
(2.50)
and

dF
F
P
dP
F
d
F
R
dR=
∂
∂
+
∂
∂
+
∂
∂NTU
NTU

(2.51)
2.3 THERMAL EFFECTIVENESS CHARTS
Broadly speaking, there are two types of heat exchanger problems: rating and sizing. To solve either
type of problem from first principles is laborious and time-consuming. However, sizing and rating
of heat exchangers are solved with the use of performance charts easily. The graphical charts were
introduced many years ago and have gained wide acceptance throughout the industry. Five types of
heat exchanger design charts are found in the literature, and the salient features of these charts are
discussed by Turton et al. [10]. These charts are shown schematically in Figure 2.3a–f. The dimen-
sionless variables used in these charts (ε, P, R, C*, F, NTU, NTUt) have been defined in Section 2.2.
Figure 2.3a is the most widely used of these charts and was introduced by Bowman et al. [11] in
1940. In this chart, the LMTD correction factor, F, is presented as a function of the effectiveness, P,
and the heat capacity rate ratio, R. Using this chart, the design problem where terminal temperatures
and flow rates are usually specified but overall U and/or A are unknown can be solved; however,
the rating problem can be solved by a trial-and-error solution. Since F compares the true MTD of a
given flow arrangement with that of the counterflow arrangement, these charts provide a well-suited
means of finding out the best of several possible flow arrangements. The one with the higher F will
require the lower NTU, that is, the lower area if U remains constant, operating with the same R and
P. Underwood [12] first derived the expression for true MTD for E1–2, E1–4, and E2–4 shell and tube
exchangers in 1934. Bowman et al. [11] published a summary of correction factors for exchangers of
different flow arrangements. Ten Broeck [13] further constructed charts using dimensionless groups,
UA/(mcp)t, P = (t2 − t1)/(T1 − t1), and R = (T1 − T2)/(t2 − t1) for direct calculation of terminal temperatures
with known surface area of a heat exchanger. At present, F charts are available for all TEMA shells.
Figure 2.3b and c are due to Kays and London [14] and TEMA [15], respectively. Figure 2.3c
is plotted on a semilog paper, since the most useful NTU and NTU, design range for compact
heat exchangers and shell and tube exchangers, respectively, is 0.2–3.0. A careful look at the lin-
ear graphical presentation of the ε-NTU results of Figure 2.3b indicates that the NTU scale in
this range is short and hence one cannot obtain the accurate values of ε or NTU from graphs.

For better appreciation, this is illustrated through the thermal relation chart (ε-NTU) for crossflow
heat exchanger in Figure 2.3. An alternative is to stretch the NTU scale in the range 0.2–3.0 by using
a logarithmic scale. Thus, the P-NTUt results are generally presented on a semilog paper, as shown
for example in Figure 2.3c, in order to obtain more accurate graphical values of P or NTUt. Using
these charts, both the sizing and rating problem can be solved. However, the LMTD correction fac-
tor F is not shown in these charts. Hence, it is to be calculated additionally.
Muller [8] proposed the charts of Figure 2.3d with its triple family of curves. This chart can be
used to solve both the sizing and rating problems and in addition gives the F values. However, Figure
2.3d is somewhat cramped and difficult to read accurately and introduces yet another parameter,
1
0
0.1 1.0 10
P
R
NTU(c)
1
1
0
0
P
R
F
NTU
P
NTU
1
(d)
1
0
F
1
0
P
10
P
RR
NTU
NTU
P
NTU
(e) (f)
1
0
0 1
F
1
0
P
R
P
0 1
NTU(a) (b)
R
1.0
0.9
0.8
0.1
C=0* 0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.00.7
0.6
0.5
0.4
0.3
ε,Thermaleffectiveness
0.2
0.1
0.0
0.5
(g)
1.0 1.5 2.0 2.5 3.0 3.5 4.0
NTU
5.0 6.0 7.0 8.04.5 5.5 6.5 7.5
FIGURE 2.3 Thermal effectiveness charts. (a) Bowman chart; (b) Kays and London chart; (c) TEMA chart;
(d) F–P–R-chart; (e) ψ chart; (f) F-P-R-NTU chart (From Turton, R. et al., Trans. ASME J. Heat Transfer, 106,
893, 1984); (g) ε-NTU chart for unmixed–unmixed crossflow, as per Eq. T4 of Table 2.4.

P/NTUt. The Muller charts have been redrawn recently by Taborek and included in HEDH [16]. The
present form of this chart is shown in Figure 2.3e. The main difference between Figure 2.3d and e
is that the F parameter curves have been omitted in the latter, and thus the problem of having to
separately calculate the F values has been retained.
In a system with four variables, F, P, R, and NTU or NTUt, any chart displays just one family
of curves, such as Figure 2.3a–c, and does not give all the interrelationships directly. On the other
hand, a chart with three families of curves, as in Figure 2.3d, has one set that is redundant. To show
all the interrelationships between these four variables requires a chart with two families of curves.
This is satisfied by Figure 2.3e.
In the graphical presentation, ψ is plotted against P and R as a parameter as shown in Figure 2.3e. The
lines of constant R originate at ψ = 1 and terminate at ψ = 0 so that the asymptotic values of P for NTU
tend to infinity. Thus the curves of constant R are similar to those for the F-P charts. In order to tie in
with the P-NTUt and LMTD methods, the lines of constant NTUt and constant F are also superimposed
on this chart. Figure 2.3e also has one limitation: It does not show directly the four parameters of interest.
Constraints due to the charts in Figure 2.3a–e are overcome by a chart, shown in Figure 2.3f, proposed
by Turton et al. [10]. The chart in Figure 2.3f extends the easy-to-read Bowman charts of Figure 2.3a to
include a second family of curves representing the variable NTU. Both the sizing and rating problems
can be solved using this form of chart, and F values can be found directly for both types of problems.
Thus to find exchanger surface area, use P and R to evaluate F and NTU. To find terminal temperature,
use NTU and R to evaluate P and F. Most of the charts included in this book are of the type of Figure 2.3f.
2.4 SYMMETRY PROPERTY AND FLOW REVERSIBILITY AND RELATION
BETWEEN THE THERMAL EFFECTIVENESS OF OVERALL PARALLEL
AND COUNTERFLOW HEAT EXCHANGER GEOMETRIES
2.4.1 Symmetry Property
The symmetry property relates the thermal behavior of a heat exchange process to that of the reverse
process, in which the directions of flow of both fluids are reversed [17]. Figure 2.4 shows four dif-
ferent flow arrangements for the TEMA E1–2 shell and tube heat exchanger that are equivalent if
complete transverse mixing of the shell fluid is satisfied.
2.4.2 Flow Reversibility
Flow reversibility establishes a relation between the thermal effectiveness of two heat exchanger
configurations that differ from each other in the inversion of either one of the two fluids [18].
t2
t1
t2
t1
t1
t2
t1
t2
T1
T1T1
T2(a) (b)
(c) (d)
T1
T2
T2
T2
FIGURE 2.4 Flow reversibility principle. (a) Basic E1-2 case, (b) basic case with tube fluid reversed, (c) basic
case with shell fluid reversed, and (d) basic case with both shell and tube fluids reversed. (Symmetry opera-
tions performed on the TEMA E1–2 shell.) (From Pignotti, A., Trans. ASME, J. Heat Transfer, 106, 361, 1984.)

Although the inversion of both fluids often does not alter the configuration, the inversion of only
one of them usually leads from one configuration to an entirely different one, as is the case in going
from a pure parallelflow to a pure counterflow arrangement or vice versa. Using this relation, if the
expression for the effectiveness, P, of a configuration as a function of the heat capacity rate ratio, R
(or C*), and the number of heat transfer units NTU is known, the corresponding expression for the
“inverse” configuration is immediately obtained from the simple relation [18]:

P R
P R
RP R
i NTU
NTU
NTU
( , )
( , )
( , )
=
−
+ −1
(2.52)
where P denotes the effectiveness of a given arrangement, and Pi, that of the same one with fluid
direction reversed. The relation is valid under the assumptions of temperature independence of
the heat transfer coefficient and heat capacity rates, when one of the fluids proceeds through the
exchanger in a single, mixed stream. In some cases with special symmetry, the inversion of both
fluids does not alter the geometry, and therefore this property is trivially satisfied. Pignotti [18]
illustrates the property of flow reversibility with several examples from the available literature. An
example to clarify the meaning of Equation 2.52 is given next. Consider the well-known expression
for the effectiveness of a parallelflow configuration:

P R
R
R
( , )
exp ( )
( )
NTU
NTU
=
− − +[ 
+
1 1
1
(2.53)
Let us derive from it the expression for the effectiveness of a pure counterflow configuration,
which we denote Pc(R, NTU). Equation 2.52 is applicable, because the counterflow geometry
is obtained from parallelflow by inverting the direction of flow of one of the fluids, and the
condition that at least one of the fluids should be mixed throughout the exchanger is satisfied.
After replacing R by −R in Equation 2.53 and performing the elementary algebraic operations
indicated in Equation 2.52, we obtain the expression for the effectiveness of the counterflow
configuration:

P R
R
R R
c NTU
NTU
exp NTU
( , )
exp ( )
( )
=
− − −[ ]{ }
− − −[ ]{ }
1 1
1 1

(2.54)
Observe also that the inversion of one fluid leads from a parallelflow connection to a counterflow
one, and likewise, from the latter to the former; therefore, Equation 2.52 can be used to go from
parallelflow to counterflow and vice versa.
The transformation property of Equation 2.52 can also be expressed in terms of the variables
referred to the mixed fluid. For example, if the thermal relation on the shellside or tubeside is
known in terms of Px, Rx, and NTUx, the thermal relation for the other side Py, Ry, and NTUy may
be obtained from the relation

P R P R
R
Ry x x
x
y x xy
= = =, ,
1
NTU NTU

(2.55)
For example, let the tubeside values of an H1–2 exchanger be P = 0.752, R = 0.7, and NTU = 2.5. Then
the shellside values will be P = 0.7 × 0.752, R = 1/0.7, and NTU = 0.7 × 2.5. For R = 1.0, both the
tubeside and shellside values are the same.
When the thermal effectiveness is the same for the original case and the inverted case, it is
referred to as stream symmetric. Typical examples for stream symmetric are parallelflow, counter-
flow, and crossflow unmixed–unmixed and mixed–mixed cases.

2.5 TEMPERATURE APPROACH, TEMPERATURE
MEET, AND TEMPERATURE CROSS
The meanings of temperature approach, temperature meet, and temperature cross are as follows.
Temperature approach is the difference of the hotside and coldside fluid temperature at any point
of a given exchanger. In a counterflow exchanger or a multipass exchanger, (1) if the cold fluid out-
let temperature tc.o is less than the hot fluid outlet temperature th.o, then this condition is referred
to as temperature approach; (2) if tc.o = th,o, this condition is referred to as temperature meet; and
(3) if tc.o is greater than th.o, the difference (tc.o − th.o) is referred to as the temperature cross or tem-
perature pinch. In this case, the temperature approach (th.o − tc.o) is negative and loses its meaning.
Temperature cross indicates a negative driving force for heat transfer between the fluids. It requires
either a large area for heat transfer or the fluid velocity to increase overall heat transfer coefficient.
The underlying meanings of these three cases are brought out in Table 2.3 and the same are shown
in Figure 2.5a.
The temperature cross is undesirable, particularly for shell and tube exchangers, because the
tube surface area is not utilized effectively and hence there is wastage of capital cost. If outlet
TABLE 2.3
Temperature Approach, Temperature Meet,
and Temperature Cross
Temperature Approach Temperature Meet Temperature Cross
th,i → th,o th,i → th,o th,i → th,o
tc,o ← tc,i tc,o ← tc,i tc,o ← tc,i
tc,o th,o tc,o = th,o tc,o th,o
T1
Normal temperature distribution(a) (b) (c)Temperature meet
Thermodynamic
violation!
Temperature cross
t1
t1
t2
t2T2
T2
t1
T2
T1
t2
T1
(d)
a
b
x
a–b—Temperature normal
a΄–b—Temperature meet
a˝–b—Temperature cross
x—Temperature cross point
a΄
a˝
t1
T2
(e)
Temperature
approach
t1
T2
t2
T1
t2
T1
FIGURE 2.5 Principle of temperature approach, temperature meet, and temperature cross. (a) Normal
temperature distribution; (b) temperature meet; (c) temperature cross; (d) temperature approach, meet,
and cross superimposed; (e) temperature distribution in an E1–2 exchanger without temperature cross;

temperatures form a temperature cross in a multiple tube pass heat exchanger, a lower than desirable
LMTD correction factor will occur. A simple way to avoid this is to use more exchanger shells in
series. Other engineers suggest that a small temperature cross may be acceptable and may provide a
less expensive design than the more complex alternatives. For a E1–2 heat exchanger, the temperature
cross occurs around a relatively narrow range of F value about 0.78–0.82. Lower values of F may be
taken as an indication that temperature cross will occur.
The concept of the temperature cross or meet at the exchanger outlet can be utilized to determine
the number of shells in series required to meet the heat duty without having a temperature cross in
any individual shell. Temperature cross is undesirable for shell and tube heat exchanger because the
tube surface area is not utilized cost-effectively. An optimum design would mean that the tempera-
ture cross or meet point lies just at the end of the second tube pass. This phenomenon is explained
in detail by Shah [2] and is briefly dealt with here with reference to an E1–2 exchanger.
For E1-2 two possible shell fluid directions with respect to the tube fluid direction are shown in
Figure 2.5b. The temperature distributions of Figure 2.5b reveal that there is a temperature cross.
In region X, the second tube pass transfers heat to the shell fluid. This is contrary to the design
objective, in which ideally the heat transfer should have taken place only in one direction (from the
shell fluid to the tube fluid, as shown in Figure 2.5a) throughout the two passes. The reason for this
temperature cross is as follows: Although an addition of surface area (a high value of NTUt, or a
low value of LMTD correction factor F) is effective in raising the temperature of the tube fluid and
rises in the second pass up to point X, beyond this point the temperature of the shell fluid is lower
than that of the tube fluid, since we have considered the shell fluid mixed at a cross section and it is
cooled rapidly by the first pass. Thus, the addition of the surface area in the second tube pass left of
point X is useless from the thermal design point of view. A “good” design avoids the temperature
cross in a shell and tube exchanger. Theoretically, the optimum design would have the temperature
cross point just at the end of the second tube pass, which will satisfy the following condition:

t t t tt,o s,o t,o s,oor= − = 0

(2.56)
This condition leads to the following formula:

P
R
=
+
1
1
(2.57)
(f)
t1
t1
T2
T1
R1
T1
(g)
t1
t1
T2
T2
t2
J
1
2
t2
R 1
T1
T1
Ti
T2
Ti
t2
t2
FIGURE 2.5 (continued) Principle of temperature approach, temperature meet, and temperature cross.
(f) with temperature cross.

Thus for a given R, Equation 2.57 provides the limiting (maximum) value of P. Corresponding to P
and R, the limiting (maximum) value of NTUt beyond which there will be a temperature cross can
be determined from its thermal relation formula. Therefore, from P, R, and NTU, F can be calcu-
lated. This F value is known as the Fmin value beyond which there will be a temperature cross. This
is illustrated for an E1–2 exchanger here. For a known value of R, determine the limiting value of P
from Equation 2.57 and NTU from the following equation:

NTU lnE1 2
1
1
2 1 1
2 1 1
2 0 5
2 0 5
2 0 5−
=
+
− + − +



− + + +

( )
( )
( )
.
.
.
R
P R R
P R R 










(2.58)
For known values of P, R, and NTU, determine F from Equation 2.36.
2.5.1 Temperature Cross for Other TEMA Shells
Temperature cross for other TEMA shells such as G1–2, H1–2, and J1–2 can be evaluated from Equation
2.57 [19]. The Fmin curves for G1–2, H1–2, and J1–2 cases are given in the next section.
2.6 THERMAL RELATION FORMULAS FOR VARIOUS FLOW
ARRANGEMENTS AND PASS ARRANGEMENTS
The heat exchanger effectiveness is defined as the ratio of the overall temperature drop of the weaker
stream to the maximum possible temperature difference between the fluid inlet temperatures. The
following assumptions are commonly made in deriving thermal effectiveness:
1. The overall heat transfer coefficient is constant throughout the exchanger.
2. Each pass has the same heat transfer area; that is, unsymmetrical pass arrangements are
not considered.
3. There is no phase change.
4. The specific heat of each fluid is constant and independent of temperature.
5. The flow rates of both streams are steady.
6. The flow of both fluids is evenly distributed over both the local and the total transfer area.
7. Heat losses from the system are negligible.
In this section, thermal relation formulas for (1) various flow arrangements—parallelflow, coun-
terflow, and crossflow—(2) various types of heat exchangers—compact and shell and tube—and (3)
multipass arrangements or multiple units of both compact and shell and tube heat exchangers are
presented. Most of the formulas are tabulated and the thermal effectiveness charts are given. Mostly
counterflow arrangements are considered. For shell and tube exchangers, formulas are given for both
parallelflow and counterflow, but thermal effectiveness charts are given only for counterflow arrange-
ments referred to tubeside (similar to TEMA Standards [15]). For stream symmetric cases, thermal
effectiveness relations referred to the shellside can be derived from the “flow reversibility” principle.
From counterflow thermal effectiveness relations, thermal effectiveness relations for parallelflow
arrangements can be easily derived (for stream symmetric cases only) from the “flow reversibility”
principle. Customarily, the ε-NTU method is employed for compact heat exchangers. In this method,
the capacity ratio C* is always ≤1. Hence, thermal effectiveness charts are given in terms of ε–C*–
NTU, and wherever possible, the thermal effectiveness charts are also given in terms of P–R–F–NTU,
instead of ε–C*–NTU.

2.6.1 Parallelflow
For a given set of values of C* or R, and NTU, (1) the thermal effectiveness is much lower for paral-
lelflow than for counterflow arrangement, except in the limiting case C* = R = 0, where it is the same
for both cases and approaches unity as NTU increases to infinity, and (2) at a given value of NTU, the
effectiveness increases with decreasing capacity ratio, C* or R. The formula for thermal effectiveness
is given by Equation T1 in Table 2.4, and the thermal effectiveness chart is given in Figure 2.6.
2.6.2 Counterflow
Among the various flow arrangements, counterflow has the highest thermal effectiveness. For coun-
terflow exchangers, at a given value of NTU, the effectiveness increases with decreasing capacity
ratio, C* or R. The formula for thermal effectiveness is given by Equation T2, and the thermal
effectiveness chart is given in Figure 2.7.
2.6.3 Crossflow Arrangement
2.6.3.1 Unmixed–Unmixed Crossflow
This is an industrially important arrangement representing the case of a large number of unmixed
channels in both sides. The original solution was due to Nusselt [20] and was later reformulated
into a more manageable equation by Mason [21]. Mason’s formula is given by Equation T3, and this
equation can be used for P–NTU–R relation. Baclic [22] presents Nusselt’s equation in terms of a
modified Bessel function of the first kind as given in Equation T4; Eckert [23] provides a simplified
formula without involving Bessel function as given by Equation T5, and this equation predicts ε
within ±1% of ε from Equation T4 for 1 NTU 7; Equations T4 and T5 can be used for formulas
involving C* ≤ 1 only. The thermal effectiveness chart as per Equation T3 is given in Figure 2.8 and
as per Equation T4 is given in Figure 2.9.
2.6.3.2 Unmixed–Mixed Crossflow
In this arrangement, one fluid is mixed and the other is unmixed. A typical example is a bare
tube compact heat exchanger in which the fluid outside the tube is mixed, whereas the tubeside
fluid is unmixed. There are two possible cases: (1) weaker fluid (Cmin) is mixed and (2) stronger
fluid (Cmax) is mixed. Formulas for thermal effectiveness for the weaker fluid mixed are given by
Equation T6 and for the stronger fluid mixed by Equation T7. The thermal effectiveness charts
are given in Figure 2.10 for the weaker fluid mixed and Figure 2.11 for the stronger fluid mixed.
For R = 1 or C* = 1, the thermal effectiveness is the same for both cases.
2.6.3.3 Mixed–Mixed Crossflow
This case has no industrial application and is shown here only as an extreme of the crossflow
arrangement. The solution is identical to the TEMA J shell with infinite tubeside passes. The for-
mula for thermal effectiveness is given by Equation T8.
2.6.3.4 Single or Multiple Rows in Crossflow
Many process heat exchangers provide a crossflow arrangement between the hot (or cold) process
fluid that flows through the tubes and the external coolant (or hot air such as supercharged engine
intake air), usually air. Because this flow arrangement is not strictly countercurrent, the MTD must be
corrected by applying a correction factor, F. The factor F depends on the terminal temperatures, the
number of tube rows per pass, and the number of passes. The basic unmixed–unmixed case shown in
Figure 2.12 assumes a large number of flow channels in both streams. For a single tubeside pass with
one or more tube rows, the thermal effectiveness formula is different from that of the basic unmixed–
unmixed case. Thermal relations for single-pass tube rows arrangements are discussed next.

TABLE 2.4
Thermal Effectiveness Relations for Basic Cases
Flow Arrangement
Equation
No./
Reference General Formula Value for R = 1 and Special Cases
1
2
Parallelflow; stream symmetric
T1 P
e
R
R
=
−
+
− +
1
1
NTU(1 )
P e R
e R
P R
= − =
= − =
= =
−
1
2
1
0
50 1
[ ]
%max
( 2NTU)
NTO
for 1
1 for
for
−
1
2
Counterflow; stream symmetric
T2 P
e
Re
R
R
=
−
−
−
−
1
1
NTU(1 )
NTU(1 )
−
−
P R
e R
=
+
=
= − =−
NTU
NTU
for
forNTU
1
1
1 0
1
2
T3 [21] P
R
e
m
e
m
m
m
k
R
m
m
k
= −








−


− −
=
∑ ∑
1
1 1
0
NTU
NTU RNTU
!
NTU
=0
NTU
!
( )













=
=
∞
∑k
R
0
1For this equation holds.,
T4 [22] ε = − +

−
−
−
1 2
1
0 1e I C C I C
C
C
C I
C[ (
( ) ( * )
*
*
* (
1+ *)NTU]
n/2
n
NTU * * 2NTU
2 NNTU
n
C* )
=
∞
∑



2
Crossflow; both the fluids unmixed;
stream symmetric
For C* = 1.
ε = − + 
−
1 0 1e I I2NTU
2NTU 2NTU( ) ( )
T5 [23] ε = − − −








1 1
0 22
0 78
exp
*
[exp( * ) ]
.
.NTU
NTU
C
C
Crossflow; one fluid mixed
and the other fluid unmixed (1)
weaker (Cmin) fluid mixed;
(2) stronger (Cmax) fluid mixed
T6
Weaker (Cmin) fluid mixed P e1
1
1= − − − −
( )NTU
e
P1 = [1 − exp(−K/R)]
K = 1 − exp(−RNTU)
1 1
2 2
T7 Stronger (Cmax) fluid mixed
P
KR
R
1
1
=
− −[ exp( )]
K = 1 − exp(−NTU)
P e1
1
1= − − − −
( )e NTU
1
2
Crossflow; mixed–mixed flow;
stream symmetric same as J1–∞
P
K
R
K
P
K
=
+ −




=
−
1
1 1
1
2 1
1 2 1NTU NTU
K1 = 1 − e(–NTU)
K2 = 1 − e(–RNTU)
T8
Note: P2 can be found using Equation 2.55;
I0, I1 and In are modified Bessel functions of the first kind.

1.0
0.9
0.8
0.7
0.6
0.5
0.4
P,Thermaleffectiveness
0.3
0.2
0.1
0.0
0.1 0.2 0.3 0.4
(a) NTU
0.5 1.0 2.0
2.0
1.8
1.6
1.4
1.2
0.1
0.2
0.3
0.4
0.5
0.6
0.8
0.9
1.0
R
=
0
2.5
3.0
3.0
4.0
4.0
5.0
5.0
10.0
10.0
0.7
3.0
1.0
NTU
0.9
0.8
0.7
0.6
10.0
5.0
4.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.5
0.1 0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
P, Thermal eﬀectiveness(b)
F,Correctionfactor
0.6
0.6
0.7
0.7
0.8
0.8
0.9 1.0
1.0
1.25
1.50
1.75
2.0
2.5
3.0
4.05.0
0.9
FIGURE 2.6 (a) Thermal effectiveness chart—parallelflow; stream symmetric, R–P–NTU chart (as per
Equation T1, Table 2.4); (b) parallelflow; stream symmetric, F–R–P–NTU chart; F as a function of P for
constant R (solid lines) and constant NTU (dashed lines) (Equation T1, Table 2.4).

1.0
0.9
0.8
0.7
0.6
P1,Thermaleffectiveness
0.5
0.4
0.3
0.2
0.1
0.0
0.1 0.2 0.3 0.4 0.5
NTU
1 2 3 4 5 10
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
R
=0
1.0
0.5
FIGURE 2.7 Thermal effectiveness chart—counterflow; stream symmetric, R–P–NTU chart (as per
Equation T2, Table 2.4).
1.00
0.2
0.4
0.6
0.8
1.0
1.2
1.4
2.5
3.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
10.0
5.0
1.6
1.8
2.0
0.95
0.90
0.85
0.80
0.75
0.70
F,Correctionfactor
P, Thermal effectiveness
0.65
0.60
0.55
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
2.5
0.1
4.0NTU
FIGURE 2.8 Thermal effectiveness chart—crossflow; both the fluids unmixed; stream symmetric; F–R–P–
NTU chart; F as a function of P for constant R (solid lines) and constant NTU (dashed lines) (as per Equation T3,
Table 2.4).

2.6.3.4.1 Single Tubeside Pass, N Rows per Pass, Both Fluids Unmixed
A common header at one end of the tubes distributes the tubeside fluid into a single pass hav-
ing N rows in parallel. A similar header at the other end collects tubeside fluid. For given ter-
minal temperatures, F increases with the number of rows per pass and the number of passes
being increased and is more sensitive to the latter. Taborek [24], Pignotti and Cordero [25], and
Pignotti [26] present values of F for a variety of crossflow configurations, applicable to air-
cooled heat exchangers.
Schedwill’s formula for the thermal effectiveness of N rows is given by [27]

P
R
Ne
i
j
K e
kj
i
j i j N
k
k
j
i
N
= −
+



=
− −
==
−
∑ ∑
1
1
1
0 01
NKR
NTU/ (NKR)( )
!
11
1
∑




























−

(2.59)
1.0
0.9
0.8
0.7
0.6
0.5
0.5 1.0
NTU
2.0 3.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
R=0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
4.0
4.0
5.0
5.0
10.0
10.0
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
FIGURE 2.9 Thermal effectiveness chart—crossflow; both the fluids unmixed; stream symmetric; R–P–
NTU chart (as per Equation T4, Table 2.4).

1.0
0.9
0.8
0.7
0.6
0.5
0.5 1.0 2.0 3.0
R
=
0
0.10.20.3
0.4
0.5
0.6
0.7
0.8
0.9
4.0 5.0 10.0
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
NTU(a)
1.75
1.25
1.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.21.4
1.61.8
2.0
3.0
4.0
5.0
10.0
2.5
1.0
0.8
0.6
0.4
0.2
1.0
0.9
0.8
0.7
0.6
0.5
0.1
0.2
0.3
NTU
0.4
0.5
0.6
0.7
0.8
0.9
1.0
2.0
2.5
3.0
4.0
5.0
P1, Thermal effectiveness
F,Correctionfactor
(b)
FIGURE 2.10 (a) Thermal effectiveness chart—crossflow: unmixed–mixed—the weaker (Cmin) fluid mixed,
R–P–NTU chart (as per Equation T6, Table 2.4); (b) F–R–P–NTU chart; F as a function of P for constant R
(solid lines) and constant NTU (dashed lines) (as per Equation T6, Table 2.4).

1.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
R
=
0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
5.0
10.0
10.0
5.0
4.0
3.0
2.0
1.0
0.5
0.4
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) NTU
0.6
1.0
0.2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
F-Correctionfactor
(b)
2.5
3.0
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.5
5.0
4.0
3.0
2.5
1.75
2.0
0.4
0.3
0.2
0.1
4.0
0.4
0.6
0.8
1.0
1.25
1.50
0.9
0.8
0.7
0.6
0.5
5.0
10.0
NTU
FIGURE 2.11 (a) Thermal effectiveness chart—crossflow: unmixed–mixed—the stronger (Cmax) fluid mixed,
ε-C*-NTU chart (as per Equation T7, Table 2.4); (b) Thermal effectiveness chart: F–R–P–NTU chart; F as a
function of P for constant R (solid lines) and constant NTU (dashed lines) (as per Equation T7, Table 2.4).

where

i
j
i
i j j





 =
−
!
( )! !

(2.60)
that is, the number of combinations of i and j taken j at a time, and

K
N
= − −



1 exp
NTU

(2.61)
By substituting N = 1, 2, 3, … in Equations 2.59 and 2.61, equations for thermal relations are
obtained for the specific arrangements by Nicole [28], and this is given in Table 2.5 (Equations T9
through T12) for one row, two rows, three rows, and four rows. For a larger number of tube rows
(for all practical purposes, when N exceeds 5), the solution approaches that of unmixed–unmixed
crossflow arrangement. Values of F for N = 1, 2, 3, 4 are shown in Figures 2.13 through 2.16 and are
always less than the basic case of unmixed–unmixed crossflow (Figure 2.8).
2.6.3.4.2 Multipass Tube Rows Cross-Counterflow Arrangements, Both Fluids Unmixed,
and Multiple Tube Rows in Multipass Tube Rows, Cross-Counterflow
Arrangements
This would apply to a manifold-type air cooler in which the tubes in one row are connected to the
next by U-bends. The solutions are based on Ref. [28]. Solutions for the 2 rows-2 pass and 3 rows-3
pass cases are based on Stevens et al. [29]. The general formula for thermal effectiveness referred to
the air side (fin side) is given by [28]

P
R
1
1
1
1
= −



ζ

(2.62)
The expressions for ζ for various cases are as follows:
1. Two-tube rows, two passes, as shown in Figure 2.17a [29]

ζ = + −




K K
e KR
2
1
2
2

(2.63a)

K = − −



1 exp
NTU
2
(2.63b)
2
1
FIGURE 2.12 Unmixed–unmixed crossflow arrangement.

TABLE 2.5
Thermal Effectiveness Relations for Tube Rows with Single Pass Arrangement
Flow Arrangement
Equation
No./
Reference
General Formula, Ref. [28]. Note: These Formulas
Are Valid for R = 1
One-tube row
1
2
T9 [28] P
R
e
K
KR
1
1
1
1
= −
= − −
−
( )
exp( NTU)
Two-tube rows
1
2
T10 [28] P
R
e RK
K
KR
1
2 21
1 1
1
2
= − +



= − −




−
( )
exp
NTU
Three-tube rows
1
2
T11 [28] P
R
e
RK K R K
K
KR
1
3
2 2 4
1
1
1
1 3 3 2
1
= −
+ − +














= − −
−
( ) ( )
exp
/
NTTU
3




Four-tube rows
1
2
T12 [28] P
R
e
RK K K R K K R K
KR
1
4
2 2 2 4 3 6
1
1
1
1 6 4 4 2 8 3
= −
+ − + + − +









−
[ ( ) ( ) ( )/





= − −K 1 exp( NTU/4)
Note: To find P2, use Equation 2.55.

1.00.90.80.70.6
1.50
1.25
1.0
0.80.60.40.2
1.0
0.9
0.8
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.75
2.0
2.5
3.0
4.0
5.06.0
0.7
0.6
0.5
0.50.40.30.20.1
NTU
FIGURE 2.14 Thermal effectiveness chart—two-tube rows; F as a function of P for constant R (solid lines)
and constant NTU (dashed lines) (as per Equation T10, Table 2.5).
1.0
0.9
0.8
0.7
0.6
1.50
1.25
1.0
0.8
0.6
0.4
0.2
1.0
0.9
0.8
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.40.3
0.2
0.1
1.75
2.0
2.5
4.05.06.0
0.7
0.6
0.5
0.5
0.4
0.3
0.2
0.1
3.0
NTU
FIGURE 2.13 Thermal effectiveness chart—one-tube row; F as a function of P for constant R (solid lines)

1.0
0.9
0.8
0.7
0.6
1.50
1.25
1.0
0.8
0.6
0.4
0.2
1.0
0.9
0.8
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.30.2
0.1
1.75
2.0
2.5
3.0
4.0
5.0
6.0
0.7
0.6
0.5
0.5
0.4
0.3
0.2
0.1
NTU
FIGURE 2.15 Thermal effectiveness chart—three-tube rows; F as a function of P for constant R (solid lines)
1.0
0.9
0.8
0.7
0.6
1.0
0.9
0.8
10.0
5.0
4.0
3.0
2.5
2.0
1.80
1.60
1.40
1.20
1.0
0.9
0.8
0.70.6
0.5
0.4
0.3
0.2
0.1
2.5
3.0
4.0
5.0
0.7
F,Correctionfactor
0.6
0.5
0.5
0.4
0.3
0.2
0.1
2.0
1.75
1.50
1.25
1.0
0.8
0.6
0.4
0.2
NTU
FIGURE 2.16 Thermal effectiveness chart—four-tube rows; F as a function of P for constant R (solid lines)

2. Three-tube rows, three passes, as shown in Figure 2.17b [29]

ζ = − − −









 + −



K
K
RK
K
e e
KKR KR
1
4
1
2
1
2
3
2

(2.64a)

K = − −



1
3
exp
NTU

(2.64b)
3. Four-tube rows, four passes, as shown in Figure 2.17c [28]

ζ = − +



 + −



 − −









 +
K K K
K
K R
K
K
e eKR
2
1
2 4
1
2
1
8
1
2
2
2 4KKR K
1
2
3
−



 (2.65a)

K = − −



1
4
exp
NTU

(2.65b)
4. Five-tube rows, five passes [28]

ζ = − + −



 − − + − − −






K K
K K
RK K K K
R
K
K
1
3
4 2 8
1
3
4
1
4 2
1
2
2 3
2 2 3 2
2













+ − +



 − −








e
K K K RK
K
KR
1
3
4
1
16
3 1
2
3 2
3




+ −



e
K
eKR KR3
4
5
1
2

(2.66a)

K = − −



1
5
exp
NTU

(2.66b)
5. Six-tube rows, six passes [28]

ζ = − + − +



 + − + − +




K
K K K K K K K K K e KR
2
1
1
2
1
8
1
3
4
5
16
1
32
2 3 4 2 3 4 2
−− − + − + − − + −










+
RK K K K K RK K K K e KR2 2 3 4 2 2 3 2
2 3 3
7
4
3
8
2 3
3
2
1
4
KK
K K K KR
K
e
KKR
2
2 2
1
2
1
8
4 1
2
1
2
3 4 2
4
4
− + −



 − −












+ −




5
6
e KR

(2.67a)
(a)
1
2 2 2
1 1
(b) (c)
FIGURE 2.17 Multipass tube rows. (a) Two rows-two pass; (b) three rows-three pass; (c) four rows-four pass.


K = − −



1
6
exp
NTU

(2.67b)
Values of F referred to the fluid outside the tubeside (air side) for N = 2, 3, 4, 5, and 6
are shown in Figures 2.18 through 2.22, respectively. The F values are always higher than
the basic case (Figure 2.8). When N becomes greater than 6, F approaches 1, that is, pure
counter current flow.
6. Multiple tube rows in multipass cross-counterflow arrangements; one fluid unmixed
throughout; other fluid (tube fluid) unmixed in each pass but mixed between passes:
a. Four rows, two passes, with two rows per pass. Tubeside fluid mixed at the header and
the other fluid is unmixed throughout, coupling in inverted order (Figure 2.23a) [28]:

P
R
R
K K RK e KKR
1
3 2 4
1
1
1
2 62
2
4 2 1
= −




= − +


 + + −
ζ
ζ
from Equation .
KK K
e
RK
KR
2 8
1
1
1
2
4
2 2
+





 −










 +( )

(2.68a)

K = −



1
4
exp Ц
NTU

(2.68b)
1.0
0.9
0.8
0.7
0.6
1.6
1.4
1.0
1.2
0.8
0.6
0.4
0.2
1.0
0.9
0.8
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.8
2.0
2.5
3.0
4.0
5.0
0.7
0.6
0.5
0.5
0.4
0.3
0.2
0.1
NTU
FIGURE 2.18 Thermal effectiveness chart—two-tube rows, two passes. Both fluids unmixed throughout;
fluid 1 inverted coupling between passes (for the flow arrangement shown in Figure 2.17a). F as a function of
P for constant R (solid lines) and constant NTU (dashed lines) (as per Equations 2.62 and 2.63).

3.0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
1.0
0.8
0.7
F,Correctionfactor
0.6
0.5
0.9
10.0
5.0
4.0
3.0
2.5
1.8
1.6
1.4
1.2
4.0
5.0
1.0
0.8
0.7
0.60.5
0.40.3
0.2
0.1
2.0
0.9
NTU
FIGURE 2.19 Thermal effectiveness chart—three-tube rows, three passes. Both fluids unmixed throughout;
fluid 1 inverted coupling between passes (for the flow arrangement shown in Figure 2.17b). F as a function of
P for constant R (solid lines) and constant NTU (dashed lines) (as per Equations 2.62 and 2.64).
0.1
0.5
0.6
0.7
0.8
0.9
1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.5 3.0 4.0
0.2 0.3 0.4
0.5 0.6 0.7 0.8 0.9 1.0
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
10.0
0.20.30.40.5
0.6
0.7
0.8
5.0
NTU
FIGURE 2.20 Thermal effectiveness chart—four-tube rows, four passes. Both fluids unmixed throughout;
fluid 1 inverted between passes (for the flow arrangement shown in Figure 2.17c). F as a function of P for con-
stant R (solid lines) and constant NTU (dashed lines) (as per Equations 2.62 and 2.65).

1.00
0.6
0.8
1.2
1.4
1.6
1.8
2.0
2.5
0.95
0.90
0.85
0.80
F,Correctionfactor
0.75
0.70
0.65
0.60
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9 1.0
3.02.5
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
5.0
4.0
1.0
0.9
0.8
0.7
0.6
0.50.40.30.2
1.0
NTU
FIGURE 2.21 Thermal effectiveness chart—five-tube rows, five passes. Both fluids unmixed throughout;
fluid 1 inverted coupling between passes. F as a function of P for constant R (solid lines) and constant NTU
(dashed lines) (as per Equations 2.62 and 2.66).
1.00
0.95
0.90
0.85
F,Correctionfactor
0.80
0.75
0.70
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.5
5.0
4.0
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.70.6
0.50.4
0.3
0.2
3.0
NTU
FIGURE 2.22 Thermal effectiveness chart—six-tube rows, six passes. Both fluids unmixed throughout;
fluid 1 inverted coupling between passes. F as a function of P for constant R (solid lines) and constant NTU
(dashed lines) (as per Equations 2.62 and 2.67).

b. Six rows, two passes, with three rows per pass. Tubeside fluid is mixed between passes,
that is, at the header, and the other fluid is unmixed throughout, coupling in inverted
order (Figure 2.23b) [26]:

P
A RA
R
1
2
2
1
=
− −
−
δ
δ
(2.69a)

A a C KR a C KR a C KR
a K
a RK K
a
= + +
= − −
= −
=
o o
o
( ) ( ) ( )
( )
( )
3 3 3
1 1
3 3 2
1 1 2 2
3
1
3
2
99
2
2 5
R K
δ = + + + + +a C KR a a C KR a a a C KR a a C KRo
2
( ) ( ) ( ) ( ) ( )o o o6 2 6 2 6 2 61 1 1
2
2 2 1 2 3 aa C KR
C z
n
z
e z
z Z
n
K
n n
z
n
2
2
4 6
1 1
2
( )
( )
!
! !
= − + + + +












=
+
−
1
11− −



exp
NTU
6

(2.69b)
Values of F for four rows, two passes (2 rows in a pass) and six rows, two passes (3 rows in a pass)
are shown in Figures 2.24 and 2.25, respectively.
2.6.4 Thermal Relations for Various TEMA Shells and Others
The thermal effectiveness relations for various TEMA shells and others are presented next, using
the following simplifying assumptions given at the beginning of this section and the additional
assumption of perfect transverse mixing of the shell fluid. Since the shellside flow arrangement is
unique with each shell type, the exchanger effectiveness is different for each shell even though the
number of tube passes may be the same. The P-NTUt or LMTD method is commonly used for the
thermal analysis of shell and tube exchangers. Therefore, thermal relation formulas and effective-
ness charts are presented as for the P-NTUt method.
1 1
2
(a) (b)
2
FIGURE 2.23 Tube rows multiples arrangement: (a) four rows-two pass; (b) six rows-two pass.

1.00.90.80.70.6
1.41.21.00.80.60.40.2
1.0
0.9
0.8
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.6 1.8
2.0
2.5
3.0
4.0
5.0
0.7
0.6
0.5
0.5
0.40.30.20.1
NTU
FIGURE 2.24 Thermal effectiveness chart—four rows-two passes with two rows per pass. One fluid is
unmixed throughout; tubeside fluid mixed between passes and in each pass unmixed; fluid 1 inverted coupling
between passes (for the flow arrangement shown in Figure 2.23a). F as a function of P for constant R (solid
lines) and constant NTU (dashed lines) (as per Equations 2.62 and 2.68).
1.00.90.80.70.6
1.41.21.00.80.60.4
1.0
0.9
0.8
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.5
0.3
0.2
0.1
1.6 1.8 2.0 2.5 3.0
0.7
0.6
0.5
0.5
F,Correctionfactor
0.4
0.30.20.1
5.0
4.0
0.4
0.6
NTU
FIGURE 2.25 Thermal effectiveness chart—six rows-two passes with three rows per pass. One fluid is
unmixed throughout; tubeside fluid mixed between passes and in each pass unmixed; fluid 1 inverted coupling
between passes (for the flow arrangement shown in Figure 2.23b). F as a function of P for constant R (solid
lines) and constant NTU (dashed lines) (as per Equations 2.62 and 2.69).

2.6.4.1 E Shell
The basic case of the E shell, one shell pass and one tube pass with parallelflow and counterflow
arrangement, is shown in Figure 2.26. For the counterflow case with more than five baffles, the F
value can be taken as 1. Thermal effectiveness charts shown in Figure 2.6 can be used for paral-
lelflow arrangement and Figure 2.7 for counterflow arrangement.
2.6.4.1.1 Multipassing on the Tubeside
On the tubeside, any number of odd or even passes is possible. Increasing the even number of tube
passes from two to four, six, etc. decreases the exchanger effectiveness slightly, and in the limit
when the number of tube passes approaches infinity with one shell pass, the exchanger effectiveness
approaches that for a single-pass crossflow exchanger with both fluids mixed. The odd number of
tube passes per shell has slightly better effectiveness when the shell fluid flows countercurrent to
E1–2
E1–4
E1–3
2
2
1
1
1
1
1
1
1
1
2
2
22
22
CounterflowParallelflow
FIGURE 2.27 Common tube pass arrangement for E1–2, E1–4, and E1–3 shells.
Counterflow
Parallelflow
FIGURE 2.26 E shell single-pass arrangement—parallelflow/counterflow. (Note: For a large number of seg-
mental baffles, the flow approaches true parallelflow and counterflow.)

the tube fluid for more than half the tube passes. However, this is an uncommon design and may
result in structural and thermal problems in manufacturing and design. Common tubeside multipass
arrangements for TEMA E1–2, E1–3, and E1–4 shells are shown in Figure 2.27.
2.6.4.1.2 Even Number of Tube Passes
One shell pass and two tube passes as shown in Figure 2.4 using a U-tube bundle is one of the most
common flow arrangements used in the single-pass TEMA E shell. The heat exchanger with this
arrangement is also simply referred to as a conventional 1–2 heat exchanger. If the shell fluid is
idealized as well mixed, its temperature is constant at any cross section. In this case, reversing the
tube fluid flow direction will not change the idealized temperature distribution and the exchanger
thermal effectiveness. Possible flow patterns of the E1–2 shell were already shown in Figure 2.4. This
is referred as “stream symmetric.”
The 1–2 and 1–4 cases were solved long ago by Bowman [11], Underwood [12], and Nagle [30].
The l–N geometry for even number of passes was solved by Baclic [31]. The thermal effectiveness
formula for the E1–2 case is given by Equation T13 in Table 2.6 and the thermal effectiveness chart is
given in Figure 2.28 along with Fmin curve. The thermal effectiveness formulas for 4 and N tubeside
passes are given by Equations T14 and T15, respectively. The thermal effectiveness chart for the
E1–4 case is shown in Figure 2.29, and this figure may be used for even N ≥ 6 cases also without loss
of much accuracy. Alternate relation (approximate) to find out F factor for even number of tubeside
passes of E Shell (E1–2, E1–4, E1–6, E1–2n) is given (Equation 2.70) as follows:

F
R
P
PR
R
P R R
P R R
=
+
−
−






− + − +
− + + +
2
2 0 5
1
1
1
2 1 1
2 1 1
ln
( 1) ln−
[ ( ) ]
[ (
.
22 0 5
) ].







(2.70)
2.6.4.1.3 Odd Number of Tube Passes
With the TEMA E shell, an odd number of tube passes can have both parallelflow and counterflow
arrangements. The thermal effectiveness relations for overall parallelflow and counterflow arrange-
ments are discussed next.
In an E1–3 overall counterflow arrangement, two tube passes are in counterflow and one tube pass
is in parallelflow, whereas in an E1–3 overall parallelflow arrangement, two tube passes are in parallel-
flow and one tube pass is in counterflow. Similarly, in an E1–5 overall counterflow arrangement, three
tube passes are in counterflow and two tube passes are in parallelflow. The flow arrangement for E1–3
is already shown in Figure 2.27 and for E1–5 is shown in Figure 2.30. Pignotti and Tamborenea [32]
obtained an analytical solution for the l−N (odd N) case and obtained effectiveness for the 1–3 and
1–5. Explicit thermal relations are given by Pignotti [18] for E1–3 parallelflow and counterflow cases.
For N = 3. Thermal effectiveness formulas for E1–3 parallelflow arrangement are given by
Equation T16 and for E1–3 counterflow arrangement by Equation T17 in Table 2.7. The thermal effec-
tiveness chart for E1–3 counterflow arrangement is given in Figure 2.31.
For N = 5. For the overall counterflow arrangement or opposite end case, the thermal effectiveness
is given by Equation T18 in Table 2.8 and the thermal effectiveness chart is given in Figure 2.32.
For the overall parallelflow arrangement or same end case, the configuration can be obtained
from that of the opposite end case (T18) by just the inversion of the direction of flow of the tube
fluid, which leads to the following expression [32]:

P X1 51= −( )*

(2.71a)

TABLE 2.6
E1–3 Shell (N Even) (Referred to Tubeside)
Flow Arrangement
Equation
No./
Reference General Formula
Value for R = 1 and Special
Cases
1
2
TEMA E1–2 shell: shell
fluid mixed, tube fluid
mixed between passes;
stream symmetric
T13 [30] P
R A A
A R
=
+ +
= +
2
1
1 2
coth( NTU/2)
P =
+
1
1 2 2coth NTU/ /( )
1
2
E1–2 shell: shell fluid
divided into two
streams, individually
mixed; tube fluid
mixed between passes
Same as
J1–1 shell
Same as J1–1 shell
1
2
TEMA E1–4 shell: shell
T14 [30] P
R
R
1
2
4
2 1
4 4
4 1
=
+ +



 +










= +
( ) tanh
( )
γ
γ
γ
coth
NTU NTU
P
A B
A
B
=
+ +
=
=
4
4 5
5 4
4
[ ]
tanh( )
coth( NTU/ )
NTU/
2
1
TEMA E1–N (even N)
shell: shell fluid mixed
and tube fluid mixed
between passes
T15 [31] P
A B C
A R
B
N N
C
N
N
1
1 1
1
2
1 2
1
2
1
1
=
+ +
= + +
=
− 



= +
coth( )
coth
NTU/
NTU
1
2
RR
N
N R
N
N
2
1
1
2 2
1
2
1
2
coth
NTU
+




=
N → ∞ results in well-known single-pass
crossflow exchanger with both fluids mixed
Same as Equation T15 with
R = 1
Note: P2(Ps) = P1R1, R2 = 1/R1, NTU2 = R1NTU1; Equation 2.55.

1.00.90.80.70.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
10
Fmin
1.0
0.9
0.8
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.9
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.61.8
2.0
2.5
3.0
4.0
0.7
0.6
0.5
0.5
F,Correctionfactor
0.40.30.20.1
NTU
FIGURE 2.28 Thermal effectiveness chart—TEMA E1–2 shell; shell fluid mixed, tube fluid mixed between
passes. Stream symmetric. F as a function of P for constant R (solid lines) and constant NTU (dashed lines)
Fmin line is also shown (as per Equation T13 and Table 2.6).
1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.9
0.8
0.7
F,Correctionfactor
0.6
0.5
0.1 0.2 0.3 0.4
0.5 0.6 0.7 0.8 0.9 1.0
5.0
4.0
3.0
2.5
2.0
1.8
0.2
0.1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
5.0
1.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
NTU
FIGURE 2.29 Thermal effectiveness chart—TEMA E1–4 shell. Shell fluid mixed, tube fluid mixed between passes.
F as a function of P for constant R (solid lines) and constant NTU (dashed lines) (as per Equation T14, Table 2.6).

(a) (b)
2
2
1
1
2
2
1
1
FIGURE 2.30 Flow arrangement of E shell with one shell pass and five tube passes (E1–5). (a) Counterflow;
(b) parallelflow.
TABLE 2.7
E1–3 Shell (Referred to Tubeside)
Flow Arrangement
Equation
No./
Reference General Formula Value for R = 1
1–3 TMA E shell: two
parallelflow and one
counterflow passes; shell
mixed, tube fluid mixed
between passes
1
2
T16 [18]
P
AC B
C
A R R R E
R R
1
2
2
2
1
1 1 2
1 1
= −
+





= − + −
− − +
χ λ λ λ
χ λ λ
1 1 1
2 2
/( )( )
( )( 11 2
1 2 2 1
1 2
/ /
/ /
/
) ( )
( ) ( )
( )
2 1
1 1
3
2
R R R
B R R R R E
C R R
λ
χ λ χ λ
χ λ
+ +
= − + + + +
= − −− − +
=
= − ±
=
+ +
−
χ λ
λ δ
δ
2 1
NTU/3)
1,2
/
)/2
( )
.
(
[ ( )]
(
.
3
0 5
3
9 4 12 0
R R E
E e
R R 55
2
R
e R
χ
δ
λ
1,2
NTU/3)1,2
=
(
Same as Equation T16
with R = 1
1–3 TEMA E shell: one
parallelflow and two
counterflow passes; shell
fluid mixed between passes
1
2
T17 [18]
P
C
AC B
A R R R E
R
1 2
2
1
1 1 2
1 1
= −
+






= + − −
− + −
( )
( )( )
( )(
χ λ λ λ
χ λ
1 1 2 1
2 2
/
RR R R R
B R R R R E
C R
λ λ
χ λ χ λ
χ λ
1 2
1 2 2 1
1 2
/ /
/ /
) ( )
( ) ( )
( )
2 1
1 1
3
2
+ −
= − − − +
= − + // /
)/2
1
NTU/3)
1,2
R R R E
E e
R R
+ + +
=
= − ±
=
+ −
χ λ
λ δ
δ
2
(
( )
.
(
[ ( )]
3
0 5
3
9 4 12 0..
(
2
5
R
e R
χ
δ
λ
1,2
NTU/3)1,2
=
with R = 1 and
A
e e
= − −
+
+
−NTU NTU/
NTU)
18 2
5
9
3
(
Note: P2(Ps) = P1R1, R2 = 1/R1, NTU2 = R1NTU1; Equation 2.55.

with

X R
X R
5
5
1*( , )
( , )
NTU
NTU
=
−
(2.71b)
2.6.4.2 TEMA F Shell
For the TEMA F shell, as is usual with two tube passes, the arrangement results in pure counterflow
with F = 1. For four tube passes, the configuration would be treated as two E1–2 exchangers in series.
As the longitudinal baffle is exposed on the one side to the hot stream and on the other side to the
cold stream, there is a conduction heat exchange that reduces the thermal effectiveness and hence
the F factor has to be corrected. The effect of thermal leakage by conduction across the baffle has
been analyzed by Whistler [33] and in nondimensional form by Rozenman and Taborek [34], with
proposed baffle correction methods. The baffle correction factor based on Ref. [34] is presented in
Ref. [35].
2.6.4.3 TEMA G Shell or Split-Flow Exchanger
PossibleflowarrangementsfortheTEMAGshellareG1–1,G1–2,andG1–4.ThesolutionoftheG1–2 coun-
terflow case is due to Schindler and Bates [36] and that of the parallelflow case is due to Pignotti [18].
ThethermaleffectivenessPofthisshellwithtwotubepassesishigherthanthatoftheconventionalE1–2
exchanger for a given NTUt and R. It is also possible to have only a single pass on the tubeside, which
is stream symmetric [37]. The thermal effectiveness formula for G1–1 is given by Equation T19 in
1.0
0.9
0.8
0.7
0.6
0.5
0.1
0.2
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.2
2.5
3.0
4.05.0
0.1
1.6
1.4
1.2
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.25
1.50
1.75
2.0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
F,Correctionfactor
0.3NTU
FIGURE 2.31 Thermal effectiveness chart—TEMA E1–3 shell. One parallelflow and two counterflow passes
(overall counterflow arrangement); shell fluid mixed, tube fluid mixed between passes. F as a function of P for
constant R (solid lines) and constant NTU (dashed lines) (as per Equation T17, Table 2.7).

TABLE 2.8
Formula for E1–5 Shell and Tube Exchanger with Three Tube Two Tube Passes
in Parallelflow Arrangement; Shell Fluid Mixed, Passes (Referred to Tubeside)
where
1
2
P X R N
X X
H
H
N
1
5
2
2
13
2 2
1 5
2
= − =
= =
−
− + + −
=
( )
( )
[( ) ]
N / for
αγ β
αγ β αξ γη βξη
α 224 11 12
22 13 12
24 13 12
11 12
13 12
2
2
2
− −
= − −
= − −
= +
= +
H H
H H H
H H H
H H
H H
β
γ
ξ
η
T18 H
R R
R N
X
R R
R N
X11
1 2
2
1
1
1 2
2 2
1 1
1
1 1
1
=
+ −
+
−
− +
+
+
( )( )
( )
( )( )
( ) 2
λ λ
λ δ
λ λ
λ δ
NN
N
X
R
R
R
N
N
N
N N
X
N
N
X R
−
+
+
−
≠
=
− +
+
−
+
+
−
+
=
1
1 1
1
2 1 1
1
1
1
3
2 2 2 3
for
NTU
for
( )
11
H
R R
R N
X
R R
R N
X12
1 2
2
1
1
1 2
2
2
2
1 1
1
1 1
1
=
+ +
−
−
+ +
−
−
( )( )
( )
( )( )
( )
λ λ
λ δ
λ λ
λ δ
RR
R
R
N
X
N
R
−
≠
=
−
− =
1
1
1
12
2
2
for
NTU
for
H
R R
R N
X
R R
R N
X13
1 2
2
1
1
1 2
2
2
2
1 1
1
1 1
1
=
+ −
+
−
− +
+
−
( )( )
( )
( )( )
( )
λ λ
λ δ
λ λ
λ δ
22
1 1
1
2 1 1
1
2
1
1
3
2 2 2 3
N
X
R
R
R
N
N
N
N N
X
N
X R
+
+
−
≠
=
− +
+
−
+
−
+
=
for
NTU
for
( )
H
R R
R N
X
R R
R N
X22
1 2
2
1
1
1 2
2
2
2
1 1
1
1 1
1
=
− +
−
−
+ −
−
+
( )( )
( )
( )( )
( )
λ λ
λ δ
λ λ
λ δ
NN
N
X
R
R
R
N
N
N
N N
X
N
N
X R
−
−
−
−
≠
=
+ −
+
+
−
+
−
−
=
3
1 1
1
2 1 1
1
3
1
4
2
2
2 4
for
NTU
for
( )
11
H
R R
R N
X
R R
R N
X24
1 2
2
1
1
1 2
2
2
2
1 1
1
1 1
1
=
− +
−
−
+ −
−
−
( )( )
( )
( )( )
( )
λ λ
λ δ
λ λ
λ δ
22
1 1
1
2 1 1
1
2
1
1
4
2 2 2
4
X
N
R
R
R
N
N
N
N N
X
X
N
R
−
−
−
≠
=
+ −
+
+
−
−
−
=
for
NTU
for
( )
Sources: Pignotti, A. and Tamborenea, P.I., Trans. ASME, J. Heat Transfer, 111, 54, 1988.
Note: Expressions for δ, λ1, λ2, X1, X2, X3 and X4 are λ1,2 = − ± + −






N N
R
R
2 4
1
1
2
2
0 5
( )
.
; λ3 = 1/R; λ4 = 1/R; δ = λ1 − λ2;
X R
1
51
= e NTU/( )λ
; X R
2
52
= e NTU/( )λ
; X R
3
53
= e NTU/( )λ
; X R
4
54
= e NTU/( )λ
;
P2(Ps) can be found using Equation 2.55.

Table 2.9, and the thermal effectiveness chart is given in Figure 2.33. For the G1–2 arrangement, the
thermal relations for the parallelflow and counterflow arrangements are given by Equations T20 and
T21, respectively, and the thermal effectiveness chart for the counterflow arrangement is given in
Figure 2.34. G1–4 arrangement was analyzed by Singh et al. [38], and the thermal effectiveness chart
is given at the end of this chapter.
2.6.4.4 TEMA H Shell
The arrangement of the TEMA H shell exchanger resembles a configuration in which two TEMA
G shell exchangers are connected side by side. The solution for the TEMA H shell with 1–2 flow
arrangement was analytically derived by Kohei Ishihara and Palen [39]. It is also possible to
have only a single pass on the tubeside [40]. The thermal effectiveness relation referred to the
shellside for H1–1 is given by Equation T22 in Table 2.10, and the thermal effectiveness chart
referred to the shellside is given in Figure 2.35. For the H1–2 arrangement, the thermal rela-
tions for the parallelflow and counterflow arrangements are given by Equations T23 and T24,
respectively, and the thermal effectiveness chart for the counterflow arrangement is given in
Figure 2.36.
2.6.4.5 TEMA J Shell or Divided-Flow Shell
The use of divided-flow exchangers with one shell pass and one or more tube passes is very com-
mon. If the shellside heat transfer resistance is not a limiting factor, and entrance and exit losses
1.0
0.9
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.8
0.7
0.6
0.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
2.5
3.0
2
4.0
5.0
0.1
1.6
1.4
1.2
NTU
FIGURE 2.32 Thermal effectiveness chart—TEMA E1–5 shell. Two parallelflow and three counterflow
passes (overall counterflow arrangement); shell fluid mixed, tube fluid mixed between passes. F as a function
P for constant R (solid lines) and constant NTU (dashed lines) (as per Equation T18, Table 2.8).

are neglected, the shellside pressure loss is approximately one-eighth of that same heat exchanger
arranged as the conventional E1–2 or E1–4 exchanger. The possible flow arrangements are
1. Divided-flow shell with one tube pass. This arrangement is equivalent to the E1–2 exchanger
with unmixed shell fluid.
2. Divided-flow shell with two tube passes.
3. Divided-flow shell with four tube passes.
4. Divided-flow shell with infinite number of tube passes.
Jaw [41] analyzed the cases with two and four tube passes. Extending the number of tube passes
to infinity, the case becomes identical to that of mixed–mixed crossflow, as derived by Gardner
[42a]. Divided flow shell with one tube pass arrangement is equivalent to E1–2 exchanger with
TABLE 2.9
G Shell (Referred to Tubeside)
Flow Arrangement
Equation
No./
Value for R = 1 and Special
Cases
1
2
1–1 G shell: tube fluid split
into two streams; shell fluid
mixed. Stream symmetric
T19 [37] P
R
A B AB R AB R
A
e
R R
B
D
D
R
= + − + +
=
−
+
=
−
−
−
1
1 1
1
1
1
1
2
[ ( ) ]
( )
( )
(
/
/
NTU(1+ )/2
//
e NTU /
R
D R
)
( )
= − −1 2
B R=
+
=
NTU
2 NTU
for 1
1
2
1–2 TEMA G shell: overall
parallelflow arrangement;
shell fluid mixed, tube fluid
T20 [18] P
B
R A R
A
R
B
R R
R
e
1
2
2
2
0 5
4 2 1
2 1
=
−
− +
=
−
−
=
− −
+
=
−
( )
( )
( . )
( )
( )
α
α
α
β
α
/
(1 )2
NTTU(2 1
NTU(2 +1)
R
R
e
– )
4
2β =
−
For
NTU
NTU NTU2 2
NTU)
R
P
R
R R R
e R
=
=
+ −
+ +
= −
0 5
1 2
4 4
1
2
.
( )
(
β
β
1
2
1–2 TEMA G shell: overall
counterflow arrangement;
shell fluid mixed, tube fluid
T21 [36] P
B
R A B R
A
R
B
R R
R
e
1
2
2
2
1
0 5
4 2 1
2 1
=
−
+ +
=
− −
+
=
− +
−
=
−
( )
( )
( )
( . )
( )
( )
α
α
β
α
/
NTTU(2 +1)
4
NTU(2 1
R
R
eβ =
− – )
2
For
NTU
NTU
NTU)
R
P
R
R R
e R
=
=
+ −
+ − −
= −
0 5
1 2
4 4 1
1
2
2
.
[ ( ) ]
(
α
α
α
Note: P2(Ps) can be found using Equation 2.55.

1.00
0.2
0.3
0.95
0.90
0.85
0.80
F,Correctionfactor
0.75
0.70
0.65
0.60
0.55
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9 1.0
0.4
0.5
0.6
0.7
0.8
1.0
1.25
1.50
1.75
2.0
2.5
3.0
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.61.4
1.2
1.0
0.9
0.8
0.70.6
0.5
0.4
0.30.2
0.1
4.05.0
NTU
FIGURE 2.33 Thermal effectiveness chart—G1–1 shell. Tube fluid split into two streams with shell of mixed
fluid. Stream symmetric. F as a function of P for constant R (solid lines) and constant NTU (dashed lines)
(as per Equation T19, Table 2.9).
1.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.25
1.50
1.75
2.0
2.5
0.2
0.1
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
2.5
3.0
4.0
5.0
10.0
1.8
2.0
3.04.05.0
0.9
0.8
0.7
F,Correctionfactor
0.6
0.5
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Fmin curve
1.0
0.9
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9 1.0
NTU
FIGURE 2.34 Thermal effectiveness chart—TEMA G1–2 shell. Overall counterflow arrangement; shell fluid
mixed, tube fluid mixed between passes. F as a function of P for constant R (solid lines) and constant NTU
(dashed lines). Fmin curve is also shown (as per Equation T21, Table 2.9).

TABLE2.10
HShell(ReferredtoTubeside)
FlowArrangementEquationNo./ReferenceGeneralFormulaValueforR=1andSpecialCases
22
1
1–1Hshell:tubefluidsplitintotwo
streams;shellfluidmixed
T22[37]P
R
EBRARABRABBR
A
R
1
1
1121212
1
112
1
=+−−+−−{}
=
+
−
()()()
(ex
//
/
pp
()()
[
−+
=−−
=−
RR
BDDR
De
E
R
NTU(11/2)/2
//
NTU(1Ц1/2R)/2]
112
==+−()ABABR//22
SameasEquationT22withR=0.5
B
R
R
=
+
NTU
NTU()2
1
22
1–2 TEMAHshell:overallparallelflow
arrangement;shellfluidmixed,tubefluid
mixedbetweenpasses
T23[39]P
BGR
D
BHE
GDDEDE
14
2
2222
1
4
1
11
11
=−
+
−






=++
=−+++
()
()()
()()()22
2
1
14
1
41
1
41
8
41
8
4
D
e
R
E
e
R
H
e
R
R
R
=
−
−
=
−
+
=
−
+
=−
=+
−
−
−
α
β
β
α
β
NTU
NTU
()
(11)
For
NTU/
R
P
BGR
D
D
=
=−
+
−






=−
025
1
4
1
8
14
.
()

1
22
1–2 TEMAHshell:overallcounterflow
arrangement;shellfluidmixed,tubefluid
mixedbetweenpasses
T24[39]
P
D
BRG
BHE
GDDED
1
4
2
2222
1
1
4
11
11
=−
−
−






=++
=−+++
()
()
()()
()()(EE
D
e
R
E
e
R
H
e
R
R
)
()
(
2
2
1
41
1
41
1
41
8
41
8
4
=
−
+
=
−
−
=
−
−
=+
=
−
−
−
α
β
β
α
β
NTU
NTU
RR−1)
For0.25
/
R
P
D
BG
B
GDx
D
=
=−
−
−






=++
=−
1
4
2
2
2
1
1
112
1
()
()
()()
()
(
αα
++++αα222
412//)()D
Note: P2(Ps)canbefoundusingEquation2.55.

1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.9
0.8
0.7
F,Correctionfactor
0.6
0.5
0.1
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.7
0.6
0.5
0.4
0.30.2
0.1
0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9 1.0
5.85.0
3.0
2.5
4.0
0.9
NTU
FIGURE 2.35 Thermal effectiveness chart—H1–1 shell. Tube fluid split into two streams. Shell mixed. F as a
function of P for constant R (solid lines) and constant NTU (dashed lines) referred to shellside (as per Equation
T22, Table 2.10).
1.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.25
1.50
1.75
2.0
2.5
3.0
5.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
5.0
10.0
4.0
0.9
0.8
0.7
F,Correctionfactor
0.6
0.5
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9 1.0
NTU
Fmin
FIGURE 2.36 Thermal effectiveness chart—TEMA H1–2 shell. Overall counterflow arrangement; shell fluid
mixed, tube fluid mixed between passes. F as a function of P for constant R (solid lines) and constant NTU
(dashed lines). Fmin curve is also shown (as per Equation T24, Table 2.10).

TABLE 2.11
J Shell (Referred to Tubeside)
Flow Arrangement
Equation No./
Values for R = 1 and
Special Cases
2
1
1–1 TEMA J shell: shell fluid
mixed
T25 [40] P
R
R
R
R
G
e
R
R1 1
2 1
2 1
2
2
= −
−
+
+
−






=
−
−
( )
( )
(
(
NTU
φ
φ
φ
+0.5)
0.5)−
For 0.5,
2 + NTU
1
R
P
=
= −
+ −
1 1
1 φ
2
1
1–2 TEMA J shell: shell fluid
mixed and tube fluid mixed
between passes
T26 [41] P
R A B C
A
B
R
R
R
R
R
1
2
2
1 2 1 2 1
1
1
1
1
=
+ + − +
=
+
−
=
−
+
+
[ ( )]
( )/
λ λ
φ
φ
φ
φ
λ
φ
λ
λ
λ
λ
λ
1+
11
1
( 1)
φ −






= +
−
=
=
+
−
R
R
R
C
e
R
R
λ
λ
λ
λφ
φ
φ
λ
1
1
1 4
2
2
2
/
NTU
2
1
1–4 J shell: shell fluid mixed and
tube mixed between passes
T27 [41] P
A R B C D
A
B
C
R
R
R
R
1
1 2
4
1 4 1 2 1
2
1
1
1
=
+ + + − +
=
+
=
+
−
=
+
[ ( )]
( )/
λ λ
φ
φ
φ
φ
φ
φ
λ
λ
λ
λ
−−
+
+
−






= +
−
=
=
+
−
1
1
1
1
1
1
1 16
4
1 2
2
λ
φ
φ
λφ
φ
φ
λ
λ
λ
λ
λ
R
R
R
R
D
e
R
R
( )/
NTU
(continued)

unmixed shell fluid as presented by Gardner [42b]. The difference in P is negligible for four or more
passes compared to the two passes arrangement in the region of interest, i.e., F 0.5. The thermal
effectiveness relations for J1–1, J1–2, J1–4, and J1–∞ arrangements are given by Equations T25 through
T28, respectively, in Table 2.11. The thermal effectiveness charts for J1–1, J1–2, and J1–4 are given in
Figures 2.37 through 2.39, respectively.
J Shell (Referred to Tubeside)
Flow Arrangement
Equation No./
Values for R = 1 and
Special Cases
2
1
Lime of 1–N J shell for N → ∞: shell
fluid mixed and tube fluid mixed
between passes; stream symmetric
T28 [42] P
R
e
R
R
=
−
+
−
−
=
1
1 1
1φ
φ
φ
φ
φ
( ) NTU
NTU
Note: P2(Ps) can be found using Equation 2.55.
1.0
0.9
0.8
F,Correctionfactor
0.7
0.6
0.5
0.1 0.2 0.3
10.0
0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
1.0
1.25
1.5
1.75
2.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.50.4
0.3
0.2
0.1 2.5
3.0
4.0
5.0
NTU
FIGURE 2.37 Thermal effectiveness chart—TEMA J1–1 shell. Shell fluid mixed. F as a function of P for
constant R (solid lines) and constant NTU (dashed lines) (as per Equation T25, Table 2.11).

1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0.9
0.8
F,Correctionfactor
0.7
0.6
0.5
0.1 0.2 0.3 0.4 0.5
P, Thermal effectiveness
0.6 0.7 0.8 0.9 1.0
5.0
4.0
3.0
2.0
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
4.0
5.0
0.3
0.2
0.12.5
2.0
3.0
1.8
Fmin
10.0
NTU
FIGURE 2.38 Thermal effectiveness chart—TEMA J1–2 shell. Shell fluid mixed and tube fluid mixed
between passes. F as a function of P for constant R (solid lines) and constant NTU (dashed lines), with Fmin to
avoid temperature cross (horizontal bowl-shaped curve) (as per Equation T26, Table 2.11).
1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.41.6
0.9
0.8
F,Correctionfactor
0.7
0.6
0.5
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9 1.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.90.8
0.7
0.6
0.50.4
5.0
0.3
0.2
0.1
2.5
2.0
3.0
1.8
10.0
4.0
NTU
FIGURE 2.39 Thermal effectiveness chart—TEMA J1–4 shell. Shell fluid mixed and tube fluid mixed
between passes. F as a function of P for constant R (solid lines) and constant NTU (dashed lines) (as per
Equation T27, Table 2.11).

2.6.4.6 TEMA X Shell
This exchanger is for very-low-pressure applications. For an X1–1 exchanger, the thermal effective-
ness is same as single-pass crossflow with both fluids unmixed, that is, the unmixed–unmixed case
[1]. An X1–2 crossflow shell and tube exchanger is equivalent to Figure 2.40a for both fluids unmixed
throughout with overall parallelflow (shell fluid entering at the tube inlet pass end) and Figure 2.40b
for overall counterflow (shell fluid entering at the tube exit pass end), respectively. The thermal rela-
tion formulas are discussed in Section 2.6.6.
2.6.5 Thermal Effectiveness of Multiple Heat Exchangers
A multiple exchanger assembly consists of two or more exchangers piped or manifolded together
into a single assembly with the exchangers arranged either in a parallel, series, or combination
of parallel/series arrangement. Multiple exchanger assemblies are used when the customer’s heat
transfer requirements are too large for either single piece or modular heat exchanger construction.
Sometimes, to utilize the allowable pressure drop effectively, multipassing is also employed; this in
turn enhances the thermal effectiveness. Multipassing by multiple units is possible with both com-
pact exchangers and shell and tube exchangers. With multipassing, two or more exchangers can be
coupled either in an overall parallel or in an overall countercurrent scheme as shown in Figure 2.41.
Multipassing is also possible in a single unit of a compact exchanger (Figure 2.42).
The fundamental formulas for the global effectiveness of multiple units are given next. These
equations are not valid for multiple tubeside passes of various TEMA shells. The following ideal-
izations are employed, in addition to those already listed at the beginning of this section:
1. Each pass has the same effectiveness, although any basic flow arrangement may be
employed in any pass. If each pass has the same flow arrangement, then NTU is equally
distributed between N passes, and NTU per pass (NTUp) is given by NTU/N.
2. The fluid properties are idealized as constant so that C* or R is the same for each pass. The
final results of this analysis are valid regardless of which fluid is being Cmax or Cmin.
2
(a) (b)
2
1 1
t2
T1
T2 X1–2 shell
t2
t1
t1
FIGURE 2.40 X1–2 shell arrangement equivalent with two-pass crossflow heat exchanger: (a) parallelflow;
(b) counterflow.

(a)
(b)
(c)
Fluid 1
(d) Fluid 2
(e)
Fluid 1
Fluid 1
Fluid 2
(f)
Fluid 1
Fluid 1
Fluid 2
Fluid 2
Cross-counterflow
Cross-parallelflow
FIGURE 2.41 Multipass assemblies. (a) Two-pass assembly, both the fluids unmixed in each pass and mixed
between passes; (b) three-pass assembly, one fluid is unmixed in each pass and mixed between passes, and
the other fluid is mixed throughout; (c) three-pass assembly, both the fluids unmixed in each pass and mixed
between passes; (d) three-pass counterflow assembly, both the fluids mixed between passes; (e) three-pass
parallel-crossflow assembly, fluid 1 is split in to three streams-single pass, fluid 2 in three passes mixed
between passes; (f) complex multipass assembly, fluid 2 is split into two streams and each stream is in two
passes and fluid 1 is in four passes.
FIGURE 2.42 Multipassing in the same unit.

2.6.5.1 Two-Pass Exchangers
The expression for the global effectiveness for the parallelflow case is given by Pignotti [43] in the
following equation:
P P P P P R2 1= + − +A B A B( )
(2.72)
and for the counterflow case by

P
P P P P R
RP P
2
1
1
=
+ − +
−
A B A B
A B
( )
( )
(2.73)
where
PA and PB are the thermal effectiveness of individual heat exchanger
R is the capacity rate ratio
2.6.5.2 N-Pass Exchangers
Counterflow arrangement: The effectiveness PN of an N-pass assembly, in terms of the effective-
ness Pi of each unit, which is equal for all units, has been described by Domingos [44]. For overall
countercurrent connection, the effectiveness is given by

P
PR
P
R
PR
P
R
i
i
N
i
i
NN for=
−
−
−






−
−
−






≠
1
1
1
1
1
1
( )
( )
( )
( )

(2.74a)

=
+ −
=
NP
N P
Ri
i1 1
1
( )
for

(2.74b)
where R is the heat capacity rate ratio, which is the same for the individual unit, as for the overall
assembly. Alternately, if PN is known, then the individual component effectiveness can be deter-
mined from the following formulas:

P
P R
P
R
P R
P
Ri
N
N
=
−
−
−






−
−
−






≠
1
1
1
1
1
1
1
1
( )
( )
( )
N
N
/
N
N
/ for

(2.75a)

=
− −
=
P
N P N
RN
N
for
( )1
1

(2.75b)
2.6.6 Multipass Crossflow Exchangers
Two or more crossflow units can be coupled in two or more passes either in an overall parallelflow or in
an overall counterflow arrangement. When both fluids are mixed in the interpass, mixing the resulting
flow arrangement can be differentiated only by the flow arrangements in each pass (unmixed–mixed or
mixed–mixed). However, if one fluid is unmixed throughout, the order in which the streams enter the next
pass must be differentiated. The coupling of the unmixed fluid from one pass to the other pass can be of

two types as shown in Figure 2.43 [1]: (1) identical order coupling and (2) inverted order coupling. The
coupling is referred to an identical order if the stream leaving one pass enters the next pass from the same
side as in the previous pass, as in Figure 2.43a, whereas a coupling is considered to be in an inverted order
if the stream leaving one pass enters the next pass from the opposite side of the previous pass, as in Figure
2.43b. Inverted-order coupling is very convenient for manufacturing and installation of heat exchangers.
Thermal effectiveness must decrease for constant NTU whenever irreversibilities take place, which may
be due to mixing between passes, or due to higher local temperature difference between the fluids, which
occurs when the order of the flow arrangement is inverted [28]. Some of the possible cases of two-pass
heat exchangers are shown in Figure 2.44a and 2.44b. All these cases were analyzed by Stevens et al.
[29], some analytically and others by numerical integration, whereas Baclic [3] solved all possible flow
arrangements of two passes units analytically. Multipass crossflow arrangements with complete mixing
between passes were analyzed by Domingos [44], and the formulas are also presented in Ref. [2].
2.6.6.1 Multipassing with Complete Mixing between Passes
The thermal effectiveness charts are given for the following cases of two- and three-pass cross-
counterflow arrangements with complete mixing between passes:
1. Weaker fluid is mixed in all the passes: For the two-pass arrangement (I-a or I-b of Figure
2.44a), the thermal effectiveness chart is given in Figure 2.45, and in Figure 2.46 for the
three-pass arrangements.
Continuous
fins
Return
header
Tube
fluid
Air
Air
Continuous
fins
Return
header
Tube
fluid
Tube
fluid
Tube
fluid
Pass-2Pass-1
Pass-2Pass-1
Air
Air(a) (b)
(c) (d)
FIGURE 2.43 Two-pass parallel-crossflow and counter-crossflow with both fluids unmixed throughout;
coupling of tubefluid between passes: (a) identical order coupling; (b) inverted order coupling. The cases
(c) and (d) are symbolic representations of cases (a) and (b), respectively. (Adapted from Shah, R.K. and
Mueller, A.C., Heat exchanger basic thermal design methods, in Handbook of Heat Transfer Applications,
2nd edn. [W.M. Rohsenow, J.P. Hartnett, and E.N. Ganic, eds.], McGraw-Hill, New York, pp. 4-1–4-77, 1985.)

2. Stronger fluid is mixed in all the passes: For the two-pass arrangement (I-a or I-b of Figure
2.44a), the thermal effectiveness chart is given in Figure 2.47, and in Figure 2.48 for the
three-pass arrangements.
3. Both the fluids unmixed–unmixed in all the passes: For the two-pass arrangements (IV-b
of Figure 2.44b), the thermal effectiveness chart is given in Figure 2.49, and in Figure 2.50
for the three-pass arrangements.
2.6.6.2 Two Passes with One Fluid Unmixed throughout,
Cross-Counterflow Arrangement
Some of the possible cases of two passes with one fluid unmixed throughout with cross-counterflow
arrangements are given here, and these cases were solved by Stevens et al. [29]:
1. Two-pass cross-counterflow arrangement: Fluid 1 unmixed throughout, inverted-order
coupling; fluid 2 mixed throughout (I-a of Figure 2.44a). Refer Equation T29 of Table 2.12.
2. Two-pass cross-counterflow arrangement: Fluid 1 mixed throughout; fluid 2 unmixed
throughout, inverted-order coupling (I-b of Figure 2.44a). Refer Equation T30 of Table 2.12.
Nature of Fluids Flow in between Passes and Coupling Order
Fluid Case I II III
Fluid 1 a
(a)
Unmixed,
inverted order
Unmixed,
identical order
Mixed
Mixed
Unmixed,
identical order
Unmixed,
inverted orderFluid 2 b
a
a
a
b
b
b
1
1 1
11
2
1
1
1
11
22
I
ε1a = ε2b
ε2a = ε1b
ε1a = ε2b
ε2a = ε1b
ε1a = ε2b
ε2a = ε1b
II
III
1
1
2
2
2 2 2
2
2
2 2
FIGURE 2.44 (a) Some of the possible cases of two-pass heat exchangers with one fluid mixed throughout
and the other fluid is unmixed in each pass. Note: εII-a εIII-a εI-a

Nature of Fluids Flow in between Passes and Coupling Order
Fluid
I II III
a
Unmixed,
inverted order
Unmixed,
inverted order
Unmixed,
inverted order
Unmixed,
inverted order
Unmixed,
identical order
Unmixed,
identical order
Unmixed,
identical order
Unmixed,
identical order
Mixed
Mixed
Mixed
Mixed
b a ab b
1
2
a b
IV(b)
c
Maximum thermal
effectiveness arrangement
1
1
Note:
1. Both the fluids
unmixed throughout
1. Both the fluids
unmixed in each pass
1. Both the fluids
unmixed throughout
2. Coupling between passes
is inverted order
2. Mixed between passes 2. Coupling between passes
is identical order
1
1
2 2 2 2 2
1
1
2
a
a
a
b
b
b
I
II
III
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2 2 22
2 22
222
ε1a = ε2b
ε2a = ε1b
ε1a = ε2b
ε2a = ε1b
ε1a = ε2b
ε2a = ε1b
FIGURE 2.44 (continued) (b) Some of the possible cases of two-pass heat exchangers with both the fluids
unmixed throughout except figure IV-b. Note: εIV-c εI-a εIV-b εIII-a εII-a εIV-a.

1.0
0.2
0.9
0.8
F,Correctionfactor
0.7
0.6
0.5
0.1 0.2 0.3 0.4 0.5
0.6 0.7 0.8 0.9 1.0
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.5
2.0
3.0
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.40.3
0.2
0.1
4.05.0
NTU
FIGURE 2.45 Thermal effectiveness chart—two-pass cross-counterflow arrangement with complete mix-
ing between passes. Each pass is unmixed–mixed arrangement with weaker fluid mixed (as per Equation T6
of Table 2.4 for single pass; for the flow arrangement shown in III-a or b of Figure 2.44a); F–R–P–NTU chart;
F as a function of P for constant R (solid lines) and constant NTU (dashed lines).
1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
0.9
0.8
0.7
F,Correctionfactor
0.6
0.5
0.1 0.2 0.3 0.4
0.5 0.6 0.7 0.8 0.9 1.0
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.60.5
0.4
0.3
0.2
0.1
5.0
NTU
FIGURE 2.46 Thermal effectiveness chart—three-pass cross-counterflow arrangement with complete
mixing between passes. Each pass is unmixed–mixed arrangement with weaker fluid mixed (as per Equation T6
of Table 2.4 for single pass; similar to the flow arrangement shown in III-a or b of Figure 2.44a); F–R–P–NTU
chart; F as a function of P for constant R (solid lines) and constant NTU (dashed lines).

3. Two-pass cross-counterflow arrangement: Fluid 1 unmixed throughout, identical-
order coupling; fluid 2 mixed throughout (II-a of Figure 2.44a). Refer Equation T31 of
Table 2.12.
4. Two-pass cross-counterflow arrangement: Fluid 1 mixed throughout; fluid 2 unmixed
throughout, identical-order coupling (II-b of Figure 2.44a). Refer Equation T32 of
Table 2.12.
Thermal relation formulas (T29 through T32) for these cases are given in Table 2.12, and thermal
effectiveness charts are given in Figures 2.51 through 2.54, respectively.
Comparison of thermal effectiveness of two-pass crossflow cases:
For the possible cases of two-pass exchangers shown in Figure 2.44a, the thermal reflectiveness
comparison is given by
ε ε εII-a III-a I-a of Figure 2.44a.
For NTU = 4 and C* = 1 [29], the thermal effectiveness of cases a, b, and c of Figure 2.44a is
less about 5%–7%.
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
F,Correctionfactor
0.1 0.2 0.3 0.4
0.5 0.6 0.7 0.8 0.9 1.0
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
5.0
4.0
FIGURE 2.47 Thermal effectiveness chart—two-pass cross-counterflow arrangement with complete mix-
ing between passes. Each pass is unmixed–mixed arrangement with stronger fluid mixed (as per Equation T7
of Table 2.4 for single pass; for the flow arrangement shown in III-a or b of Figure 2.44a); F–R–P–NTU
chart; F as a function of P for constant R (solid lines) and constant NTU (dashed lines).

2.6.6.3 Two Passes with Both Fluids Unmixed–Unmixed in Each Pass and One
Fluid Unmixed throughout, Cross-Counterflow Arrangement
Possible cases of two passes with both fluids unmixed–unmixed in each pass and one fluid unmixed
throughout with cross-counterflow arrangements are the following:
1. Two-pass cross-counterflow arrangement: fluid 1 unmixed throughout, inverted-order
coupling; fluid 2 unmixed in each pass and mixed between passes (II-a of Figure 2.44b).
(Refer Equation T33 of Table 2.13 [45].)
2. Two-pass cross-counterflow arrangement: fluid 1 unmixed in each pass and mixed between
passes; fluid 2 unmixed throughout, inverted-order coupling (II-b of Figure 2.44b). (Refer
Equation T34 of Table 2.13 [45].)
3. Two-pass cross-counterflow arrangement: fluid 1 unmixed throughout, identical-order
coupling; fluid 2 mixed between passes and unmixed in each pass (I-a of Figure 2.44b).
4. Two-pass cross-counterflow arrangement: fluid 1 mixed between passes and unmixed in
each pass; fluid 2 unmixed throughout, identical-order coupling (II-b of Figure 2.44b).
Thermal relation formulas (T33 through T36) for these cases are given in Table 2.13. The thermal
effectiveness chart for case 2 is given in Figure 2.55 and for case 3 in Figure 2.56.
1.00
0.95
0.90
0.85
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
5.0
0.40.3
0.2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.04.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.80
0.75
0.60
0.65
0.70
NTU
FIGURE 2.48 Thermal effectiveness chart—three-pass cross-counterflow arrangement with complete
mixing between passes. Each pass is unmixed–mixed arrangement with stronger fluid mixed (as per
Equation T7 of Table 2.4 for single pass; similar to the flow arrangement shown in to III-a or b of Figure
2.44a); F–R–P–NTU chart; F as a function of P for constant R (solid lines) and constant NTU (dashed
lines).

1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
5.0
10.0
R
=
0
0.9
0.8
0.7
0.6
0.5
0.4
NTU(a)
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
1.0 2.0 3.0 4.0 5.0 10.0
1.0
0.5
1.00
0.95
0.90
0.85
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.80.7
0.6
0.5
4.05.0
0.4
0.3
0.2
0.1
P1, Thermal effectiveness(b)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.80
0.75
0.70
NTU
FIGURE 2.49 (a) Thermal effectiveness chart—two-pass cross-counterflow arrangement with complete
mixing between passes. In each pass, both the fluids unmixed; R–P–NTU chart; (b) F–R–P–NTU chart; F as
a function of P for constant R (solid lines) and constant NTU (dashed lines) (for the flow arrangement shown
in IV-b of Figure 2.44b).

1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
4.0
5.0
1.0
R
=
0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
NTU(a)
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
1
2
3
4
5
10
0.5
1.00
0.95
0.90
0.85
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.00.9
0.80.7
0.6
0.5
2.5
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
5.0
0.4
0.3
0.2
0.1
P1, Thermal effectiveness(b)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.80
0.75
0.70
NTU
FIGURE 2.50 (a) Thermal effectiveness chart—three-pass cross-counterflow arrangement with complete
mixing between passes. In each pass, both the fluids unmixed (for the flow arrangement shown in Figure 2.41c);
R–P–NTU chart; (b) F–R–P–NTU chart; F as a function of P for constant R (solid lines) and constant NTU
(dashed lines) (for the flow arrangement shown in Figure 2.41c).

2.6.6.4 Two Passes with Both Fluids Unmixed throughout,
Cross-Counterflow Arrangement
1. Fluid 1 unmixed throughout; fluid 2 unmixed throughout. Both fluids coupling in inverted
order (IV-a of Figure 2.44b). The thermal effectiveness chart is given in Figure 2.57. This
is also equivalent to the TEMA X-shell, two passes on the tubeside with counterflow
arrangement.
TABLE 2.12
Thermal Effectiveness Relations for Two-Pass Assemblies of Heat Exchangers Arrangement
with One Fluid Unmixed Throughout
Flow Arrangement
Equation No./
Reference
Formula for Overall Cross-Counterflow
Exchangers
2 2
11
Fluid 1 unmixed throughout; fluid 2 mixed throughout
T29 [28] P
R K K
e
K e
KR
1
2
2
1
1
1
2
1
2
1
= −
+ −
















= − −( )NTU/
Equation for P2 = Equation T30
2 2
11
Fluid 1 mixed throughout; fluid 2 unmixed throughout
T30 [28] P
K K
K e
K R
R
1
2
2
1
1
2
1
2
1
= −
+ −
















= − −
e /
NTU/
( )
( )
2 2
1 1
Fluid 1 unmixed throughout, identical order; fluid 2
mixed throughout
T31 [28] P
R
e
e K R
K
KR
KR1 2
2
1
1
1
= −
−






= −
−
−
e NTU( / )
22
1 1
Fluid 1 mixed throughout; fluid 2 unmixed throughout,
identical order
T32 [28] P
e
e K R
K
K R
K R
R
1 2
2
1
1
= −
−






= −
−
−
/
/
NTU/
/
e( )
Note: For an individual case, at R = 1, P1 = P2.

1.0
0.9
0.8
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
4.05.0
0.1
0.4
0.30.2
2.0
3.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
2.5
2.0
0.7
0.6
0.5
NTU
FIGURE 2.51 Thermal effectiveness chart—two-pass cross-counterflow arrangement. Fluid 1 unmixed through-
out, inverted order coupling; fluid 2 mixed throughout. F as a function of P for constant R (solid lines) and constant
NTU (dashed lines) (as per Equation T29 of Table 2.12, for the configuration shown in I-a of Figure 2.44a).
1.0
0.9
0.8
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
5.0
0.1
0.4
0.3
0.2
4.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
3.0
2.5
2.0
0.7
0.6
0.5
NTU
FIGURE 2.52 Thermal effectiveness chart—two-pass cross-counterflow arrangement. Fluid 1 mixed through-
out; fluid 2 unmixed throughout, inverted order coupling. F as a function of P for constant R (solid lines) and con-
stant NTU (dashed lines) (as per Equation T30 of Table 2.12, for the configuration shown in I-b of Figure 2.44a).

1.0
0.9
0.8
F,Correctionfactor
10.0
5.0
4.0
0.4
0.6
0.8
1.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
4.05.03.0
0.4
0.3
0.2
0.1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.8
1.6
1.4
1.2
2.5
2.0
0.7
0.6
0.5
NTU
FIGURE 2.53 Thermal effectiveness chart—two-pass cross-counterflow arrangement. Fluid 1 unmixed
throughout, identical order coupling; fluid 2 mixed throughout. F as a function of P for constant R (solid lines)
and constant NTU (dashed lines) (as per Equation T31 of Table 2.12, for the configuration shown in II-a of
Figure 2.44a).
1.0
0.9
0.8
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
5.0
4.0
0.4
0.3
0.2
0.1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
3.0
2.5
2.0
0.2
0.7
0.6
0.5
NTU
FIGURE 2.54 Thermal effectiveness chart—two-pass cross-counterflow arrangement. Fluid 1 mixed
throughout; fluid 2 unmixed throughout, identical order coupling. F as a function of P for constant R (solid
lines) and constant NTU (dashed lines) (as per Equation T32 of Table 2.12, for the configuration shown in II-b
of Figure 2.44a).

TABLE 2.13
Thermal Effectiveness Relations for Two-Pass Assemblies of Heat Exchangers
Arrangement with Both Fluids Unmixed in the Passes
Flow Arrangement
Equation
No./
Reference
Formula for Overall
Cross-Counterflow
Exchangers
2 2
11
Fluid 1 unmixed throughout; fluid 2 unmixed in each pass and mixed
between passes
T33 [45] ε
ν
ν µ
1
/
/ /
=
1
C *
1
2
1 2
1 2 1 2
−
+






Equation for ε2 = T34
22
11
Fluid 1 unmixed in each pass and mixed between passes; fluid 2 unmixed
throughout
T34 [45] ε
ν
ν µ
1
/
/ 1/2
= −
+
1 1 2
2
1 2
2 2
1 1
Fluid 1 unmixed throughout, identical order; fluid 2 mixed between passes
and unmixed in each pass
T35 [46] ε
ν
ν ν
1
/
/ /
= −
+ −






1
1
1 2 2
2
1 2
1 2 2 2C *
22
1 1
Fluid 1 mixed between passes and unmixed in each pass; fluid 2 unmixed
throughout, identical order
T36 [46] ε
ν
ν ν
1
/
/ /
= −
+ −
1
1 2 2
1 2
2
1 2 2 2
Note: For individual case at C* = 1, ε1 = ε2.
Terms of the equations:
µ1/2
*NTU
NTU NTU
=
− + 


=
∞
=
∞
+∑∑
2 1
2 200
2
C
n m
n m
V
C
V
m
mm
m
( ) ( )!
! !
*
, nn
C
+



2
2 2
NTU NTU
,
*
(A)
Set C* = 1/C*, NTU = C*NTU and C*NTU = NTU in Equation (A), then, Equation (B) is
obtained by
µ1/2
NTU
NTU NTU
=
− + 


=
∞
=
∞
+ +∑∑
2 1
2 200
2
( ) ( )!
! !
,
*m
nn
m n
n m
n m
V
C
V 22
2 2
C *
,
NTU NTU



in which
(B)
V e I0 0 2( ) ( )( )
ξ η ξ ηξ η
, = − +
(C)
V e
n
m
I mm
n m
n
n( , ) ( )( )
ξ η
η
ξ
ξ ηξ η
=
−







 ≥− +
= −
∞
∑ 1
2 1
1
2/
(D)
ν( , ) ( ) ( ) ( )( )
a b e I a b b a I ab
a
b
b
a
a b
n
= + − −











− +
0 12 2 1/
//2
2
2
n
nI a b
=
∞
∑ 
( ) (E)

For cross-parallelflow, the thermal effectiveness is given by [45]

ε µ µ= +1/2 1/2
1
C*
(2.76)
where the terms of the equation were defined earlier. This is also equivalent to the TEMA
X-shell, two passes on the tubeside with parallelflow arrangement.
2. Fluid 1 unmixed throughout, coupling in identical order; fluid 2 unmixed throughout, cou-
pling in inverted order (III-b of Figure 2.44b).
3. Fluid 1 unmixed throughout, coupling in inverted order; fluid 2 unmixed throughout, cou-
pling in identical order (III-a of Figure 2.44b). The thermal effectiveness chart is shown in
Figure 2.58.
4. Fluid 1 unmixed throughout; fluid 2 unmixed throughout. Both fluids coupling in identical
order (I-b of Figure 2.44b).
Thermal Effectiveness Relations for Two-Pass Assemblies of Heat Exchangers
Arrangement with Both Fluids Unmixed in the Passes
Flow Arrangement
Equation
No./
Reference
Formula for Overall
Cross-Counterflow
Exchangers
The expressions for ν1/2 and ν1/2 are given by
ν1 2
0 1
1
2
1
/
NTU
NTU NTU
= − +






× + −
−
exp ( *)
( *) * ( *)
*
*
( *)
C
I C C I C
C
C
C nn
n
nI C/
NTU2
2=
∞
∑


 ( *)
(F)
ν1/2 exp
*
*
*
( *)
*
( *) ( * ) (
= −
+





× + − −
1
2
1
10 1
C
C
C
I C
C
I C C
NTU
NTU NTU CC I Cn
n
n*) ( *)−
=
∞
∑








/
NTU2
2
(G)
Various forms of Equation (E): ν– = ν–
1/1 = ν(NTU, C*NTU); ν–
1/2 = ν(NTU/2, C*NTU/2);
ν–
2/2 = ν(NTU/2, C*NTU); ν– = ν–
1/1 = ν(C*NTU,NTU); ν–
1/2 = ν(C*NTU/2, NTU/2);
ν–
2/2 = ν(C*NTU/2, NTU).
Sources: Shah, R.K. and Mueller, A.C., Heat exchanger basic thermal design methods, in Handbook of Heat Transfer
Applications, 2nd edn., W.M. Rohsenow, J.P. Hartnett, and E.N. Ganic, eds., McGraw-Hill, New York, pp. 4-1–4-
77, 1985; Baclic, B.S. and Gvozdenac, D.D., Exact explicit equations for some two- and three-pass cross-flow heat
exchanger effectiveness, in Heat Exchangers; Thermal-Hydraulic Fundamentals and Design, S. Kakac, A.E.
Bergles, and F. Mayinger, eds., Hemisphere, Washington, DC, pp. 481–494, 1981; Baclic, B.S. and Gvozdenac,
D.D., NTU relationships for inverted order flow arrangements of two-pass crossflow heat exchangers, in
Regenerative and Recuperative Heat Exchangers, Vol. 21, R.K. Shah and D.E. Metzger, eds., ASME, New York,
pp. 27–41, 1981.

The thermal effectiveness charts shown in Figures 2.57 and 2.58 were arrived at by a numerical
method as described by Stevens et al. [29]. For all these four cases, a closed-form solution is given
by Baclic [3].
For the flow arrangement of IV-c of Figure 2.44b, the most efficient case, the thermal effective-
ness for C* = 0.5 is less by 1.8% (approx.) compared to the corresponding counterflow case. The
maximum difference is in the NTU range 3.5–4.0, and for other values of NTU, the difference is
fast decreasing and approaches zero. Also, for 0.0 C* 0.5, the difference is decreasing with C*
and it is zero for C* = 0.0. For C* = 1.0, the thermal effectiveness is less by 2.9% (approx.) compared
to the corresponding counterflow case. The maximum difference is in the NTU range 4–6, and for
other values of NTU, the difference is fast decreasing and approaches to zero. Also, for 0.5 C* 1,
the difference is decreasing with decrease in C*.
1.0
0.5
1.0
0.9
0.8
0.7
0.6
0.5
0.4
NTU
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
1.0
2.0
3.0
4.0
5.0
10.0
0.5
c*=0
FIGURE 2.55 Thermal effectiveness chart—two-pass cross-counterflow arrangement. Fluid 1 unmixed in
each pass mixed between passes; fluid 2 unmixed throughout, inverted order coupling (as per Equation T34 of
Table 2.13, for the configuration shown in II-b of Figure 2.44b).

Comparison of thermal effectiveness of two-pass crossflow cases:
For the possible cases of two pass exchangers shown in Figure 2.44b, the thermal reflectiveness
comparison is given by
ε ε ε ε ε εIV c I a IV b III a II a IV a− − − − − −
For NTU = 4 and C* = 1 [29],
ε ε ε εIV c IV a IV c I a/ 1 38 and / 1 12− − − −= =. .0 0
1.0
c*=
0
0.5
0.4
1.0
0.9
0.8
0.7
0.6
0.5
0.4
NTU
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
1.0
2.0
3.0
4.0
5.0
10.0
0.5
throughout, identical order coupling; fluid 2 mixed between passes and unmixed in each pass (as per Equation T35
of Table 2.13, for the configuration shown in I-a of Figure 2.44b).

2.6.7 Thermal Effectiveness of Multiple-Pass Shell and Tube Heat Exchangers
Since the 1 – N exchanger has lower effectiveness, multipassing on the shellside may be employed
to approach the counterflow effectiveness. With this concept, the heat exchanger would have M
shell passes and N tube passes. Figure 2.59 represents few such multipassing arrangements for E1–2
and E1–3 shells [32]. But multipassing on the shellside decreases the transfer area on the shellside,
it is very difficult to fit the partition walls, and the possibility of leakage through the partition
plates cannot be ruled out. Therefore, this difficulty is overcome by multiple shells with basic shell
arrangements. A configuration with M shell passes, each one with N tube passes (similar to Figure 2.59),
is equivalent to a series assembly of M shells each with N tube passes. This is illustrated in Figure
2.60 for E1–2.
Multiple E shells in series, each with two tube passes, E1–2: The thermal effectiveness charts for
2E1–2, 3E1–2, 4E1–2, 5E1–2, and 6E1–2 are given in Figures 2.61 through 2.65.
1.0
c*=
0
0.5
1.0
0.9
0.8
0.7
0.6
0.5
0.4
NTU
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
1.0
2.0
3.0
4.0
5.0
10.0
0.5
FIGURE 2.57 Thermal effectiveness chart—two-pass cross-counterflow arrangement. Fluid 1 unmixed through-
out; fluid 2 unmixed throughout, both the fluids coupling in inverted order (equivalent to TEMA X1–2 shell with two
passes on the tubeside, counterflow arrangement) (for the configuration shown in IV-a of Figure 2.44b).

1.0
c*=
0
0.5
1.0
0.9
0.8
0.7
0.6
0.5
0.4
NTU
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
1.0
2.0
3.0
4.0
5.0
10.0
throughout; fluid 2 unmixed throughout, coupling in identical order (for the configuration shown in III-a of
Figure 2.44b).
2–6 0E
2×E1–3
2–4
2 × E1–2
2–6 SE
2×E1–3
FIGURE 2.59 Shellside multipass arrangement for E shell. (From Pignotti, A. and Tamborenea, P.I., Trans.
ASME, J. Heat Transfer, 111, 54, 1988.)

One
shell
(a)
TwoshellsThreeshellsFiveshells
SixshellsFourshellsTwoshells
(b)
(d)
(f) (g)
(e)
(c)
=
FIGURE 2.60 M-shell passes and each shell with N-tube pass is equivalent to M-shells in series, each with
N-tube passes. (a) Basic E1–2 shell; (b) and (c) two E1–2 shells in series; (d) three E1–2 shells in series; (e) four
E1–2 shells in series; (f) five E1–2 shells in series; (g) six E1–2 shells in series.
1.0
0.9
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
5.0
4.0
0.4
0.3
3.0
0.2
0.1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
2.0
1.75
1.50
1.25
1.0
0.8
0.6
0.4
2.5
0.2
0.8
0.5
0.6
0.7
NTU
FIGURE 2.61 Two E1–2 shells in series; shell fluid mixed, tube fluid mixed between passes with stream sym-
metric (for the flow arrangement shown in Figure 2.60b). F as a function of P for constant R (solid lines) and
constant NTU (dashed lines).

1.00
0.95
0.90
0.85
F,Correctionfactor
10.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
5.0
4.0
0.4
0.3
0.2
0.1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
2.0
1.75
1.5
1.25
1.0
0.8
0.6
0.4
3.0
2.5
0.20.80
0.75
0.60
0.70
0.65
NTU
FIGURE 2.62 Three E1–2 shells in series; shell fluid mixed, tube fluid mixed between passes with stream
symmetric (for the flow arrangement shown in Figure 2.60d). F as a function of P for constant R (solid lines)
and constant NTU (dashed lines).
1.00
0.95
0.90
0.85
F,Correctionfactor
10.0
0.4
0.6
0.81.01.2
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.6
0.5
5.0
0.4
0.3
0.2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.04.0
3.0
2.5
2.0
1.8
1.6
1.4
0.2
0.80
0.75
0.60
0.65
0.70
NTU
FIGURE 2.63 Four E1–2 shells in series; shell fluid mixed, tube fluid mixed between passes with stream
symmetric (for the flow arrangement shown in Figure 2.60e). F as a function of P for constant R (solid lines)
and constant NTU (dashed lines).

1.00
0.95
0.90
0.85
F,Correctionfactor
10.0
0.4
0.6
0.81.01.21.41.61.82.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.7
0.60.5
0.4
0.3
0.2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.05.0
4.0
3.0
2.5
0.2
0.80
0.75
0.60
0.70
0.65
NTU
FIGURE 2.64 Five E1–2 shells in series; shell fluid mixed, tube fluid mixed between passes with stream sym-
metric (for the flow arrangement shown in Figure 2.60f). F as a function of P for constant R (solid lines) and
1.00
0.95
0.90
0.85
F,Correctionfactor
10.0
0.4
0.6
0.8
1.01.21.41.61.82.0
5.0
4.0
3.0
2.5
2.0
1.8
1.6
1.4
1.2
1.0
0.9
0.8
0.70.6
0.50.40.30.2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.05.0
4.0
3.0
2.5
0.80
0.75
0.70
NTU
FIGURE 2.65 Six E1–2 shells in series; shell fluid mixed, tube fluid mixed between passes with stream sym-
metric (for the flow arrangement shown in Figure 2.60g). F as a function of P for constant R (solid lines) and

ACKNOWLEDGMENT
The author acknowledges Dr. R.K. Shah for providing the thermal relation formulas for various
cases of crossflow arrangements and shell and tube heat exchangers.
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Transfer, 100, 746–747 (1978).
23. Eckert, E. R. G., Heat Transfer, 2nd edn., McGraw-Hill, New York, 1959, p. 483.
24. Taborek, J., F and θ charts for crossflow arrangements, in Heat Exchanger Design Handbook, Vol. 1,
Section 1.5.3 (E.V. Schlunder, editor-in-chief), Hemisphere,Washington, DC, 1983, pp. 1.5.3-1–1.5.3-15.

25. (a) Pignotti, A. and Cordero, G. O., Mean temperature difference in multipass crossflow, Trans. ASME,
J. Heat Transfer, 105, 584–591 (1983); (b) Pignotti, A. and Cordero, G. O., Mean temperature difference
charts for air coolers, Trans. ASME, J. Heat Transfer, 105, 592–597 (1983).
26. (a) Pignotti, A., Analytical techniques for basic thermal design of complex heat exchanger configura-
tions, Heat Transfer, Eighth International Conference, San Francisco, CA, 1986; (b) Pignotti, A., Matrix
formalism for complex heat exchangers, Trans. ASME, J. Heat Transfer, 106, 352–360 (1984).
27. Schedwill, H., Thermische Auslegung von Kreuzstromwarmeaustauschern, Fortschr-Ber. VDI-Z Reihe 6
Nr. 19, VDI-Verlag, Dusseldorf, Germany, 1968.
28. Nicole, F. J. L., Mean temperature difference for heat exchanger design, Council for Scientific and
Industrial Research, Special Report Chem. 223, Pretoria, South Africa, 1972.
29. Stevens, R. A., Fernandez, J., and Woolf, J. R., Mean temperature difference in one, two, three-pass
crossflow heat exchangers, Trans. ASME, 79, 287–297 (1957).
30. Nagle,W. M., Mean temperature difference in multipass heat exchanger, Ind. Eng. Chem., 25, 604–609 (1933).
31. Baclic, B. S., 1–2N shell and tube exchanger effectiveness: A simplified Kraus-Kern equation, Trans.
32. Pignotti, A. and Tamborenea, P. I., Thermal effectiveness of multiple shell and tube pass TEMA E heat
exchangers, Trans. ASME, J. Heat Transfer, 111, 54–59 (1988).
33. Whistler, A. M., Correction for heat conduction through longitudinal baffle of heat exchanger, Trans.
ASME, 69, 683–685 (1947).
34. Rozenmann, T. and Taborek, J., The effect of leakage through the longitudinal baffle on the perfor-
mance of two pass shell exchangers, Heat Transfer–Tulsa, 1972, AIChE Symposium Series No. 118,
68, 12–20 (1972).
35. Taborek, J., F and θ charts for shell and tube exchangers, in Heat Exchanger Design Handbook, Vol. 1,
Section 1.5.2 (E.V. Schlunder, editor-in-chief), Hemisphere,Washington, DC, 1983, pp. 1.5.2-1–1.5.2-15.
36. Schlinder, D. L. and Bates, H. T., True temperature difference in a 1–2 divided flow heat exchanger, heat
transfer—Starrs, Chem. Eng. Prog. Symp. Ser., 56, 203–206 (1960).
37. Murty, K. N., Heat transfer characteristics of one- and two-pass split flow heat exchangers, Heat Transfer
Eng., 4(3–4), 26–34 (1983).
38. Singh, K. P. and Holtz, M. J., Generalization of the split flow heat exchanger geometry for enhanced heat
transfer, heat transfer—San Diego, AIChE Symp. Ser., 75, 219–226 (1979).
39. Ishihara, K. and Palen, J. W., Mean temperature difference correction factor for the TEMA H shell,
Proceedings of the Eighth International Heat Transfer Conference, San Francisco, CA (C. L. Tien, V. P.
Carey, and J. K. Ferrel, eds.), Hemisphere, Washington, DC, 1986, pp. 2709–2714.
40. Shah, R. K. and Pignotti, A., Heat exchanger basic design theory and results, A report prepared under
NSF Grant No. INT-8513531, Buffalo, NY, 1989. TEMA G1–1 exchanger results are also derived in this
report by the chain rule methodology.
41. Jaw, L., Temperature relations in shell and tube exchangers having one pass splitflow shells, Trans.
42. (a) Gardner, K. A., Mean temperature difference in multipass exchangers—Correction factors with shell
fluid unmixed, Ind. Eng. Chem., 33, 1495–1500 (1941); (b) Gardner, K. A., Mean temperature difference
in multipass exchangers, Ind. Eng. Chem., 33, 1215 -1223(1941).
43. Pignotti, A., Effectiveness of series assemblies of divided-flow heat exchanger, Trans. ASME, J. Heat
Transfer, 108, 141–146 (1986).
44. Domingos, J. D., Analysis of complex assemblies of heat exchangers, Int. J. Heat Mass Transfer, 12,
537–548 (1969).
45. Baclic, B. S. and Gvozdenac, D. D., Exact explicit equations for some two- and three-pass cross-
flow heat exchanger effectiveness, in Heat Exchangers; Thermal-Hydraulic Fundamentals and
Design (S. Kakac, A. E. Bergles, and F. Mayinger, eds.), Hemisphere, Washington, DC, 1981, pp.
481–494.
46. Baclic, B. S. and Gvozdenac, D. D., NTU relationships for inverted order flow arrangements of two-pass
crossflow heat exchangers, in Regenerative and Recuperative Heat Exchangers, Vol. 21 (R. K. Shah and
D. E. Metzger, eds.), ASME, New York, 1981, pp. 27–41.

BIBLIOGRAPHY
Cho, S. M., Basic thermal design methods for heat exchangers, in Heat Transfer Equipment Design (R. K.
Shah, E. C. Subbarao, and R. A. Mashelikar, eds.), Hemisphere, Washington, DC, 1988, pp. 23–38.
Effectiveness-Ntu Relationships for Design and Performance Evaluation of Two-Stream Heat Exchangers,
Engineering Sciences Data Unit Item No. 86018, July 1986, ESDU International Ltd., McLean, VA.
Effectiveness-Ntu Relationships for the Design and Performance Evaluation of Multi-Pass Crossflow Heat
Exchangers, Engineering Sciences Data Unit Item No. 87020, October 1987, ESDU International Ltd.,
McLean, VA.
Gardner, K. A. and Taborek, J., Mean temperature difference: A reappraisal, AIChE J., 23, 777–786 (1977).
Kays, W. M. and London, A. L., Compact Heat Exchangers, 3rd edn., McGraw-Hill, New York, 1984.

117
3 Heat Exchanger
Thermal Design
3.1 FUNDAMENTALS OF HEAT EXCHANGER DESIGN METHODOLOGY
Heat exchanger design methodology, shown in Figure 3.1, involves the following major design
considerations [1]:
1. Process/design specifications
2. Thermohydraulic design to ensure the required heat exchanger performance and to satisfy
the pressure-drop requirements for each stream
3. Flow-induced vibration in the case of shell and tube heat exchanger and individual fin-tube
and bare tube bank compact heat exchanger
4. Mechanical design to provide the mechanical integrity required by design codes and
operating conditions
5. Cost and manufacturing considerations
6. Trade-off factors and system-based optimization
Most of these considerations are dependent on each other and should be considered simultaneously to
arrive at the optimum exchanger design. Of these design considerations, items 1 and 2 are discussed
in this chapter, flow-induced vibration and mechanical design are discussed in Chapters 10 and 11,
respectively, and item 5 was discussed earlier in Chapter 1. The remaining item, trade-off factors and
system-based optimization, is not within the scope of this book.
3.1.1 Process/Design Specifications
Process or design specifications include all the necessary information to design and optimize the
exchanger for a specific application. It includes the following information [1]: (1) problem specifica-
tion; (2) exchanger construction type; (3) flow arrangement; (4) construction materials; (5) design
considerations like preferred tube sizes, tube layout pattern, maximum shell dimensions and main-
tenance consideration; (6) design standard and construction code; (7) safety and protection, high
product purity; and (8) special operating considerations such as cycling, upset conditions, etc.
3.1.1.1 Problem Specification
The problem specification involves the process parameters, operating conditions, and environment
in which the heat exchanger is going to be operated. Typical details pertaining to problem speci-
fication include design parameters such as inlet temperatures and pressures; flow rates (including
composition for mixtures); vapor quality, heat duty, allowable pressure drops, and fluctuations in the
process parameters; overall size, layout, weight, etc.; and corrosiveness and fouling characteristics
of fluid. Other factors that must be considered are
1. Climatic conditions—minimum ambient, frost, snow, hail, and humidity
2. Operating environment—maritime, desert, tropical, seismic, cyclonic, and dust
3. Site layout—proximity to buildings or other cooling equipment, prevailing wind directions,
duct allowances, length of pipe runs, and access

3.1.1.2 Exchanger Construction
Based on the problem specifications and experience, the exchanger construction type and flow arrange-
ment are first selected. Selection of the construction type depends upon the following parameters [1]:
1. Fluids (gas, liquids, or condensing/evaporating) used on each side of a two-fluid exchanger
2. Operating pressures and temperatures
Problem specification
Select construction type,
flow arrangement, surface
selection, fluid allocation,
size and shape consideration
and consider limitations,
if any
Determine surface
geometrical properties,
j and f
Thermohydraulic design
Heat transfer and
pressure drop
Is the
design
acceptable?
Yes
No
Modify the variables
Analyze for flow-induced
vibration of shellside in
the case of shell and
tube exchanger
Mechanical design
Manufacturing
considerations and
cost estimates
Trade-off factors Optimum solution
Thermophysical fluid
properties
FIGURE 3.1 Heat exchanger design methodology.

119Heat Exchanger Thermal Design
3. Fouling
4. Whether leakage or contamination of one fluid to the other is allowed or not
5. Cost and available heat exchanger manufacturing technology
3.1.1.3 Surface Selection
Compact heat exchanger: Factors that influence the surface selection include the operating pressures,
fouling, maintenance requirements, erosion, fabricability, cost, etc.
Shell and tube heat exchanger: For shell and tube exchangers, the criteria for selecting core
geometry or configurations are the desired heat transfer performance within specified pressure
drops, fouling, corrosion, maintenance, repair, cleanability by mechanical means, minimal operational
problems (flow-induced vibrations), safety, and cost; additionally, the allocation of fluids on the
shellside and the tubeside is an important consideration.
3.1.2 Thermohydraulic Design
Heat exchanger thermohydraulic design involves quantitative heat transfer and pressure-drop
evaluation or exchanger sizing. Basic thermohydraulic design methods and inputs to these analyses
are as follows.
3.1.2.1 Basic Thermohydraulic Design Methods
As discussed in Chapter 2, the ε-NTU, P-NTU, LMTD, or ψ-P method can be used for solving the
thermal design problem.
3.1.2.2 Thermophysical Properties
For heat transfer and pressure-drop analysis, the following thermophysical properties of the fluids
are needed: dynamic viscosity µ, density, specific heat cp, surface tension, and thermal conductivity k.
For the conduction wall, thermal conductivity is needed.
3.1.2.3 Surface Geometrical Properties
For heat transfer and pressure-drop analyses, at least the following surface geometrical properties
are needed on each side of a two-fluid compact heat exchanger:
• Heat transfer area, A, which includes both primary and secondary surface area if any
• Core frontal area, Afr
• Minimum free flow area, Ao
• Hydraulic diameter, Dh
• Flow length, L
• Fin thickness and fin conduction length
• Core volume, V and core dimensions L1, L2, and L3
These quantities are computed from the basic dimensions of the core and heat transfer surface.
On the shellside of a shell and tube heat exchanger, various leakage and bypass flow areas are also
needed. The procedure to compute these quantities is presented elsewhere.
3.1.2.4 Surface Characteristics
Surface characteristics for heat transfer, j, and flow friction, f, are key inputs for the exchanger heat
transfer and pressure-drop analysis, respectively. Experimental results for a variety of exchanger
surfaces are presented in Kays and London [2], and correlations in Shah and Bhatti [3]. More
references on j and f factors are furnished in Chapter 4.

3.2 DESIGN PROCEDURE
The design of heat exchangers requires the consideration of the factors just outlined. It is unlikely
that any two designers will arrive at exactly the same design for a given set of conditions, as the
design process involves many judgments while carrying out the design [4]. Gollin [4] describes the
step-by-step design procedure for a heat exchanger. Important steps in the heat exchanger design
procedure include the following:
1. Assess the heat transfer mechanisms involved
2. Select the heat exchanger class
3. Determine the construction details and select the surface geometry
4. Determine size and layout parameters keeping in mind the constraints imposed by the
purchaser/client
5. Perform preliminary thermal design known as approximate sizing
6. Perform the detailed design
7. Check the design
8. Optimize the design
9. Perform the check for flow-induced vibration in the case of shell and tube heat exchanger,
individually finned tube, and bare tube bank compact heat exchangers
10. Perform mechanical design
11. Estimate cost and finalize the design as per trade considerations
3.3 HEAT EXCHANGER DESIGN PROBLEMS
In a broad sense, the design of a new heat exchanger means the selection of exchanger construction
type, flow arrangement, tube and fin material, and the physical size of an exchanger to meet the
specified heat transfer and pressure-drop requirements. Two most common heat exchanger design
problems are the rating and sizing. For an existing exchanger, the performance evaluation problem
is referred to as the rating problem. The sizing problem is also referred to as the design problem.
Rating and sizing problems are discussed here. For more details on the rating and sizing problems,
refer to Refs. [2,5] and Bell [6].
3.3.1 Rating
Determination of heat transfer and pressure-drop performance of either an existing exchanger or an
already sized exchanger is referred to as a rating problem. Inputs to the rating problem include [1]
(1) heat exchanger construction details, (2) flow arrangement, (3) overall dimensions, (4) material
details, (5) surface geometries and surface characteristics (j and f factors), (6) fluid flow rates,
(7) inlet temperatures, and (8) fouling factors. The designer’s task is to predict the fluid outlet tempera-
tures, total heat transfer rate, and pressure drop on each side.
3.3.1.1 Rating of a Compact Exchanger
The rating problems for a two-fluid direct-transfer type compact heat exchanger that has gas as
a working fluid at least on one side is discussed briefly here, and the detailed rating of a cross-
flow and counter-crossflow exchanger is described separately. Customarily, the ε-NTU method is
employed for compact heat exchangers. Hence, the solution procedure is outlined here using the
ε-NTU method. The basic steps involved in the analysis of a rating problem are the determination of
1. Surface geometrical parameters
2. Thermophysical fluid properties
3. Reynolds numbers
4. Surface characteristics, j and f

5. Corrections to the temperature-dependent fluid properties
6. Heat transfer coefficients
7. Fin effectiveness and overall surface effectiveness
8. Thermal resistance due to conduction wall
9. Overall heat transfer coefficient
10. NTU, C*, and exchanger effectiveness, ε
11. Heat transfer rate, outlet temperatures, and pressure drop on each side
3.3.1.2 Rating of a Shell and Tube Exchanger
“Rating” implies that a specific heat exchanger is fairly completely described geometrically (with
the possible exception of the length) and the process specifications for the two streams are given.
The Bell-Delaware method is a rating method. The basic rating program of the Bell-Delaware
method is shown in Figure 3.2, and the method is described in detail in Chapter 5.
3.3.2 Sizing
In a sizing or design problem, we determine the physical size (length, width, height, and surface
area on each side) of an exchanger. Inputs to the sizing problem are the fluid inlet and outlet tem-
peratures, flow rates, fouling factors, and the pressure drop on each side. The designer’s task is to
select construction type, flow arrangement, materials, and surface geometry on each side. With the
selection of construction types and surface geometries on each side, the problem then reduces to
the determination of the core dimensions for the specified heat transfer and pressure-drop perfor-
mance. However, one can reduce the sizing problem to the rating problem by tentatively specifying
the dimensions, then predicting the performance [1]. If the computed results do not agree with the
specified values, a new size is assumed and the calculations are repeated.
3.3.2.1 Size of a Heat Exchanger
For a given heat duty, the size of the heat exchanger is a function of the following parameters:
1. Thermal effectiveness
2. Fluid flow rate
3. Secondary surface area per unit volume
4. Heat transfer surface performance parameters
5. Heat transfer augmentation devices, if any
6. Conductance ratio of the process fluids
Process specification Rating program Output
Outlet temperatures
Pressure drop
Thermohydraulic designSpecify heat duty, flow rates, temperature
and pressure for both the fluids
at inlet conditions
Thermophysical properties of
fluids at mean temperature
Tube material selection and thermal
conductivity of heat transfer surface
Fouling resistances on both sides
Exchanger configuration and geometry:
Tube layout, pitch, tube dia.
Calculate surface geometrical
parameters for core
Establish heat transfer and
pressure drop correlations
Calculate fin efficiency if
requied, film coefficients and
pressure drop on both sides
Calculate overall heat transfer
coefficient, thermal effectiveness
FIGURE 3.2 Rating of shell and tube heat exchanger (Modified from Bell, K. J., Overall design methodology for
shell and tube exchangers, in Heat Transfer Equipment Design [R. K. Shah, E. C. Subbarao, and R. A. Mashelkar,
eds.], Hemisphere, Washington, DC, 1988, pp. 131–144).

3.3.2.2 Sensitivity Analysis
In a sizing problem, sometimes one is interested in determining the sensitivity of certain vari-
ables individually. For example, how does the heat transfer vary when changing the fin density in
a compact heat exchanger with secondary surface? In such a case, one inputs a series of values of
fin densities at one time, runs the performance (rating) calculations, obtains a series of results, and
analyzes them.
3.3.2.3 Sizing of a Compact Heat Exchanger
The principle of compact heat exchanger sizing is discussed in Chapter 4.
3.3.2.4 Sizing of a Shell and Tube Heat Exchanger
Shell and tube heat exchanger design or sizing is based upon (1) design conditions, that is, fluid flow
rates, terminal temperatures, thermophysical fluid properties, and allowable pressure drop; (2) assump-
tions, heat transfer surface area, overall heat transfer coefficient, or size, length, or number of tubes;
and (3) pressure drop across the heat exchanger [7]. The design conditions are fixed by overall plant
design and determine the expected performance of the exchanger. Trial-and-error calculations of the
film coefficients are used to check the assumptions, which are also checked by an overall heat balance.
Finally, the pressure drop is calculated and compared with the allowable values. If the calculated
pressure drop is too high, a new set of assumptions is made and rechecked as before.
3.3.2.5 Heat Exchanger Optimization
The solution to the sizing problem in general is not adequate for the design of a new exchanger, since
other constraints in addition to pressure drop are imposed on the design, and the objective of the design
is to minimize the weight, volume, and heat transfer surface, and minimum pumping power, pressure
drop, or other considerations in addition to meeting the required heat transfer. This is achieved by
heat exchanger optimization. Shah et al. [8] reviewed various methods used in the literature for heat
exchanger optimization and described numerical nonlinear programming techniques.
3.3.3 Solution to the Rating and Sizing Problem
Now let us discuss the basic steps involved in the solution of the two design problems, the rating and sizing.
3.3.3.1 Rating
The basic steps involved in the solution to the rating problem are as follows [9].
ε-NTU method:
1. Compute C* and NTU from the input specifications.
2. Determine ε for known NTU, C*, and the flow arrangement.
3. Compute q from
q C t t= −ε min( )h,i c,i
and outlet temperatures from
t t
q
C
t t
q
C
h,o h,i
c,o c,i
c
= −
= +
h
and compare with those of step 2.

LMTD method:
1. Compute R from R = Ct/Cs.
2. Assume the outlet temperatures to determine P, or assume P and calculate outlet temperatures.
Also calculate LMTD.
3. Determine LMTD correction factor, F.
4. Determine q from q = UAF(LMTD).
5. Evaluate the outlet temperatures from known q, Cc, and Ch, and compare with those of step 2.
6. Repeat steps 2–5 until the desired convergence is achieved.
3.3.3.2 Solution to the Sizing Problem
In a sizing problem, U, Cc, Ch, and the terminal temperatures are specified, and the surface area
A is to be determined. Or U may be calculated from the specified convective film coefficients and
the fouling resistances. The basic steps involved in sizing by the ε-NTU and LMTD methods are
as follows [9].
ε-NTU method:
1. Compute ε from the specified inlet and outlet temperatures and calculate C*.
2. Determine NTU from known ε, C*, and the flow arrangement.
3. Calculate the required surface area A from A = (NTU)Cmin/U and from terminal temperatures.
LMTD method:
1. Compute P and R from the specified inlet and outlet temperatures.
2. Determine F from F-P curves for known P, R, and the flow arrangement.
3. Calculate the heat transfer rate q and LMTD.
4. Calculate A from A = q/[UF(LMTD)].
A trial-and-error approach is needed for the solution of the rating problem by the LMTD
method.
3.4 COMPUTER-AIDED THERMAL DESIGN
In the present computer era, thermal design is almost exclusively performed by industry using
computers. Chenoweth et al. [10], Bell [11], and Palen [12] discuss computer-aided design methods
for shell and tube exchangers. Shah [13] discusses in detail the computer-aided thermal design
methodology for both compact and shell and tube exchangers. Although there are similarities in
the overall structure of the computer programs, the details vary significantly between compact and
shell and tube exchangers. In the following sections, we discuss the structure of a computer design
method for thermal design of (1) compact heat exchangers and (2) shell and tube heat exchangers.
Salient features of this computer program are discussed.
3.4.1 Overall Structure of a Thermal Design Computer Program
The overall structure of a thermal design computer program for a compact heat exchanger consists
at a minimum of the following subroutines [13]: (1) input subroutines, (2) geometry subroutine,
(3) fluid properties subroutine, (4) surface characteristics subroutine, (5) fin efficiency subroutine,
(6) ε-NTU subroutine, (7) pressure-drop subroutine, (8) rating problem subroutine, (9) sizing problem
subroutine, (10) optimization subroutines, and (11) output subroutines.

Input subroutines: These serve (1) to feed the problem specifications/process data, and (2) to
convert the given unit from one system to other.
Geometry subroutine: The geometry subroutine calculates the various surface geometrical
parameters for commonly used surfaces. For uncommon surfaces, calculated values are fed through
the input subroutine or the terminal.
Fluid properties subroutine: This subroutine provides fluid properties for commonly used fluids
in the form of specific or generalized correlations together with heat release/added curve. For oth-
ers, they may be transferred through input data. Methods or correlations should be incorporated for
evaluating properties of fluid mixtures.
Surface characteristics subroutine: For common surfaces, j and f versus Reynolds number data
may be stored in the subroutine, or correlations may be built in. For uncommon surfaces, such
information may be transferred through the input subroutine or through the terminal.
Fin efficiency subroutine: This subroutine calculates the fin efficiency and overall surface
effectiveness for various types of extended surfaces.
ε-NTU subroutine: ε-NTU formulas for all flow arrangements of interest are built into this
subroutine. The subroutine could be used for solving both the rating and sizing problems. That
means, for a rating problem, it computes ε when NTU and C* are given, and for a sizing problem
it computes NTU when ε and C* are given.
Pressure-drop subroutine: The friction factor f is fed through the surface characteristic subroutine.
Provisions must be made to compute the pressure drop in manifolds, headers, turns, or sudden area
changes at manifold/header inlet/outlet sections.
Rating problem subroutine: Since outlet temperatures are not known initially, they are therefore
guessed, and the solution to the rating problem is iterated on the fluid properties once or twice until
the desired convergence is achieved.
Sizing problem subroutine: All of the subroutines (except the rating problem subroutine) discussed
so far are used in sizing problem. The sizing problem is solved by first determining an approximate
mass velocity G that accounts for both specified heat transfer and pressure drop. The sizing problem is
iterated on G until the desired convergence is met.
Optimization subroutines: In a sophisticated computer program, not only are the options of
solving straightforward rating and sizing problems available, but also optimization procedures are
incorporated. Such a program logically searches among feasible solutions and arrives at an optimum
objective function.
Output subroutines: These serve to print all the output results in the desired units along with
the desired input data and error messages. All important output results should be verified for their
basic validity.
3.4.1.1 Guidelines on Program Logic
Shah [13] lists several points that should be taken into account in the initial organization and writing
of the program:
1. The program should be written in a modular form containing many subroutines rather than
one big main program. This allows flexibility in thorough debugging and modification of
the program while running the program.
2. Error messages subroutines should be inbuilt that monitor the warning and minor and
major errors for the input data and throughout the problem execution.
3. All of the iterative calculations should have a maximum number of iterations specified.
4. For a sophisticated computer program to be good, it must satisfy the requirements of
individuals with diverse yet specific interests. The program should provide correct
answers and ease of use, and it will be viable only as long its developers provide user
support [10].

3.4.2 Program Structure for a Shell and Tube Exchanger
For a shell and tube exchanger, most of the structures of the subroutines mentioned so far are common
but the contents slightly vary as follows:
1. Geometry subroutine: This should include the auxiliary calculations on the shellside and
a range of geometries including the shell type, number of shells in series, number of shells
in parallel, shell diameter, tube length, baffles and baffle cut, various shellside clearances,
tube count, and nozzles.
2. Various shellside correction factors calculated for heat transfer and pressure drop.
3. The thermal effectiveness subroutine: P-NTUt relations should be built in for all
possible flow arrangements and TEMA shells, including the check for “temperature
cross.”
3.5 PRESSURE-DROP ANALYSIS, TEMPERATURE-DEPENDENT
FLUID PROPERTIES, PERFORMANCE FAILURES, FLOW
MALDISTRIBUTION, FOULING, AND CORROSION
3.5.1 Heat Exchanger Pressure-Drop Analysis
The term “pressure drop” refers to the pressure loss that is not recoverable in the circuit. The
determination of pressure drop in a heat exchanger is essential for many applications for at least
two reasons [9]:
1. The operating cost of a heat exchanger is primarily the cost of the power to run fluid-moving
devices such as pumps, fans, and blowers. This pumping power, Pp, is proportional to the
exchanger pressure drop as given by

P
M p
p =
∆
ρ

(3.1)
where
M is the mass flow rate
∆p is the pressure drop
ρ is the fluid density
2. The heat transfer rate can be significantly influenced by the saturation temperature change
for a condensing/evaporating fluid for a large pressure drop.
The principle of pressure-drop analysis for a heat exchanger is described by Kays [14] and is
extended to all types of heat exchangers. In this section, pressure-drop analysis for various types of
heat exchangers as per Ref. [10] is discussed.
3.5.1.1 Pressure-Drop Evaluation for Heat Exchangers
The pressure drop associated with a heat exchanger may be considered as having two major
components: (1) pressure drop associated with the core or matrix, and (2) pressure drop in
inlet and outlet headers, manifolds, nozzles, or ducting due to change in flow area, flow turning,
etc. In this section, core pressure drop for extended surface exchangers, regenerators, and
tubular exchangers is presented, followed by the pressure drop associated with bends and flow
turnings.

3.5.1.2 Pressure Drop through a Heat Exchanger
The pressure drop on any one side consists of pressure losses due to sudden contraction at the
core inlet, ∆p1–2, core pressure drop, ∆p2–3, and the pressure rise due to sudden expansion at the
core outlet, ∆p3–4. Therefore, the total pressure drop on any one side of the exchanger is given by

∆ ∆ ∆ ∆p p p p= + −− − −1 2 2 3 3 4

(3.2)
Pressure drop for various compact heat exchangers: Pressure drop for various compact heat
exchangers on the fin side is given in the following [9,10].
1. Plate-fin heat exchangers

∆p
p
G
p
K f
L
ri i i
i
i
m
= − + + −



 +



 − −
2
2
02
1
1 2 1
1
1
gc
c
hρ
σ
ρ
ρ
ρ
ρ
( ) ( σσ
ρ
ρ
2
0
−








K i
e )

(3.3)
1.1 For simplified formula, refer to Chapter 4, Section 4.3.3.2.
2a. Tube-fin heat exchangers (individually finned)

∆p
p
G
p
f
L
ri i i
i
i
m
= −



 +












2
2
1
2 1
1
gc 0 hρ
ρ
ρ
ρ
ρ

(3.4)
2b. Tube-fin heat exchangers (continuously finned)
∆p
p
G
p
f
L
D
G
i i i
i
i
m
= −



 +












+
′2
0
2
2
1
2 1
4 1
2gc hρ
ρ
ρ
ρ
ρ gg
where
c
2
c e
1
1 1 2
0p
K K
G G
i i
i
ρ
σ σ
ρ
ρ
( ) ( )− ′ + − − ′ −






σ = ′σ′ (3.5)
3. Regenerator both plate-fin type and randomly staked matrix—same as Equations 3.3 and 3.4.
4. For plate heat exchanger, refer to Chapter 7, Section 7.8.4.2.
5. For shell and tube heat exchanger, refer to Chapter 5, Section 5.16.6.
Generally, the core frictional pressure drop is a dominating term, accounting for about 90% or
more of the pressure drop. The entrance and exit losses are important at low values of σ (short flow
length) and L (i.e., short core), high values of Reynolds number and for gases. They are negligible
for liquids. The values of Kc and Ke are presented in Ref. [14]. The definitions of terms used in
Equations 3.3 through 3.5 are as hereunder:
1. Kc is the contraction loss coefficient. Values of Kc are given in Ref. [14] for four different
entrance flow passage geometries.
2.
1
ρ




m
is defined as

1
2
1
2
1 10
ρ ρ ρ



 = =
+
= +




m
m
i
o
v
v v
i

(3.6)

where v denotes specific volume, ρi denotes density of the fluid at inlet conditions and ρo at
the outlet conditions. For a perfect gas,

1
ρ



 =
m
lm
ave
R T
P
c

(3.7)
where
Rc is the gas constant
Pave = (pi + po)/2
Tlm = Tm ± LMTD
Here, Tm is the average temperature of the fluid on the other side of the exchanger.
3. Ke is the expansion coefficient. Values of Ke for four different flow passage geometries are
presented in Ref. [4].
4. Mass velocity G is given by

G
M
A
=
o
(3.8)
where Ao is the minimum free flow area.
5. σ′ for continuously finned tube-fin heat exchangers (Figure 4.25) is given by [15]:

′ =
−
σ
δL L L N L
L L
3 1 3 1
3 1
f

(3.9a)
and
G Gσ σ= ′ ′ (3.9b)
3.5.1.3 Shell and Tube Heat Exchangers
The pressure drop on the tubeside is determined from Equation 3.3 with proper values of f, Kc,
and Ke. However, in shell and tube exchangers, Kc and Ke for the tube flow are generally neglected
since their contribution is small compared to the losses associated with inlet and outlet headers/
channels. If U-tubes or hairpins are used in a multipass unit, additional pressure drop due to a
180° bend needs to be included. The pressure drop associated with such a bend is discussed next.
3.5.1.4 Pressure Drop due to Flow Turning
The pressure drop associated with flow turning, ∆pt is expressed in the general form as

∆p K Ut
2
=




1
2
ρ

(3.10)
where
K is the turning loss coefficient
U is the upstream velocity based on unaffected flow area
ρ is the fluid density at the bulk mean temperature
For a 180° turning, ∆pt is expressed in terms of mass velocity G by

∆p
G
gc
t
Velocity head
=
= ×
4
2
4
2
ρ

(3.11)

3.5.1.5 Pressure Drop in the Nozzles
Pressure drop in the inlet nozzle, ∆pn,i, in terms of mass velocity through nozzle, Gn is given by

∆p
G
g
n,i
n
2
c
1.0
2
1.0 Velocity head
=
= ×
ρ
(3.12)
Pressure drop in the outlet nozzle, ∆pn,e, is given by

∆p
G
gc
n,e
n
Velocity head
=
= ×
0 5
2
0 5
2
.
.
ρ
(3.13)
Total pressure drop associated with the inlet and outlet nozzles, ∆pn, is given by

∆p
G
g
n
n
c
Velocity head
=
= ×
1 5
2
1 5
2
.
.
ρ
(3.14)
where Gn is the mass velocity through nozzle.
3.5.2 Temperature-Dependent Fluid Properties Correction
One of the basic idealizations made in the theoretical solutions for Colburn j factor and friction
factor f is that the fluid properties are constant. Most of the experimental j and f data obtained
involve small temperature differences so that the fluid properties do not vary significantly. For those
problems that involve large temperature differences, the constant-property results would deviate
substantially and need to be modified [2,5]. Two schemes for such correction commonly used are
1. The property ratio method, which is extensively used for the internal flow problem
2. The reference temperature method, which is most common for the external flow problem
One of the two methods, the property ratio method, is described next. In the property ratio method,
all properties are evaluated at the bulk mean temperature, and then all of the variable properties
effects are lumped into a function. Shah’s approach [5] to temperature-dependent fluid properties
correction via the property ratio method is discussed here.
3.5.2.1 Gases
For gases, the viscosity, thermal conductivity, and density are functions of the absolute temperature T;
they generally increase with temperature. The temperature-dependent property effects for gases in
terms of Stanton number St are correlated by the following equations:

Nu
Nu
St
St
T
T
n
cp cp
w
m
= =





(3.15)


f
f
T
T
m
cp
w
m
=





(3.16)
where
Tw is the tube wall temperature
Tm is the bulk mean temperature of the fluid
where the subscript cp refers to the constant property variable and all temperatures are absolute. All of
the properties in dimensionless groups of Equations 3.15 and 3.16 are evaluated at the bulk mean temper-
ature. The values of the exponents n and m depend upon the flow regime, namely, laminar or turbulent.
Laminar flow: For laminar flow, the exponents n and m are given by [16]

n m
T
T
= = 0 0 1 00 3. , . ( )for 1 heatingw
m
(3.17)

n m
T
T
= = 0 0 0 81 1. , . ( )for 0.5 coolingw
m
(3.18)
Turbulent flow:
Gas heating: For gas heating, Sleicher and Rouse [17] recommend the following correlations:

Nu
T
T
n
=



5+ 0.012 Re (Pr + 0.29)0.83 w
m

(3.19)
where

n
T
T
= −









 +log .
.
10
0 25
0 3w
m

(3.20)
Equations 3.19 and 3.20 are valid for 0.6 Pr 0.9, 104 Re 106, 1 Tw/Tm 5, L/Dh 40. All
the fluid properties in Nu, Re, and Pr are evaluated at the bulk mean temperature. (Nu is Nusslet
number, Re is Reynolds number and Pr is Prandtl number.)
Further, m = −0.10 for 1 Tw/Tm 2.4.
Gas cooling: Kays and Crawford [18] recommend n = 0.0 and m = −0.10.
3.5.2.2 Liquids
For liquids, only the viscosity varies greatly with temperature. Thus, the temperature-dependent
effects for liquids are correlated by the following equations:

Nu
Nu
n
cp
w
m
=




µ
µ

(3.21)

f
f
m
cp
w
m
=




µ
µ
(3.22)
where
μw is the viscosity of the fluid at tube wall temperature
μm is the bulk mean temperature of the fluid

Laminar flow: For laminar flow through a circular tube, the exponents n and m are given by Deissler
[19] for heating and by Shannon and Depew [20] for cooling as

n m= − = 0 14 0 58 1. , . ( )for heatingw
m
µ
µ
(3.23)

n m= − = + 0 14 0 54 1. , . for ( )
µ
µ
w
m
cooling

(3.24)
Turbulent flow: Petukhov [21] recommends the following values for the exponents n and m:

n = − 0.11 for 0.0.8 ( )w
m
µ
µ
1 heating

(3.25)

n = − 0.25 for 40 1
µ
µ
w
m
(cooling)

(3.26)
which are valid for 2 ≤ Pr ≤ 140, 104 ≤ Re ≤ 1.25 × 105. Also,

m = 0 25 1. ( )for 0.35 heatingw
m
µ
µ
(3.27)

m = 0 24 1. ( )for 2 coolingw
m
µ
µ
(3.28)
which are valid for 1.3 ≤ Pr ≤ 10, 104 ≤ Re ≤ 2.3 × 105.
For liquid heating, Petukhov [21] correlates the variable property friction data in the following forms:

f
fcp
1
6
7 for 0.35 1= −




µ
µ
µ
µ
m
w
w
m

(3.29)
Equation 3.29 is based on the following data: 1.3 ≤ Pr ≤ 10, 104 ≤ Re ≤ 2.3 × 105, and 0.35–2
for µw/µm.
3.5.3 Performance Failures
Satisfactory performance of heat exchangers can be obtained only from units that are properly designed
and have built-in quality. Correct installation and preventive maintenance are user responsibilities. The
failure of heat exchanger equipment to perform satisfactorily may be caused by one or more factors:
1. Improper thermal design
2. Operating conditions differing from design conditions
3. Uncertainties in the design parameters
4. Excessive fouling
5. Air or gas blanketing
6. Flow maldistribution
7. Deterioration in the geometrical parameters that cause bypassing the main fluids

3.5.4 Maldistribution
A serious deterioration in performance results for a heat exchanger when the flow through the core
is not uniformly distributed. This is known as maldistribution. Maldistribution of flow takes place
when the flow is not uniformly distributed over the frontal area of the core. This is due to inher-
ent design constraints in accommodating the distributor. Due to maldistribution, the flow passages
nearer to the distributor will be flush with more fluids, whereas the passages further away will have
lean flow or starve for want of fluids. Maldistribution causes the following:
1. Thermal performance deterioration
2. Enhanced pressure drop
3. Erosive wear of flow passages with high mass velocity
Typical causes of maldistribution are the following:
1. Poor header design; for example, too small header or distributor located in one end of the
core; flow commences from one end of the core and flows perpendicular to the core
2. Blocking of fin passages due to fouling, mechanical damage of core passages
3. Damage of flow passages either at the entrance or at the exit
Maldistribution due to unfavorable nozzle location can be corrected either by relocating the nozzles
(Figure 3.3) or using deflecting vanes (for side entry nozzle), or baffle plates or perforated plates
in the header to direct the fluid uniformly through the tubes [22]. The baffle plate/perforated plate
should be installed parallel to the tubesheet.
3.5.5 Fouling
Fouling of the shellside heat transfer surfaces is common. Generally, the effects of fouling are
to reduce the leakage of fluid between baffles and tubes by blocking these gaps, and it also
results in less leakage paths [23]. Industrial practice is generally to evaluate the heat transfer in
the clean condition and apply appropriate fouling resistances (refer Chapter 9) to arrive at the
heat transfer surface area required in the fouled condition. Pressure drop is lower during com-
missioning and start-up after cleaning and gradually increases to values those predicted in the
fouled condition.
Air in
+
+
+ +
+
+
+ +
+
+
+
+ +
+
+
+ +
+
+
Water out
Original
Air inAir out Air out
Water out
Water in
Water in
FIGURE 3.3 Maldistribution due to nozzle location with 2 passes on the tubeside corrected by relocating
the nozzles.

3.5.6 Corrosion Allowance
Corrosion allowances are required for the various heat exchanger components to allow for the mate-
rial loss due to corrosion in service. Corrosion allowances are specified according to the severity
of corrosion and the corrosion resistance property of the material. Corrosion allowance is usually
specified by the purchaser and goes hand-in-hand with the material selection.
3.6 COOPERATIVE RESEARCH PROGRAMS ON HEAT EXCHANGER DESIGN
Nowadays, thermal design of most of the exchangers are carried out using commercially available soft-
ware such as those developed by cooperative research organizations like Heat transfer Research
Inc. (HTRI) and Heat transfer and Fluid Flow Services (HTFS). Other softwares are Advanced
Pressure Vessel of Computer Engineering, Inc., Blue Springs, MO, Intergraph® PV Elite™,
Houston, TX, and COMPRESS of CODEWARE, Houston, TX (www.codeware.com). These pro-
grams offer design and cost analysis for all primary heat exchanger types and incorporate multiple
design codes and standards. However, these programs are application oriented and contain com-
pany proprietary data.
3.6.1 HTRI
Heat Transfer Research, Inc. (HTRI), Alhambra, CA, is a cooperative research organization whose
membership includes many of the leading users of heat exchangers, engineering contractors, and
heat exchanger manufacturers. One of the major activities of HTRI is the development of computer
programs that enable its members to design and rate heat exchangers. The scope of HTRI software
HTRI Xchanger Suite6® includes design, rating, and simulation of (a) air-cooled heat exchangers,
heat recovery bundles, and air preheaters, (b) hairpin heat exchangers, (c) single- and two-phase
shell and tube heat exchangers, including kettle and thermosiphon, reboilers, falling film evapora-
tors, and reflux condensers, (d) plate heat exchangers, and (e) spiral plate heat exchangers; graphical
stand-alone tube layout software and flow-induced vibration analysis of individual tubes in a heat
exchanger bundle.
3.6.2 HTFS
Heat transfer and fluid flow service (HTFS) is a cooperative venture between industry and the
United Kingdom and Canadian governments. Aspen Technology, Inc., is a leading supplier of soft-
ware and services for the analysis, design, and automation of process manufacturing plants in indus-
tries such as chemical, petroleum, pharmaceuticals, electric power, pulp and paper, and metals.
Process manufacturers use AspenTech’s solutions to improve the way they design, operate, and
manage their plants. These solutions enable customers to reduce their raw material, energy, and cap-
ital expenses, meet environmental and safety regulations, improve product quality, and shorten the
time required to get new production processes on stream. The headquarters of Aspen Technologies
is at Cambridge, MA. HTFS software, Aspen, will simulate and design and rate the shell and tube
heat exchanger, crossflow heat exchanger, plate heat exchanger, etc. The scope of various HTFS
ASPEN software includes mechanical design, rating of shell, and tube heat exchangers or basic
pressure vessels, design checking and simulation of air-cooled or other crossflow heat exchangers,
of multi-stream plate-fin heat exchanger, plate heat exchangers, or brazed plate heat exchanger—it
models both single-phase and two-phase streams and multistream plate-fin heat exchanger made of
aluminum, stainless steel, and titanium. Simulation covers thermosiphon and crossflow pattern and
also detailed layer-by-layer analysis.

3.7 UNCERTAINTIES IN THERMAL DESIGN OF HEAT EXCHANGERS
A major problem constantly faced by heat exchanger designers is to predict accurately the perfor-
mance of a given heat exchanger or a system of heat exchangers for a given set of service conditions.
The problem is complicated by the fact that uncertainties exist in most of the design parameters and
in the design procedures themselves [24]. The design parameters that are used in the basic thermal
design calculations of a heat exchanger include process parameters, heat transfer coefficients, tube
dimensions (e.g., tube diameter and wall thickness), thermal conductivity of the tube material, and
thermophysical properties of the fluids. Nominal or mean values of these parameters are used in
the design calculations. However, uncertainties in these parameters prevent us from predicting the
exact performance of the unit.
The effect of the uncertainties is mostly in the performance degradation in service. Hence, there
is an imperative need to consider all the uncertainties and to critically evaluate them and correctly
predict the thermal performance of a heat exchanger. This is particularly true for critical applica-
tions. In this section, various uncertainties that influence the thermal performance and a method to
account for these uncertainties in the design calculations are presented.
3.7.1 Uncertainties in Heat Exchanger Design
Uncertainties in the design parameters are summarized by Al-Zakri et al. [24], Cho [25], and
Mahbub Uddin and Bell [26]. Various uncertainties and their reasons are the following:
1. Fluid flow rates, temperatures, pressures, and compositions vary from the design conditions.
2. Temperatures of cooling water and air used to cool process fluids vary with seasonal tem-
perature changes.
3. Physical properties of the process fluids are often poorly known, especially for mixtures.
4. Heat transfer and pressure-drop correlations from which one computes convective heat
transfer coefficients and pressure drop have data spreads around the mean values.
5. Manufacturing of heat transfer tubes and other component dimensions influencing thermal
performance does not produce precise tube dimensions.
6. Manufacturing tolerances in equipment lead to significant differences in thermohydraulic
performance between nominally identical units.
7. Fouling of heat transfer surface is poorly predictable.
8. Miscellaneous factors influence the thermal performance.
In this section, the following uncertainties are discussed:
1. Uncertainty in process conditions
2. Uncertainty in the physical properties of the process fluids
3. Flow nonuniformity
4. Nonuniform flow passages
5. Uncertainty in the basic design correlations
6. Uncertainty due to thermodynamically defined mixed or unmixed flows for crossflow heat
exchangers
7. Bypass path on the air side of compact fin-tube exchangers
8. Nonuniform heat transfer coefficient
9. Uncertainties in fouling
10. Miscellaneous effects
Items 1–3, 5, and 8–10 are common both for shell and tube exchangers and compact heat exchangers.
Items 4, 6, and 7 pertain to compact heat exchangers only.

3.7.1.1 Uncertainty in Process Conditions
Heat exchangers are designed for a nominal set of operating conditions chosen to represent a rela-
tively ideal state of a system. In general, a heat exchanger will not operate under the ideal design
conditions. Process stream flow rates, compositions, and temperatures can all be expected to vary
during the lifetime of the exchanger, and seasonal changes in weather constantly change cooling
water and air temperatures.
3.7.1.2 Uncertainty in the Physical Properties of the Process Fluids
Correlations for heat transfer coefficients and pressure drops, and the heat transfer rate equa-
tion, require values of one or more of the following physical properties: density, specific heat,
viscosity, thermal conductivity, latent heat, etc. There are substantial uncertainties in the physi-
cal properties of all but a few fluids. Uncertainties in these physical properties are due to the
following reasons [27]:
1. Measure error.
2. Extrapolation and interpolation errors—interpolation errors may be very small, whereas
extrapolation errors may substantial.
3. Estimation errors.
4. Errors in estimated temperatures and pressures.
5. Mixture properties calculated from component properties.
6. Physical properties closer to the critical temperature and pressure change rapidly and sig-
nificantly. Any attempt to get mixture properties via individual properties of components
around their critical points needs great care.
7. If the fluid is a mixture, the uncertainties will normally be larger than those for a pure
component.
3.7.1.3 Flow Nonuniformity
To obtain maximum thermal performance, the flow should be uniform across the entire frontal
area of the core. However, the flow may not be uniform due to unfavorable header design, nozzle
location, and nonuniform flow passages in the case of tube-fin and plate-fin heat exchangers. For
example, automobile radiators are usually designed with the assumptions that the cooling air is
uniformly distributed over the radiator core, and the cooling water is uniformly distributed over the
radiator tubes [28]. According to Chiou [28], these assumptions are normally not met due to these
reasons: flow nonuniformity on the cooling airside is usually due to unfavorable location of fan
with respect to the radiators and due to crowded radiator compartment. The flow nonuniformity on
the engine coolant side is the result of the unfavorable arrangement and configuration of the inlet
manifold of the coolant to the radiator. Nonuniform flow distribution adversely affects the thermal
performance and also could produce high-velocity regions leading to erosion–corrosion of flow pas-
sages. Chiou presents a mathematical method to determine the thermal effectiveness of the engine
radiator accounting for two-dimensional nonuniform fluid flow distribution on both cooling air and
engine coolant sides. Flow nonuniformity due to header design and due to unfavorable location of
radiator fan of a diesel electric locomotive are discussed next.
Flow nonuniformity due to header design: Normally the frontal area of a compact heat exchanger
is very large compared to the dimensions of the nozzles and the core depth. The large frontal area
requires turning the streams in a system of headers. The turnings have marked area changes through
the headers, leading to nonuniform flow through the core (Figure. 3.4), even though there may be
uniform flow passages. Therefore, the header design has a profound effect on the thermal performance
of the core. The main objective in designing the header is to ensure uniform distribution of fluids
over the entire frontal area of the core and to have minimum pressure drop due to flow turning.
Maldistribution due to unfavorable nozzle location can be corrected as discussed earlier. The thermal

performance degradation due to unfavorable nozzle location on the tubeside can be evaluated as dis-
cussed by Muller [29]. If the tubeside film coefficient is not controlling the overall thermal resistance,
the effect of maldistribution on the overall heat transfer coefficient will be negligible.
Maldistribution due to unfavorable location of radiator fan in a diesel electric locomotive: Flow
nonuniformity on diesel locomotive radiators is usually due to inherent problems on the air side due
to unfavorable location of the fan with respect to the radiators. In diesel locomotives, the left and
right radiators are mounted vertically; the radiator fan is mounted at the top but at the center of the
radiators, which results in nonuniform flow distribution over the radiators. Other reasons for flow
nonuniformity are crowded radiator compartment fitted with lube oil cooler and filter, and radiator
fan drives.
3.7.1.4 Nonuniform Flow Passages
For high-surface-density compact heat exchangers such as tube-fin and plate-fin units with paral-
lel fins, the identified nonuniform flow passages are due to [30] (1) nonuniform fin spacing, (2)
recurved fin, and (3) open fin. For mechanically bonded tube-fin cores, there is ample scope for
bunching of fins due to deficiency in bullet expansion, thermal fatigue, and cracking of fin collars.
Maldistribution due to nonuniform flow passages as shown in Figure 3.5 does not adversely affect
the thermal performance in the case of either turbulent flow or highly interrupted laminar flow
surfaces like offset strip fins and louvered fins, but can have a marked effect in fully developed lami-
nar flow in continuous cylindrical passage geometries, such as those employed in disk-type rotary
regenerators [31]. As a result, the reduction in Colburn j factor is substantial, with a slight reduction
in friction factor f. The theoretical analysis of this problem for low Reynolds number laminar flow
surfaces is discussed in Refs. [30–32]. To a certain extent, nonuniform flow passages due to fin
bunching of mechanically bonded cores or soldered radiator cores can be overcome by combing of
fins during maintenance schedules.
3.7.1.5 Uncertainty in the Basic Design Correlations
All of the correlations for the basic fluid flow and heat transfer mechanisms in heat exchangers show
scatter when compared to experimental data. Some processes such as nucleate boiling are only very
crudely predictable a priori [24].
FIGURE 3.4 Nonuniform flow due to flow turning in a header.
Uniform passages Nonuniform passages
FIGURE 3.5 Nonuniform flow passages of a compact heat exchanger.

3.7.1.6 Uncertainty due to Thermodynamically Defined Mixed or Unmixed
Flows for Crossflow Heat Exchangers, after Digiovanni and Webb
The thermal effectiveness of crossflow heat exchangers is evaluated for known values of NTU and
capacity rate ratio C*, from the thermodynamically defined fluid mixedness and unmixedness and/
or both through the core. The typical patterns of flow mixedness across the core are the following:
1. Unmixed–unmixed; for example, brazed plate-fin exchanger with plain fins and continuously
finned tube compact heat exchanger
2. Unmixed–mixed
3. Mixed–mixed
However, the thermodynamic definitions do not tell whether a specific geometry will provide mixed
or unmixed flow. For any values of NTU and C*, the unmixed–unmixed arrangement yields the
highest thermal effectiveness and the mixed–mixed arrangement has the lowest, and the unmixed–
mixed case offers the intermediate values.
Generally there is always some mixedness on the air side in the cases of individually finned tube
banks and offset strip fins. During the design stage if these cases are assumed to act as a thermo-
dynamically unmixed case, the actual thermal effectiveness will be less than the predicted value.
For a tube bank, the level of mixedness depends on the tube layout patterns, pitch ratios, Reynolds
number, size of the eddies in the transverse direction, etc.
Correction for partial mixing. Digiovanni and Webb [33] developed a procedure to calculate the
effectiveness of crossflow heat exchangers for partially mixed flow. To calculate the correction fac-
tor, it is necessary to provide a quantitative definition of the “percent mixing,” which is designated
as 100y. The partially mixed condition is defined by linear interpolation between the unmixed and
the mixed flow effectiveness values. If y = 0, the flow stream is unmixed, and y = 1 represents the fully
mixed stream. There are three possible cases of interest for the partially mixed condition:
1. Partially mixed flow on one stream and unmixed in the other stream
2. One stream partially mixed and the other stream mixed
3. Both streams partially mixed
They presented equations to define y for the three cases of interest. For case 1, y has been defined;
for the other two cases refer to Ref. [33].
Case 1: If the measured effectiveness of the partially mixed exchangers is εpm,u, then

y =
−
−
ε ε
ε ε
u,u pm,u
u,u m,u

(3.30)
From Equation 3.30, for y% mixedness, εpm,u is given by

ε ε ε εpm,u u,u u,u m,u= − −y( )

(3.31)
3.7.1.7 Nonuniform Heat Transfer Coefficient
The idealization that the heat transfer coefficient, h, is constant throughout its flow length is not
correct. It varies with location, the entrance length effect (due to the boundary layer development),
surface temperature, maldistribution, fouling, manufacturing imperfections, fluid physical proper-
ties, etc. [34]. Thermal performance degradation due to uncertainties in heat transfer will be felt
more in the case of highly viscous fluids and units in which phase change takes place. Temperature
effects and thermal entry length effect are significant in laminar flows; the latter effect is generally
not significant in turbulent flow except for low Prandtl number fluids. Approximate methods to
account for specific variations in heat transfer coefficient for counterflow are analyzed by Colburn [35]

and Butterworth [36], for crossflow by Sider-Tate [37] and Roetzel [38], and for 1 – 2N shell flow by
Bowman et al. [39]. These methods are summarized in Refs. [33,34]. The state of the art on nonuni-
form heat transfer coefficient is reviewed in Ref. [34].
3.7.1.8 Bypass Path on the Air Side of Compact Tube-Fin Exchangers
Owing to the construction requirements, there are various clearances on the shellside of a shell
and tube exchanger leading to various bypass paths. Modern procedures for shellside heat transfer
calculations do take care of various leakages and bypass streams while evaluating shellside perfor-
mance. In the case of finned-tube banks, the bypass paths are inevitable between (1) the sidesheet
assembly and the outermost tubes, and (2) the core assembly and the housing in which the core is
housed. The thermal performance deterioration due to these clearances can be overcome by the
following means:
1. Attach seals to the sidesheet assembly to block the clearance between the sidesheet assembly
and the outermost tubes
2. Permanently weld strips to the housing (without hindering the fitment of the core), which
will block the bypass path between the core assembly and the housing in which the core is
housed
These measures will be discussed in Chapter 4.
3.7.1.9 Uncertainty in Fouling
The influence of uncertainties inherent in fouling factors is generally greater than that of uncer-
tainties in physical properties, flow rates, or temperatures, such as in heat exchange between dirty
aqueous fluids, in which fouling resistances can completely dominate the thermal design [40].
Planned fouling prevention, maintenance, and cleaning schedules make it possible to allow lower
resistance values.
3.7.1.10 Miscellaneous Effects
Depending upon the individual design/constructional features, there exist certain miscellaneous
effects that add uncertainties on thermal performance. Such effects include stagnant regions,
radiation effects, allowance for in-service tube plugging due to leakages that cannot be corrected,
influence of brazing/soldering, etc. Compact soldered finned-tube cores and brazed PFHEs will
suffer from soldering/brazing-induced surface roughness/partial blockage due to melting of braz-
ing filler metal. This may reduce the j factor slightly but increase the f factor substantially.
3.7.2 Determination of Uncertainties
The method usually used by heat exchanger designers is to ignore in the original calculations uncer-
tainties in the design parameters. After the area has been calculated, it is multiplied by a safety factor
assigned by the designer to ensure that the exchanger will perform adequately. The safety factor is
based mostly upon the designer’s experience and judgment and can vary from 15% to 100%. Such
methods can unnecessarily add to the cost of the equipment in capital investment [24].
3.7.2.1 Computational Procedures
Buckley [41] was the first to use a statistical approach to the sizing of process equipment. His approach
was to first size the unit with nominal values of design parameters. Then, based on the assumption
that uncertainties follow the normal distribution, he determined the standard deviation for each vari-
able. From the individual uncertainty (standard deviation), its effect on the overall uncertainty of the
area was determined. Once the effects of all uncertain parameters on the overall heat transfer area are
known, the oversizing can be determined according to the desired confidence level.

Mahbub Uddin and Bell [26] presents a Monte Carlo procedure for dealing with the effect of
uncertainties on the design, performance, and operation of systems of process heat exchangers.
Cho [25] presents a simple method of assessing the uncertainties in the design of heat exchangers
assuming a Gaussian form of data distribution for “uncertain” parameters, which leads to the root
sum square (RSS) method of establishing the probability, or confidence level, that the heat exchanger
design will meet its performance requirements. This method is briefly discussed next.
Cho’s method of uncertainty analysis [25]: The degree of data spread around the mean value
may be quantified using the concept of standard deviation, σ. Suppose that the distribution of
data points for a certain parameter has a Gaussian or normal distribution. Then the procedure
to incorporate the effect of data spread into the design of a heat exchanger is as follows. For
example, consider the convective heat transfer coefficient, h, which has a data spread as shown
in Figure 3.6a. The probability of the value of h falling below the mean value is of concern.
Therefore, if one takes

X h Z X1 = − = ∞σh 2and

(3.32a)
or

Z Z Z1 = − = ∞and 2

(3.32b)
then the probability that h will attain a value greater than h
–
− Zσh is

P X h Z X e dZZ
( , )1 2
21
2
= − = ∞ = −
−
∞
∫σ
π
h
/
z
2

(3.33)
where

Z
Z X
=
−


σ

(3.34)
This probability is known as the cumulative probability or one-sided confidence level and the
numerical values are given in Ref. [25]. Here, Z indicates the degree of the design confidence level;
for example, if one desires a 90% confidence level, the value of Z becomes 1.282. This means the
value of h should be reduced to h
–
− 1.282σh to obtain a 90% level of design confidence. Due to
f f
th
X1=h– Zσh(a) (b) X2=t +Zσt
FIGURE 3.6 Normal distribution of (a) heat transfer coefficient, h, and (b) tube-wall thickness, t.

the reduction in the heat transfer coefficient, the surface area is to be increased to get the desired
thermal performance. Equations 3.32 and 3.33 are applicable to uncertain parameters whose lower
values are of design concern, like heat transfer coefficients and tube-wall thermal conductivity.
Now consider the effect of tube-wall thickness, t, which has a data spread as shown in Figure 3.6b.
The value of t greater than the mean value is of concern here. Therefore, if one takes

X X t Z1 = −∞ = +* and 2 tσ

(3.35a)
or

Z Z1 = −∞ = +and Z2

(3.35b)
then the probability that t
–
will attain a value less than t
–
+ Zσt is

P X X t Z e dZZ
z
( , )
1
1 2
2
2
2
= −∞ = + = −
−
∞
∫σ
π
t
/

(3.36)
Again, Z indicates the degree of the design confidence level. A 90% level of design confidence
requires the use of an increased thickness, t
–
+ 1.282σt in the sizing calculation. The reduction in
heat transfer rate due to increased thickness is to be compensated by increase in heat transfer sur-
face area. Equations 3.35 and 3.36 are applicable to uncertain parameters whose upper values are of
design concern, like tube-wall thickness and fouling resistance.
The effects of data spreads have been discussed for individual parameters. These individual
effects usually take place simultaneously, and the combined effect can be assessed for normally
distributed parameters, using the RSS method [25]:

∆ ∆X Xi
i
=
=
∑( )2
1
N

(3.37)
3.7.3.2 Additional Surface Area Required due to Uncertainty
The effects of data spread have been discussed for individual parameters. These individual effects usu-
ally take place simultaneously and the combined effect is assessed using the RSS method. The total
additional surface area ∆Ai required to obtain a certain level of design confidence is calculated from [25]

∆ = ∆
=
∑A Ai
i
( )2
1
N

(3.38)
3.7.3.3 Additional Pressure Drop due to Uncertainty
Equation 3.37 can also be applied to determine the additional pressure drop, ∆(∆p), required to
obtain a certain level of design confidence, as given by the following equation [25]:

∆ ∆ = ∆ ∆[ ]∑( ) ( )
N
p p i
i
2
=l

(3.39)

NOMENCLATURE
A total heat heat transfer area, m2 (ft2)
Ao minimum free flow area, m2 (ft2)
cp specific heat, J/kg °C (Btu/lbm.°F)
C specific heat of cold fluid, J/kg °C (Btu/lbm.°F)
Cc specific heat of cold fluid, J/kg °C (Btu/lbm.°F)
Ch specific heat of hold fluid, J/kg °C (Btu/lbm.°F)
C* = heat capacity rate ratio = (mcp)min/(mcp)max
Dh hydraulic diameter, (4rh), m (ft)
F LMTD correction factor
f Fanning friction factor
G mass velocity, kg/m2·s (lbm/h·ft2)
gc acceleration due to gravity or proportionality constant 9.81 m/s2 (32.17 ft/s2)
= 1 and dimensionless in SI units
h convective heat transfer coefficient, W/m2·°C (Btu/ft2 h·°F)
j Colburn heat transfer factor
Kc fluid entrance contraction coefficient
Ke fluid exit expansion coefficient
k thermal conductivity of the fluid, W/m°C (Btu/h·ft·°F)
L length in the fluid flow direction, m (ft)
L1, L2, L3 heat exchanger core dimensions of a tube bank, m (ft)
M mass flow rate of the fluid, kg/s (lbm/h)
m exponent
NTU number of transfer units,
Nu Nusselt number
n exponent
Pp fluid pumping power
p pressure, Pa (lbf/ft2)
Pr Prandtl number
Q total heat duty of the exchanger, W·s (Btu)
q heat transfer rate, W (Btu/h)
R heat capacity rate ratio of shell and tube heat exchanger fluids
Re Reynolds number
rh hydraulic radius, m (ft) = Dh/4
P thermal effectiveness of shell and tube heat exchanger
P fluid friction power
St Stanton number
T Temperature, °C (°F)
t Temperature, °C (°F)
U upstream fluid velicity, m/s (ft/s)
U overall heat transfer coefficient, W/m2·°C (Btu/h·fr2·°F)
∆p pressure drop, Pa (lbf/ft2)
ε thermal effectiveness
μm viscosity of the fliud at bulk mean temperature, kg/m·s or Pa·s (lbm/h·ft)
μw viscosity of the fliud at wall temperature, kg/m·s or Pa·s (lbm/h·ft)
ρ fluid density, kg/m3 (lbm/ft3)
β area density, m2/m3 (ft2/ft3)
∆p = pressure drop

ηo fin efficiency or the overall surface efficiency
σ = the ratio of minimum free flow area to frontal area
Subscripts
ave average
c cold
h hot
cp constant property
e exit
i inlet
lm log mean
m mean
n nozzle
o outlet
s shell
t tube
m,u mixed, unmixed
pu,u partially unmixed, unmixed
u,u unmixed, unmixed
w wall temperature conditions
1 inlet of the exchanger
2 outlet of the exchanger
min minimum
max maxim
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Subbarao, and R. A. Mashelikar, eds.), Hemisphere, Washington, DC, 1988, pp. 17–22.
2. Kays, W. M. and London, A. L., Compact Heat Exchangers, 3rd edn., McGraw-Hill, New York,
1984.
3. Shah, R. K. and Bhatti, M. S., Assessment of correlations for single-phase heat exchangers, in Two-Phase
Flow Heat Exchangers—Thermal-Hydraulic Fundamentals and Design (S. Kakac, A. E. Bergles, and
F. E. Oliveira, eds.), Kluwer Academic Publishers, London, U.K., 1988, pp. 81–122.
4. Gollin, M., Heat exchanger design and rating, in Handbook of Applied Thermal Design (E. C. Guyer,
ed.), McGraw-Hill, New York, 1984, pp. 7-24–7-36.
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Fundamentals and Design (S. Kakac, A. E. Bergles, and F. Mayinger, eds.), Hemisphere, Washington,
DC, 1981, pp. 495–536.
6. Bell, K. J., Delaware method for shellside design, in Heat Transfer Equipment Design (R. K. Shah, E. C.
Subbarao, and R. A. Mashelkar, eds.), Hemisphere, Washington, DC, 1988, pp. 145–166.
7. Cardwell, Optimum tube size for shell and tube type heat exchangers, Trans. ASME, 72, 1061–1065
(1950).
8. Shah, R. K., Afimiwala, K. A., and Mayne, R. W., Heat exchanger optimization, in Heat Transfer, Vol. 4,
Transfer Applications, 2nd edn. (W. M. Rohsenow, J. P. Hartnett, and E. N. Ganic, eds.), McGraw-Hill,
New York, 1985, pp. 4-1–4-77.
10. Shah, R. K., Heat exchanger basic design methods, in Low Reynolds Number Flow Heat Exchangers
(S. Kakac, R. K. Shah, and A. E. Bergles, eds.), Hemisphere, Washington, DC, 1983, pp. 21–71.
11. Chenoweth, J. M. and Kistler, R. S., Computer program as a tool for heat exchanger rating and design,
ASME Paper No. 76-WA/HT-4, 1976.

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design, in Low Reynolds Number Flow Heat Exchangers (S. Kakac, R. K., Shah, and A. E. Bergles, eds.),
14. Kays, W. M., Loss coefficients for abrupt changes in flow cross section with low Reynolds number flow
in single and multiple tube system, Trans. ASME, 1067–1074 (1950).
15. Shah, R. K., Personal Communication, dt. 3.1.1998. Senior Staff Research Scientist, Heat Exchanger
Development, DELPHI Harrison Thermal Systems, Lockport, NY.
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(W. M. Rohsenow and J. P. Hartnett, eds.), McGraw-Hill, New York, 1973.
17. Sleicher, C. A. and Rouse, M. W., A convenient correlation for heat transfer to constant and variable
property fluids in turbulent pipe flow, Int. J. Heat Mass Transfer, 18, 677–683 (1975).
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New York, 1980.
19. Deissler, R. G., Analytical investigation of fully developed laminar flow in tubes with heat transfer with
fluid properties variable along the radius, NACA TN 2410, NACA, Washington, DC, 1951.
20. Shannon, R. L. and Depew, C. A., Forced laminar flow convection in a horizontal tube with variable
viscosity and free convection effects, Trans. ASME J. Heat Transfer, 91, 251–258 (1969).
21. Petukhov, B. S., Heat transfer and friction in turbulent pipe flow with variable physical properties, in
Advances in Heat Transfer, Vol. 6, Academic Press, New York, 1970, pp. 503–564.
22. Shah, R. K., Compact heat exchangers, in Handbook of Heat Transfer Applications (W. M. Rohsenow, J. P.
Harnett, and E. N. Ganic, eds.), McGraw-Hill, NewYork, 1985, pp. 4-174–4-312.
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Heat Transfer 1990-Jerusalem, Paper No. KN-22, Vol. 1, 1990, pp. 355–362.
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39–49 (1981).
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Thermal/Mechanical Heat Exchanger Design—Karl Gardner Memorial Session, Vol. 64, (K. P. Singh
and S. M. Shenkman, eds.), American Society of Mechanical Engineers Winter Meeting, Anaheim, CA,
December 7, 1986, 1985, pp. 33–41.
26. Mahbub Uddin,A. K. M. and Bell, K. J., Effect of uncertainties on the design and operation of systems of heat
exchangers, in Heat Transfer Equipment Design (R. K. Shah, E. C. Subbarao, and R. A. Mashelikar, eds.),
27. Haseler, L. E., Owen, R. G., and Sardesai, R. G., The sensitivity of heat exchanger calculations to uncer-
tainties in the physical properties of the process fluids, in Practical Application of Heat Transfer, IMechE
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pp. 222–230.
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273–287 (1976).
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Trans. ASME J. Eng. Power Ser. A, 92, 46–56 (1970).
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Eng. Power, 99, 657–663 (1977).
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Exchanger Technology (R. K. Shah and A. Hashemi, eds.), Elsevier Science Publishers, Amsterdam, the
Netherlands, 1993, pp. 417–445.
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Fundamentals and Design (S. Kakac, A. E. Bergles, and F. Mayinger, eds.), Hemisphere/McGraw-Hill,
Washington, DC, 1981, pp. 647–679.
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1429–1435 (1936).

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283–294 (1940).
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BIBLIOGRAPHY
Bell, K. J., Overall design methodology for shell and tube exchangers, in Heat Transfer Equipment Design
(R. K. Shah, E. C. Subbarao, and R.A. Mashelkar, eds.), Hemisphere,Washington, DC, 1988, pp. 131–144.
Breber, G., Computer programs for design of heat exchangers, in Heat Transfer Equipment Design (R. K. Shah,
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Shah, E. C. Subbarao, and R. A. Mashelikar, eds.), Hemisphere, Washington, DC, 1988, pp. 23–38.
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145
4 Compact Heat Exchangers
4.1 CLASSIFICATION AND CONSTRUCTION DETAILS
OF TUBE-FIN COMPACT HEAT EXCHANGERS
Compact heat exchangers are used in a wide variety of applications. Typical among them are the
heat exchangers used in automobiles, air conditioning, electronics cooling, waste and process heat
recovery, cryogenics, aircraft and spacecraft, ocean thermal energy conservation, solar, and geo-
thermal systems. The need for light-weight, space-saving, and economical heat exchangers has
driven the development of compact surfaces.
4.1.1 Characteristics of Compact Heat Exchangers
SpecificcharacteristicsofcompactheatexchangersarediscussedbyShah[1–4]andincludethefollowing:
1. Usually with extended surfaces.
2. A high heat transfer surface area per unit volume of the core, usually in excess of 700 m2/m3
on at least one of the fluid sides, which usually has gas flow.
3. Small hydraulic diameter.
4. Usually at least one of the fluids is a gas.
5. Fluids must be clean and relatively nonfouling because of small hydraulic diameter (Dh)
flow passages and difficulty in cleaning; plain uninterrupted fins are used when “moderate”
fouling is expected.
6. The fluid pumping power (i.e., pressure drop) consideration is as important as the heat
transfer rate.
7. Operating pressures and temperatures are limited to a certain extent compared to shell and
tube exchangers due to thin fins and/or joining of the fins to plates or tubes by brazing,
mechanical expansion, etc.
8. The use of highly compact surfaces results in an exchanger with a large frontal area and a
short flow length; therefore, the header design of a compact heat exchanger is important for
a uniform flow distribution.
9. Fluid contamination is generally not a problem.
10. Variety of surfaces are available having different order of magnitudes of surface area density.
11. Flexibility in distributing surface area on the hot or cold side as desired by the designer.
Other features of compact heat exchangers are as follows:
Materials for the manufacture of fins are limited by the operating temperature of certain applica-
tions. For low- to moderate-temperature applications, fins can be made from aluminum, copper, or
brass and thus maintain high-fin efficiency. For high-temperature applications, stainless steel and
heat-resistant alloys may be used with possibly a reduction in the fin efficiency. Consequently, suit-
able high-performance surfaces may be selected to offset the reduction in fin efficiency or the fin
thickness should be reduced.
Manufacture is by brazing or welding. For low- or moderate-temperature applications, the fins
can be mechanically bonded. Low-fin tubes are extruded.
Flow arrangements: Compact exchangers are mostly used as single-pass crossflow or multipass
cross-counterflow exchangers.

4.1.2 Construction Types of Compact Heat Exchangers
Basic construction types of compact heat exchangers are
1. Tube-fin
2. Plate-fin
3. Regenerators
Tube-fin and plate-fin heat exchangers are discussed in this chapter. Regenerators, exclusively used
in gas-to-gas applications, could have more compact surface area density compared to plate-fin or
tube-fin surfaces. They are covered in detail in a separate chapter. The unique characteristics of
compact extended-surface plate-fin and tube-fin exchangers that favor them as compared with the
conventional shell and tube exchangers include the following [1,3,4]:
1. Many surfaces are available having different orders of magnitude of surface area
density.
2. Flexibility in distributing surface area on the hot and cold sides as warranted by design
considerations.
3. Generally substantial cost, weight, or volume savings.
The following factors mainly determine the choice among the three types of compact heat
exchangers:
1. Operating pressure and temperature
2. Phases of the fluids dealt with
3. Fouling characteristics of the fluid
4. Allowable pressure drop
5. Strength and ruggedness
6. Restrictions on size and/or weight
7. Acceptable intermixing of the fluids dealt with
4.1.3 Tube-Fin Heat Exchangers
Tube-fin heat exchangers are widely used throughout the industry in a variety of applications.
They are employed when one fluid stream is at a higher pressure and/or has a significantly
higher heat transfer coefficient compared to the other fluid stream. For example, in a gas-to-
liquid exchanger, the heat transfer coefficient on the liquid side is generally very high compared
to the gas side. Fins are used on the gas side to increase surface area. In a tube-fin exchanger,
round and rectangular tubes are most commonly used (although elliptical tubes are also used),
and fins are employed either on the outside or on the inside, or on both sides of the tubes,
depending upon the application. Fins on the outside of the tubes (Figure 4.1) may be catego-
rized as follows:
1. Normal fins on individual tubes (Figure 4.1a), referred to as individually finned tubes.
2. Longitudinal fins on individual tubes (Figure 4.1b), which are generally used in condensing
applications and for viscous fluids in double-pipe heat exchangers.
3. Flat or continuous (plain, wavy, or interrupted) external fins on an array of tubes (either
circular or flat tube) as shown in Figure 4.1c,d. Since interrupted fins are more prone to
fouling, many users prefer plain continuous fins in situations where fouling, particularly by
fibrous matter, is a serious problem.

147Compact Heat Exchangers
4.1.3.1 Specific Qualitative Considerations for Tube-Fin Surfaces
Specific qualitative considerations for the tube-fin surfaces include the following:
• Tube-fin exchangers usually have lower compactness than plate-fin units.
• A tube-fin exchanger may be designed for a wide range of tube fluid operating pressures,
with the other fluid being at low pressure.
• Reasonable fouling can be tolerated on the tubeside if the tubes can be cleaned.
(a) (b)
(c) (i) (ii)
(i) (ii)(d)
FIGURE 4.1 (a) Aluminum L foot tube fin and (b) welded longitudinal fin. (Courtesy of Vulcan Finned
Tubes, Tomball, TX.) (c) Continuous finned tube heat exchanger—(i) cupronickel tube-fin heat exchanger
and (ii) flat-tube heat exchanger to cool hydraulics (ALEX Core). (Courtesy of Lytron Inc., Woburn, MA.) (d)
Continuous finned compact cooler. (Courtesy of GEA Heat Exchangers, Catoosa, OK.)

4.1.3.2 Applications
Tube-fin exchangers are extensively used as condensers and evaporators in air-conditioning and
refrigeration applications, for cooling of water or oil of vehicular or stationary internal combustion
engines, and as air-cooled exchangers in the process and power industries. The usual arrangement
is that water, oil, or refrigerant flows in the tubes, while air flows across the finned tubes.
4.1.3.3 Individually Finned Tubes
Individually finned tube geometry is much more rugged than the continuous fin geometry, but has
lower compactness. The most common individual finned tubes are with plain circular, helical, or
annular enhanced fin geometries like segmented, studded, slotted, or wire-loop fins [5]. Figure 4.2
shows some of the fin geometries (schematic) that have been used on circular tubes (few of these
geometries are discussed as heat transfer enhancement fins in Chapter 8), Figure 4.3 shows photos
of fin-tube geometries, and Figure 4.4 shows circular fin-tube geometrical parameters. Fins are
attached to the tubes by a tight mechanical fit, tension winding, adhesive bonding, soldering, braz-
ing, welding, or extrusion or sleeving a liner containing extruded fins on a base metal. Figure 4.5
shows common circular tube-fin classification and manufacturing techniques. Details of various fin
geometries are discussed next.
4.1.3.3.1 Plain Circular Fins
Plain circular fins are the simplest and most common. They are manufactured by tension wrapping
the fin strip around a tube, forming a continuous helical fin, or by mounting circular fin disks on the
tube. Helically wrapped and extruded fins on circular tubes are frequently used in the process indus-
tries and in heat recovery applications. Classification of plain circular fin tubes in terms of fin height
is discussed next.
4.1.3.3.2 Fin Height and Classification of Finned Tubes
Fin height and classification of finned tubes are discussed by Wen-Jei Yan [6]. According to fin
height, the finned tubes are called low-fin tubes, medium-fin tubes, and high-fin tubes as follows:
1. In low-fin tubes, fins are extruded from the tube material with fin heights on the order of
1–2 mm. Fins of nominal 1.6 mm (1/16 in.) height have become standard for the low-fin
type of duty usually required in shell and tube exchangers. Low-fin tubes are generally
manufactured by raising the fin from base tube metal by a fabrication operation (possibly
by an extrusion process). Integral fining ensures the maximum thermal efficiency of the
tube since there is no possibility of fins becoming loose (and hence increase in thermal
contact resistance) due to corrosion, thermal expansion and contraction, or by mechanical
damage in handling.
(d) (e) (f)Studded Wire loop Helical slotted
(a) Helical (b) (c)Annular Helical segmented
FIGURE 4.2 Forms of individually finned tubes. (a) Helical, (b) annular, (c) helical segmented, (d) studded,
(e) wire loop, and (f) helical slotted.

(a) (b)
(c)
(d) (e)
FIGURE 4.3 (a) Helical spiral wound crimped finned tube. (b) Annular fin or stamped fin tube. (a and b
Courtesy of Fin Tube Products, Inc., Wadsworth, OH.) (c) TURB-XHF (serrated or segmented fin). (d) Stud
welded tube. (c and d Courtesy of Fin Tube, LLC, Tulsa, OK; www.fintubellc.com) (e) Wire loop fintube.
(TAAM Engineering, Maharastra, India.)
Tubedia.
Wallthick.
Unfinned end Unfinned end
Findia.
Finheight
Length
No. of fins/in.
FIGURE 4.4 Individually finned tube details.

2. Fins of approximately 3.2 mm (1/8 in.) are referred to as medium fins and are usually
employed in shell and tube exchangers.
3. Air-cooled exchangers require high fins, which have the height of 6.4–25 mm (1/4−1.0 in.).
Heat recovery systems prefer medium to high fins in tube banks of inline arrangement.
However, Rabas and Taborek [7] classify low-fin tubes as having a fin height less than 6.35 mm
(0.25 in.). The major reasons for using low-finned tubes in various types of heat exchangers are [7]
as follows:
1. To balance heat transfer resistance
2. To maintain fin bond integrity
3. To reduce fouling
4. To satisfy the tube material specification
4.1.3.3.3 Enhanced Fin Geometries
Segmented or spine fins: Segmented or spine fins are made by helically winding a continuous strip
of metal that has been partially cut into narrow sections. Upon winding, the narrow sections sepa-
rate and form the narrow strip fins that are connected at the base.
Studded fins: A studded fin is similar to the segmented fin, but individual studs are welded to
the tubes.
Slotted fins: Slotted fins have slots in the radial direction; when radially slitted material is wound
on a tube, the slits open.
Wire loops around the tube: The wire loops are held in the tube by a tensioned wire within the
helix or by soldering. The enhancement characteristic of small-diameter wires is important at low
flows where the enhancement of other interrupted fins diminishes.
All of these geometries provide enhancement by the periodic development of thin boundary lay-
ers on small-diameter wires or flat strips, followed by their dissipation in the wake region between
elements [8].
4.1.3.3.4 Construction Materials
The materials to be used for the tubes, headers, and water tanks depend on the specific requirements
of the application. The most common materials for tubes and fins are copper, aluminum, and steel.
Circular finned tube
Spiral fin Studded fin
Tension wound fin–
welded or embedded
Extruded fin
Smooth Segmented Slitted/
slotted
Corrugated
(crimped)
Extrusion Machining Brazing
Annular fin
FIGURE 4.5 Tube-fin classification.

For open-circuit installations, the tubes are made from copper, phosphorus-deoxidized copper, alu-
minum, brass, and copper–nickel–iron alloys, that is, cupronickels, and carbon steel for heat recov-
ery applications. Fins are mostly from aluminum and copper; for heat recovery applications they are
made from carbon steel. Headers and tube plates are made of carbon steel.
4.1.3.3.5 Tube Layout
The two basic arrangements of the tubes in a tube bank are staggered and inline. These arrange-
ments are shown in Figure 4.6. The only construction difference between these two is that in the
staggered arrangement each alternate row is shifted half a transverse pitch, and the two arrange-
ments differ in flow dynamics. Due to compactness and higher heat transfer, the staggered layouts
are mostly used. However, if the air stream is laden with dust, abrasive particles, etc., inline layout
is preferred, being less affected and having ease of cleaning.
4.1.4 Continuous Fins on a Tube Array
This type of tube-fin geometry is most commonly used in (1) air-conditioning and refrigeration
exchangers known as coils, in which high-pressure refrigerant is contained on the tubeside, (2) as
radiators for internal combustion engines, and (3) for charge air coolers and intercoolers for cool-
ing supercharged engine intake air of diesel locomotives, etc. The tube layout pattern is mostly
staggered.
4.1.4.1 Tube: Primary Surface
All tubes feature seamless tubes supplied to ASTM/ASME specifications. Return bends can
be supplied of heavier wall tubing to ensure adequately formed thickness in applications
where erosion is a concern. Round or flat tubes (rectangular tubes with rounded corners)
usually with a staggered tube arrangement are used. Elliptical tubes are also being used.
Round tubes are used for high-pressure applications and also when considerable fouling is
anticipated. The use of flat tubes is limited to low-pressure applications, such as vehicular
radiators. Flat or elliptical tubes, instead of round tubes, are used for increased heat transfer
in the tube and reduced pressure drop outside the tubes [2,9]. High-parasitic-form drag is
associated with flow normal to the round tubes. In contrast, the flat tubes yield lower pres-
sure loss for flow normal to the tubes due to lower form drag and avoid the low-performance
wake region behind the tubes.
4.1.4.2 Fin: Secondary Surface
All coils or continuous fin exchangers feature die formed, flat or patterned plate-fins of either alu-
minum or copper. The fins are attached to the tubes by mechanical expansion of the tube, ensuring
(a) (b)
FIGURE 4.6 Tube-fin layout: (a) inline and (b) staggered.

a permanent fin-to-tube bond. Full fin collars allow for both precise fin spacing and maximum fin-
to-tube contact. Fin pattern is optimized to produce highly energy efficient operation, resistance to
airflow and cleanability.
Flat fin: Flat fin has no corrugation, which provides the lowest possible air pressure drop and
lowest fan horsepower.
Star fin: Star fin pattern corrugation around the tubes provides higher heat transfer than the flat
fin with a slight increase in air pressure drop.
Wavy fin: Wave fin corrugation across the fin provides the maximum heat transfer rate for a given
surface area.
Louvered fin: Heat exchangers with flat tubes and louver fins are widely used due to higher heat
transfer and reduced size.
4.1.4.3 Headers
Coils feature either steel or nonferrous manifold headers with threaded pipe connections. Cooling
coils are supplied with vents and drains. Header tube holes are drilled. Headers provide proper joint
clearances and to allow optimum braze metal application. Coils have steel or copper tubesheets and
removable steel headers with threaded connections. Header thickness, gasket surface area, and bolt
area are designed and tested to provide a leak tight gasket seal.
4.1.4.4 Tube-to-Header Joints
Tube-to-header joints are either roller-expanded or brazed or soldered.
4.1.4.5 Casings or Tube Frame
The coil incorporates a heavy-duty rectangular structural tube frame, which improves rigidity,
squareness, and long-term stability and double flanged for coil stacking. Coil casings are either gal-
vanized or stainless steel. Casing supports are provided on various centers for extra support during
handling. Coil casings are furnished without mounting holes unless required.
4.1.4.6 Circuiting
Each coil is individually circuited for specific applications in recirculated, flooded, direct expan-
sion, or control pressure receiver refrigeration systems along with water, glycols, or brines.
4.1.4.7 Exchangers for Air Conditioning and Refrigeration
Evaporators and condensers for air conditioning and refrigeration are usually the tube-fin type when
air is one of the fluids. These exchangers are referred to as coils (Figure 4.7) when air is one of the
Refrigerant
inlet
Refrigerant
outlet
FIGURE 4.7 Heating/cooling coils—schematic.

fluids. Tube-fin geometry is becoming widespread in the current energy conservation era, because
the bond between the fin and tube is made by mechanically or hydraulically expanding the tube
against the fin, instead of employing welding, brazing, or soldering [2]. Formation of a mechanical
bond requires very little energy compared to the energy required to solder, braze, or weld the fin to
the tube. Because of the mechanical bond, the operating temperature is limited.
To specify a continuous fin-tube heat exchanger or coil, the following parameters are required:
1. Coil type
2. Fin details
a. Fins per inch (fpi)
b. Material—aluminum, copper, stainless steel, carbon steel
c. Fin size
d. Fin pattern/type—flat, star, wavy, louvered
3. Rows
4. Header material (copper, brass, carbon steel or stainless steel)
5. Tube material and tube wall thickness
6. Casing material, either galvanized steel or stainless steel (also specify if mounting holes
are required)
7. Connection type (MPT, Butt Weld, or Flanged) (also specify if top or bottom supply)
8. Horizontal or vertical airflow
Tube-fin details for air-conditioning and refrigeration applications are furnished by Shah [2]:
Evaporator coils for small-capacity systems (less than 20 tons) use 7.9, 9.5, and 12.7 mm (5/16, 3/8,
and 1/2 in.) tubes and fin densities in the range of 315–551 fins/m (8–14 fins/in.). For refrigeration
applications, lower fin densities (157–315 fins/m or 4–8 fins/in.) are used due to the possibility of
frosting and blockage. For condenser coils, tube diameters used are 7.9, 9.5, and 12.7 mm (5/16, 3/8,
and 1/2 in.), and fin densities range from 394 to 787 fins/m (10–20 fins/in.) and fin thickness from
0.09 to 0.25 mm (0.0035–0.10 in.).
4.1.4.8 Radiators
Radiators are compact liquid-to-air heat exchangers widely used in automotive vehicles. Major con-
struction types used for radiators include (1) soldered design with flat brass tubes with flat plain or
louvered copper fins—tubes and header sheets are made from brass and the water tank from brass
or plastics—and (2) brazed aluminum design with flat tube and corrugated fins, usually louvered
fins or flat tube continuous fins. These construction types are shown in Figure 4.8. Louvered cores
are preferred as they allow a lower fin density than a nonlouvered core of the same area for the
same thermal performance. The soldered brass tubes and copper fins were primarily used before
the 1980s. Because of lightweight and significantly better durability and operating life, brazed alu-
minum tubes and aluminum corrugated multilouver fin radiators have almost replaced the copper-
brass radiators [2]. Typical fin density ranges from 400 to 1000 fins/m (10–25 fins/in.), and the
surface area density (β) ranges from 900 to 1650 m2/m3 (275–500 ft2/ft3).
4.1.4.9 Effect of Fin Density on Fouling
A major question in the choice of detailed dimensions for a core is the appropriate fin spacing.
As the number of fins per inch (or per meter) is increased, the unit can be made progressively
more compact. At the same time, it becomes more sensitive to clogging by dirt, soot, airborne
dirts, insects, and the like, and more sensitive to nonuniformity in the fin spacing. In practice, it
has been found that for most automotive applications, radiators can have 10–12 fins/in. Fourteen
fins per inch can be fabricated with little increase in cost per unit surface area, and this closer fin
spacing may be justified for installations where space is a constraint and fouling of the surfaces
is not a problem [9].

4.1.4.10 One-Row Radiator
In conventional multirow radiators, the fin array is not in contact with the tubes over the full fin depth.
The region of no contact occurs between the tube rows and is illustrated in Figure 4.9. This hinders heat
conduction from the tubes to the fin region between the tube rows. If the fins are louvered in this region,
the conduction path is further impaired. Hence the thermal performance per unit fin depth is low com-
pared to the fin region in contact with the tubes. Remedies for this problem are as follows [10]:
1. Use a one-row core (Figure 4.10) in place of the multirow design. This design eliminates
the low-performance fin area between tube rows, and offers either material savings and
lower air pressure drop, or increased thermal performance. In the United States, manufac-
turers usually make 19.1 mm (3/4 in.) tubes in 0.152 mm (0.006 in.) thick brass. To prevent
the tube wall from becoming concave during core assembly, heavier wall thickness is usu-
ally adopted. Another method followed to prevent the tube wall from becoming concave
during assembly is to use cross-ribbed turbulator tubes. The indented cross ribs increase
the cross-sectional moment of inertia of the tube wall, increasing its stiffness. The indenta-
tions in the wall of turbulator tubes may be beneficial for low-flow-rate applications, where
Louver fin
Fin
Tube cross section
L
L
W
p
Tube Louver Unlouvered
area
Flat tube
Louver
Airflow
(c) (d)
Flat tube
Plain fin
Airflow Airflow
Louvered plate fin
(a) (b)
Flat tube Louver
FIGURE 4.8 Tube-fin details of radiator: (a) continuous plain fin-flat tube radiator, (b) continuous louvered
fin-flat tube design, (c) single flat tube row louvered fin radiator design, and (d) tube-fin details.

the flow may be laminar. For turbulent flow, the increase in coolant-side heat transfer
coefficient will be marginal, because the dominant thermal resistance is typically on the
airside, and the ribs or indentations produce large increase in pressure drop.
2. An alternative method of eliminating the ineffective fin area is to eliminate the space
between the tube rows. In other words, have the tubes touching in the axial direction. This
is referred to as the “tubes-touching” design. To achieve tubes-touching design, the ends
of the tubes must be shaped to provide the requirement of minimum ligament between the
tubes in the header plate. For the same fin depth in the airflow direction, the tubes-touching
design should provide the same thermal performance as a one-row design.
4.1.4.11 Manufacture of Continuous Finned Tube Heat Exchangers
The manufacturing procedure for continuous finned tube heat exchanger is discussed next. Detailed
manufacturing practices are further described in the chapter on Heat Exchanger Fabrication:
Brazing and Soldering.
Mechanically bonded core: In a rounded hole design, the flat fins are formed with holes larger
than the tubes to be inserted. Tubes are assembled in a fixture and fins are inserted. The fin gap
(i.e., the fin density) is controlled by the ferrule height (Figure 4.11). After assembly, the tubes are
FIGURE 4.9 Region of no contact between flat tube rows of a radiator.
Brass tube with
cross ribbed turbulator
thickness –0.152 mm
25.4mm
19.1mm
FIGURE 4.10 Single tube row radiator design.
FIGURE 4.11 Ferrule height of a tube-fin heat exchanger.

expanded so that metal-to-metal contact is being achieved. The tube ends are generally expanded
into the header plates. Sometimes, on thinner tube plates, the tubes are brazed. The tubes, fins, and
headers together form the core, which is then attached to the side sheet assembly and the header for
the tubeside fluid or water tank, as the case may be, and tightly sealed with gaskets.
Soldered core: In a soldered design, which is mostly followed for flat tube-fin exchangers, the radia-
tor cores are built from tinned brass tubes and copper fin sheets. The fins are punched with holes slightly
larger than the tube dimension, and tubes are inserted through the holes. The tube outer surfaces and
fin surfaces are solder coated for achieving bonding. After the header plates are assembled, the core is
baked in an oven. During baking the solder metal on the tube outer surface and on the fin surface melts
and give perfect metal-to-metal contact. Alternately, a fluxed core assembly is dip soldered.
4.1.5 Surface Selection
Various surfaces are being used in compact heat exchanger applications. A proper selection of a
surface is one of the most important considerations in compact heat exchanger design. The selec-
tion criteria for these surfaces are dependent upon (1) the qualitative and (2) the quantitative con-
siderations [11].
4.1.5.1 Qualitative Considerations
The qualitative considerations include the following:
1. Heat transfer requirements
2. Operating temperature and pressure
3. Flow resistance
4. Size or compactness and weight
5. Mechanical integrity
6. Fouling characteristics
7. Availability of surfaces, manufacturing considerations
8. Low capital cost, and low operating cost, especially low pumping cost
9. Designer’s experience and judgment
10. Maintenance requirements, reliability, and safety
Heat transfer requirements with low flow resistance to minimize the pumping cost and a compact,
low-weight unit are the important criteria for selecting a surface for a compact heat exchanger.
These aspects are common for all types of heat exchangers and have been covered earlier. Surface
selection influenced by fouling, manufacturing considerations, and cost are discussed next with
additional details.
Fouling of compact exchangers: Fouling is one of the major problems in compact heat exchang-
ers, particularly with various fin geometries and fine flow passages that cannot be cleaned mechani-
cally. Hence, compact heat exchangers may not be applicable in highly fouling applications. There
is a belief and some evidence that integral and low-finned tubes foul either at essentially the same
rate or in some cases at a lower rate than plain tubes and also they are easier to clean the most types
of fouling [7]. Other than low-finned tubes, if fouling is a problem, with the understanding of the
problem and applying innovative means to prevent/minimize fouling, compact heat exchangers may
be used in at least low to moderate fouling applications. Methods to reduce fouling are discussed
in Chapter 9.
Manufacturing considerations: Most of the heat exchanger manufacturing industries make only
a limited number of surfaces due to limited availability of tools and to market potential. Select a
surface that a company can manufacture, even though theory and analysis can be used to arrive at
some high-performance surfaces that may pose problems to manufacture.

Cost: Cost is one of the most important factors in the selection of surfaces, such that the overall
heat exchanger is least expensive either in initial cost or in both initial and operating costs. If a plain
fin surface can do the job for an application, a plain surface is preferable to expensive complicated
surface geometries.
4.1.5.2 Quantitative Considerations
The quantitative considerations include performance comparison of surfaces with some simple
“yardsticks.” Surface selection by a quantitative method is made by comparing performance of
various heat exchanger surfaces and choosing the best under some specified criteria for a given heat
exchanger application. Shah [11] categorizes the surface selection method as follows:
1. Comparisons based on j and f factors
2. Comparison of heat transfer as a function of fluid pumping power
3. Miscellaneous direct comparison methods
4. Performance comparisons with a reference surface
These methods are discussed in Chapter 8.
4.2 PLATE-FIN HEAT EXCHANGERS
Two important sources on PFHE and brazed aluminum plate-fin heat exchanger are ALPEMA
Standard [12] and The Plate-Fin Heat Exchangers Guide to Their Specification and Use [13]. The
definition for PFHE given in Ref. [13] is as follows: Plate-fin heat exchangers (PFHE) are a form
of compact heat exchanger consisting of a stack of alternate flat plates called “parting sheets” and
fin corrugations, brazed together as a block. The basic elements of PFHE, two types of crossflow
arrangements are shown in Figure 4.12 and counterflow arrangement is shown in Figure 4.13.
Fluid streams flow along the passages made by the corrugations between the parting sheets.
Parting sheet
Edge seal or
side bar
Fin
(a)
(b)
FIGURE 4.12 Plate-fin heat exchanger: (a) basic elements, (b) two types of flow arrangements.

The corrugations serve as both secondary heat transfer surfaces and mechanical supports for the
internal pressures between layers. In liquid or phase-change (to gas) applications, the parting sheets
may be replaced by flat tubes on the liquid or phase-change side. Further, PFHEs are widely used
in various industrial applications because of their compactness. For many years, PFHEs have been
widely used for gas separation in cryogenic applications and for aircraft cooling duties. In aerospace
applications weight saving is of paramount importance. In the following sections, first the salient
features of PFHE are covered followed by specific features of brazed aluminum PFHEs as per
ALPEMA Standard [12].
4.2.1 PFHE: Essential Features
Salient features of PFHE as discussed by Shah include the following [1,2]:
1. Plate-fin surfaces are commonly used in gas-to-gas exchanger applications. They offer
high area densities (up to about 6000 m2/m3 or 1800 ft2/ft3).
2. The passage height on each side could be easily varied. Different fins (such as [a] rectan-
gular or triangular fin either plain or with louver or perforation, [b] offset strip fin (OSF),
and [c] wavy fin) can be used between plates for different applications.
3. Plate-fin exchangers are generally designed for low-pressure applications, which operating
pressures limited to about 1000 kPag (150 psig).
4. The maximum operating temperatures are limited by the type of fin-to-plate bonding
and the materials employed. Plate-fin exchangers have been designed from low cryogenic
operating temperatures (all-aluminum PFHE) to about 800°C (1500°F) (made of heat-
resistant alloys).
5. Fluid contamination (mixing) is generally not a problem since there is practically zero fluid
leakage from one side to the other of the exchanger.
4.2.2 Application for Fouling Service
The PFHE is limited in application to relatively clean streams because of its small flow passages. It
is generally not designed for applications involving heavy fouling since there is no easy method of
cleaning the exchanger. If there is a risk of fouling, use wavy fins and avoid serrated fins. Upstream
strainers should be employed where there is any doubt about solids in the feed. Measures to over-
come fouling problems with PFHE are described by Shah [2].
FIGURE 4.13 Counterflow plate-fin heat exchanger—schematic. (Photo courtesy of Fives Cryo, Golbey,
France.)

4.2.3 Size
Maximum size is limited by the brazing furnace dimensions, and by the furnace lifting capacity.
The heating characteristics of denser blocks also impose limitations on the maximum size which
can be brazed. Typical maximum dimensions for low-pressure aluminum PFHEs are 1.2 m × 1.2 m
in cross section × 6.2 m along the direction of flow [1,2,13], and 1.0 m × 1.0 m × 1.5 m for nonalumi-
num PFHEs [13]. Higher pressure units, being heavier per volume, make both handling and brazing
more difficult, thus reducing the economic maximum size. Duties that call for larger units are met
by welding together several blocks, or by manifolding pipework.
4.2.4 Advantages of PFHEs
The principal advantages of PFHEs over other forms of heat exchangers are summarized in Ref. [13]
and include the following:
1. Plate-fin heat exchangers, in general, are superior in thermal performance to those of the
other type of heat exchangers employing extended surfaces.
2. PFHE can achieve temperature approaches as low as 1°C between single-phase streams
and 3°C between multiphase streams. Typically, overall mean temperature differences of
3°C–6°C are employed in aluminum PFHE applications [13].
3. With their high surface compactness, ability to handle multiple streams, and with alu-
minum’s highly desirable low temperature properties, brazed aluminum plate-fins are an
obvious choice for cryogenic applications.
4. Very high thermal effectiveness can be achieved; for cryogenic applications, effectiveness
of the order of 95% and above is common.
5. Provided the streams are reasonably clean, PFHEs can be used to exchange heat in most pro-
cesses, for the wide range of stream compositions and pressure/temperature envelopes [13].
6. Large heat transfer surface per unit volume is possible.
7. Low weight per unit heat transfer.
8. Possibility of heat exchange between many process streams.
9. Providedcorrectmaterialsareselected,thePFHEcanbespecifiedfortemperaturesrangingfrom
near absolute zero to more than 800°C, and for pressures up to at least 140 bar [1]. According to
Shah [1], usually PFHEs do not involve both high temperature and high pressure together.
10. PFHE offers about 25 times more surface area per equipment weight than the shell and
tube heat exchanger [13].
4.2.5 Limitations of PFHEs
Limitations other than fouling and size include the following [1]:
1. With a high-effectiveness heat exchanger and/or large frontal area, flow maldistribution
becomes important.
2. Due to short transient times, a careful design of controls is required for startup compared
with shell and tube exchangers.
3. Flow oscillations could be a problem.
4.2.6 Applications
Current areas of application include [13] the following:
1. Cryogenics/air separation
2. Petrochemical production

3. Syngas production
4. Aerospace
5. Land transport (automotive, locomotive)
6. Oil and natural gas processing
PFHEs are used in all modes of heat duty, including [13] the following:
1. Heat exchange between gases, liquids, or both
2. Condensing
3. Boiling
4. Sublimation (“reversing” heat exchangers)
5. Heat or cold storage
4.2.7 Economics
The PFHE is not necessarily cheaper for a given heat duty than other forms of heat exchangers,
because the method used for constructing PFHEs is complex and energy-intensive [13].
4.2.8 Flow Arrangements
The fins on each side can be easily arranged such that overall flow arrangement of the two fluids can
result in crossflow, counterflow, cross-counterflow, or parallelflow, though parallelflow is mostly not
used. Properly designed, the PFHE can be made to exchange heat in perfect counterflow, which per-
mits PFHEs to satisfy duties requiring a high thermal effectiveness. The construction of a multifluid
plate-fin exchanger is relatively straightforward except for the inlet and outlet headers for each fluid.
Some of the possible flow arrangements are shown in Figure 4.14.
4.2.9 Fin Geometry Selection and Performance Factors
Plate-fin surfaces have plain triangular, plain rectangular, wavy, offset strip, louver, perforated, or
pin fin geometries. These fin geometries are shown in Figure 4.15 [8]. PFHEs are superior to tube-
fin heat exchangers from heat transfer and pressure-drop points of view for the given total packag-
ing space. Fin density varies from 120 to 700 fins/m (3–18 fins/in.), thickness from 0.05 to 0.25 mm
(0.002–0.01 in.), and fin heights may range from 2 to 25 mm (0.08–1.0 in.) [2].
4.2.9.1 Plain Fin
Plain fin corrugation is the simplest type of fining. These surfaces are straight fins that are uninter-
rupted (uncut) in the fluid flow direction. Triangular and rectangular passages are more common.
The triangular fin is generally not structurally as strong as the rectangular fin for the same passage
size and fin thickness. When the fins are straight along the flow length, the boundary layers tend
to be thick resulting in lower values of the heat transfer coefficient. When they are wavy or off-set
strip fin along the flow length, the boundary layers are thinner or the growth of boundary layers is
disrupted periodically, respectively, resulting in a higher heat transfer coefficient.
Plain fin surfaces have pressure-drop and heat transfer characteristics similar to flow through
small-bore tubes, i.e., relatively low pressure drop and heat transfer, but a high ratio of heat transfer
to pressure drop [13]. For a flow channel with rectangular or triangular cross section, under turbu-
lent flow conditions, standard equations for turbulent flow in circular tubes may be used to calculate
j and f, provided the Reynolds number (Re) is based on the hydraulic diameter, Dh. If the Re based
on hydraulic diameter is less than 2000, one may use theoretical laminar flow solutions for j and f.
Plain fins are preferred for very low Reynolds number applications and in applications where
the pressure drop is very critical. Condensing duties require minimal pressure drop or else the

heat release curve can significantly alter and the overall duty may not be met. Therefore, for con-
densation, plain fins are normally specified.
4.2.9.2 Plain-Perforated Fin
Perforated fins have either round or rectangular perforations, having the size and longitudinal and
transverse spacings as major perforation variables. The flow passages are either triangular or rect-
angular. A metal strip is first perforated, then corrugated. Perforated areas vary from about 5% to
25% of the sheet area [13]. When the corrugations are laid across the flow, the stream is forced to
pass through these small holes. Salient performance features include:
1. The perforated holes promote turbulence, which increases the local heat transfer coeffi-
cient compared to plain fins, but as the percentage of perforated holes increase, the loss of
heat transfer surface offsets this advantage [13].
2. The perforated surface is prone to flow-induced noise and vibration.
Crossflow
Cross contraflow
Cross contraflow
with internal turnround
(serpentine)
Contraflow, type 1
Contraflow, type 2
Contraflow, type 3
FIGURE 4.14 Fluid flow arrangement through PFHE. (Note: contraflow is to be read as counterflow).
(Courtesy of Chart Industries Inc., Garfield Heights, OH.)
Rectangular fin Triangular fin Offset fin Wavy fin Louvered fin Perforated fin Pin fin
FIGURE 4.15 PFHE fin geometries.

Applications: Perforated fins are now used in only a limited number of applications [14].
Typical applications include the following:
1. “Turbulators” in oil coolers.
2. In boiling applications to maintain a wetted surface and minimize depositions/concentra-
tions [13]. Perforated corrugations permit interchannel fluid migration, which evens out
surges and vibration and avoids localized concentrations or depositions.
3. Perforated fins were once used in two-phase cryogenic air separation exchangers, but now
they have been replaced by OSFs.
Shah [15] provides a very detailed evaluation of the perforated fin geometries.
4.2.9.3 Offset Strip Fin
The offset strip fin (OSF) is the commonly used geometry in PFHEs. The fin has a rectangular cross
section; it is cut into small strips of length l, and every alternate strip is offset by about 50% of the
fin pitch in the transverse direction as schematically shown in Figure 4.16a. Fin spacing, fin height,
fin thickness, and strip length in the flow direction are the major variables of OSFs.
OSF geometry is characterized by high heat transfer area per unit volume, and high heat
transfer coefficients. The heat transfer mechanism in OSFs is described by Joshi and Webb
[16] and is as follows. The heat transfer enhancement is obtained by periodic growth of lam-
inar boundary layers on the fin length, and their dissipation in the fin wakes as shown in
Figure 4.16b. This enhancement is accompanied by an increase in pressure drop because of
increased friction factor. A form drag force, due to the finite thickness of the fins, also contrib-
utes to the pressure drop. Fluid interchange between channels is possible. OSFs are used in the
(a) (i) (ii)
Partition sheet
Partition sheet
S
tf
hf
(b)
FIGURE 4.16 (a) Offset strip fin—schematic. (b) Flow past offset strip fin—formation of turbulence behind the fin.
(Photo courtesy of Fives Cryo, Golbey, France.)

approximate Reynolds number range of 500–10,000 [14]. Salient features pertaining to thermal
performance include the following [13]:
1. Commonly used in air separation plants where high thermal effectiveness at low mass
velocities is required [13].
2. The heat transfer performance of OSFs is increased by a factor of about 1.5–4 over plain
fins of similar geometry, but at the expense of higher pressure drop [14].
3. At high Reynolds numbers, the j factor decreases, while the friction factor remains con-
stant because of the high form drag. Therefore, offset fins are used less frequently for very
high Reynolds number applications.
4. They are used at low Reynolds number applications calling for accurate performance predic-
tions, such as some aerospace applications; other fin performance data are not as repeatable.
4.2.9.4 Serrated Fins
It is similar to OSF. Serrated fin is formed by simultaneously folding and cutting alternative sections
of fins (Figure 4.23a and 4.24d). These fins are also known as lanced fins.
4.2.9.5 Herringbone or Wavy Fin
Since wavy fins have noninterrupted walls in each flow channel, they are less likely to catch par-
ticulates and foul than are OSFs. Their performance is competitive with that of the OSF, but the
friction factor continues to fall with increasing Reynolds numbers [13]. The waveform in the flow
direction provides effective interruptions to flow and induces very complex flows. The augmenta-
tion is due to Goertler vortices, which form as the fluid passes over the concave wave surfaces.
These are counterrotating vortices, which produce a corkscrew-like pattern and probable local
flow separation that will occur on the downstream side of the convex surface [8,14]. In the low-
turbulence regime (Re of about 6000–8000), the wall corrugations increase the heat transfer by
about nearly three times compared with the smooth wall channel. Therefore, wavy fins are often
a better choice at the higher Reynolds numbers typical of the hydrocarbon industry; the smooth
surface allows the friction factor to fall with increasing Reynolds number. Kays and London [17]
provide curves of j and f versus Reynolds number for two wavy-fin geometries.
4.2.9.6 Louver Fins
The louvers are essentially formed by cutting the sheet metal of the fin at intervals and by rotat-
ing the strips of metal thus formed out of the plane of the fin. Louvers can be made in many
different geometries, some of which are shown in Figure 4.17. Note that the parallel louver fin
and OSF both have small strips aligned parallel to the flow. The louvered fin geometry bears a
similarity to the offset strip (Figure 4.16a). Rather than offsetting slit strips, the entire slit fin
is rotated 20°–60° relative to the airflow direction. As such, they are similar in principle to the
OSF. Louvered fins enhance heat transfer by providing multiple flat plate leading edges with
their associated high values of heat transfer coefficient. Salient features of louver fins are as
follows:
• The louvered fin strip length is usually longer than that of OSF, e.g., 6–18 mm, versus 3–9
mm for the OSF [8]; the louvered fin gage is generally thinner than that of an offset strip
of the fin.
• The fin corrugations normally form a triangular passage. Hence, it is generally not as
strong as an OSF, since the latter has a “large” flat area for brazing, thus providing
strength [14].
• The louver fins may have a slightly higher potential of fouling compared to the OSFs [14].
• The louvered fin can provide heat transfer coefficients comparable to the OSF. However,
the ratio of j/f tends to be lower because of the considerable form drag on the bent fins [8].

• Louver fins can enhance heat transfer by a factor of two or three compared with the equiva-
lent unlouvered surfaces [13].
• A wide range in performance can be achieved by varying the louver angle, louver width,
and louver form.
The operating Reynolds number range is 100–5000, depending upon the type of louver geometry
employed [14].
Applications: Their attractive thermal performance characteristics in terms of compactness,
light weight, and low pumping power for a given heat transfer duty make louver fins a potential can-
didate for aerospace applications [18]. They are recognized as very effective heat transfer surfaces,
leading to compact solutions to cooling problems. Louvered fin surfaces are now used widely for
engine cooling equipment, air-conditioning heat exchangers (evaporators and condensers), and air-
craft oil and air coolers. They share this quality with the OSF surfaces [19]. The louvered surface is
the standard geometry for automotive radiators. For the same strip width, the louvered fin geometry
provides heat transfer coefficients comparable to the OSF.
4.2.9.7 Pin Fins
An array of wall-attached cylinders (e.g., rods, wires) mounted perpendicular to the wall is known as
pin fins. They can be manufactured at a very high speed continuously from a thin wire. After the wire is
(b)
lp
lh
ll
(c)
ll
α°
Tube
Tube Louver(a) Unlouvered
Fin
FIGURE 4.17 Louvered fin details. (a) Tube-louver fin arrangement, (b) louver fin geometry, and (c) fluid
flow through louver. (Note: lh is louver height, lp is louver pitch, ll is louver length and α is louver angle.)

formed into rectangular passages, the top and bottom horizontal wire portions are flattened for brazing
or soldering with the plates. Pins can be of circular or elliptical shapes. The enhancement mechanism
due to a pin array is the same as that of the OSF, namely, repeated boundary-layer growth and wake dis-
sipation [8]. The potential application for pin fins is at very low Reynolds number (Re 500) for which
the pressure drop is of no major concern. Present applications for pin fins include [14] (1) electronic
cooling devices with generally free convective flows over the pin fins and (2) to cool turbine blades.
Limitations of pin fins:
1. The surface compactness achieved by the pin fin geometry is much lower than that achieved
by the strip fin or louver fin surfaces.
2. Due to vortex shedding behind the circular pins, noise and flow-induced vibrations can
take place.
Table 4.1 shows commonly used plate-fin geometries and their relative merits.
4.2.9.8 FIN Corrugation Code
A commonly encountered code for fin corrugation is [13] 350S1808. The first three digits give
the fin height in thousandths of an inch (350 = 0.35 in.). The letter gives the type of corrugation
TABLE 4.1
Commonly Used Plate-Fin Geometries and Their Relative Merits
Corrugation Description Application
Features
Relative Heat
Transfer
Relative
Pressure Drop
Plain Straight fins (rectangular or
triangular)
Low Reynolds number
applications and in
applications where the
pressure drop is very critical,
e.g., condensation
Lowest Lowest
Perforated Straight fin with small holes For general use Low Low
Herringbone
or wavy fin
Smooth but wavy, about
10 mm pitch
In the Re range of 6000–8000,
the wall corrugations increase
the heat transfer by about
three times compared with the
smooth wall channel due to
Goertler vortices.
Less likely to catch
particulates and foul than are
OSFs
High High
Louvered fin The louvers are formed by
cutting the sheet metal of the
fin at intervals and by
rotating the strips of metal
thus formed out of the plane
of the fin
Radiators, air conditioning heat
exchangers (evaporators and
condensers), and aircraft oil
and air coolers
Highest Highest
OSF Straight but offset by half a
pitch (usually about every
3–4 mm)
Air separation plants and low
Reynolds number applications
calling for accurate
performance predictions, e.g.,
aerospace applications
Highest Highest

(S = serrated). Other types are P = plain, R = perforated, H = herringbone. The next two digits
give the fins per inch (18 = 18 fpi). The following two digits give the fin thickness in thousandths
of an inch (08 = 0.008 in.). The time following the oblique stroke (if any) is used only for perfo-
rated fin and it is the porosity, σ.
4.2.10 Corrugation Selection
Corrugations, edge bars, and parting sheets are chosen primarily to contain the appropriate pres-
sure. Corrugation selection depends on factors such as [13] compactness, pressure, mechanical
integrity, manufacture, performance, velocity limits, and fouling.
4.2.11 Materials of Construction
PFHEs are made in a variety of materials to suit a wide range of process streams, temperatures and
pressures. Material specifications should comply with the appropriate section of the ASME or to
other applicable codes.
4.2.11.1 Aluminum
Aluminum is preferred for cryogenic duties, because of its relatively high thermal conductivity, strength
at low temperatures, and low cost. For cryogenic services, aluminum alloy 3003 is generally used for
the parting sheets, fins, and edge bars that form the rectangular PFHE block. Headers and nozzles are
made from aluminum alloy 3003, 5154, 5083, 5086, or 5454 [13]. Above ambient temperature, with
increase in temperature, most aluminum alloys rapidly lose their strength. For land-based transport
vehicles, aluminum PFHEs are used up to 170°C–180°C to cool supercharged engine intake air.
4.2.11.2 Other Metals
Stainless steels and most nickel alloys are used for PFHEs, particularly for high-temperature
services. Stainless steels have poor thermal conductivity, but their higher strength allows thinner
parting plates and fins than with aluminum, which offsets some of the reduction in heat transfer.
4.2.12 Mechanical Design
The PFHE is a pressure vessel. It is required to be designed and constructed in accordance with
a recognized Pressure Vessel Code. The mechanical design of a PFHE can be divided into the
conventional pressure vessel area of header tanks, nozzle, nozzle reinforcements, lifting devices,
pipe loads, etc., and the less familiar area of the block itself. Details on mechanical design of vessel
components are given in Chapter 11.
4.2.13 Manufacture, Inspection, and Quality Control
PFHEs are manufactured by brazing. Heat exchanger manufacture by brazing is described in
Chapter 15. The manufacturer is responsible for the mechanical design and for the thermal design
where the latter is not specified by the purchaser. Salient features of quality control and inspection
of PFHE are detailed in Refs. [13,14].
4.2.14 Brazed Aluminum Plate-Fin Heat Exchanger (BAHX)
4.2.14.1 ALPEMA Standard
Though most of the details on PFHE are covered before, specific details on aluminum PFHE
are discussed here. Over the past 40 years, brazed aluminum plate-fin heat exchangers (BAHXs)
have become the preferred type of exchanger for a variety of applications, mainly in heating

and cooling of liquids and gases, and condensing and boiling with single and multicomponent
streams. BAHXs are capable of handling a wide variety of noncorrosive streams, up to a pres-
sure of 100 bar (1450 psi) and from cryogenic temperature of −269°C to 204°C (−452°F to
400°F). BAHXs can handle several streams in the same exchanger. A brazed aluminum PFHE
is shown in Figure 4.18 and a collection of different shapes/configuration of PFHEs are shown
in Figures 4.19 and 4.20. Brazed aluminum PFHEs are designed and manufactured as per the
guidelines of ALPEMA Standard, 3rd edition, 2010 [12]. Members of ALPEMA Standards are
(in alphabetical order)
1. Chart Energy and Chemicals Inc., 2191 Ward Avenue, La Crosse, WI
2. FivesCryo, 25, Rue du Fort BP 8788194 Golbey, Cedex, France
3. Kobe Steel Ltd., Energy System Center, Takasago Equipment Plant, 2-3-1, Shinhama,
Arai-cho, Takasago-Shi, Hyogo-Ken, 676-8670, Japan
4. LINDE AG, Engineering Division, Works Schalchen, D-83342 Tacherting, Germany
5. Sumitomo Precision Products Co Ltd., Thermal Energy Systems Engineering Department,
1-10 Fuso-cho, Amagasaki, Hyogo Pref. 660-0891, Japan
Other PFHE manufacturer among others include, 1. Lytron Inc., 55 Dragon Court, Woburn, MA.
The ALPEMA standards comprise the following chapters:
1. General description and nomenclature
2. Tolerances
3. General fabrication and contractual information
4. Installation, operation, and maintenance
5. Mechanical standards
6. Materials
7. Thermal and hydraulic design
8. Recommended good practice
FIGURE 4.18 Brazed aluminum plate-fin heat exchanger. (Courtesy of Fives Cryo, Golbey, France.)

Industrial use
oil coolers
Oil coolers for
Shinkansen
IGBT coolers for
Shinkansen
Heat sinks
FIGURE 4.20 Varieties of brazed aluminum plate-fin heat exchangers. (Courtesy of Sumitomo Precision
Products Co. Ltd., Thermal Energy Systems Engineering Department, Japan.)
(a) (b)
(c)
FIGURE 4.19 Varieties of brazed aluminum PFHEs configuration—(a) heat exchanger with single continu-
ous piece of aluminum flat tube, (b) flat tube heat exchanger with curved tubes, and (c) plate-fin heat exchanger
for air-to-air application. (Courtesy of Lytron Inc., Woburn, MA.)

PFHEs can be used for a wide range of applications, especially for low temperature services and treat-
ment of clean fluids. Such applications among others include, petrochemical plants, gas treatment plants,
natural gas liquefaction plants, air separation plants, and helium liquefaction plants.
4.2.14.3 Heat Exchanger Core
Each heat exchanger is built by stacking layers of fins separated by parting sheets and sealed along the
edges with side bars. The matrix assembly is brazed in a vacuum/controlled atmosphere brazing (CAB)
furnace to form an integral, rigid heat exchanger block. Headers and supports welded onto the
brazed matrix complete the unit. Design variations in the configuration of the heat exchanger matrix
can accommodate an almost unlimited range of flow options, including counterflow, crossflow, par-
allelflow, multipass and multistreams formats. The structure and components of brazed aluminum
heat exchangers (BAHXs) is shown in Figure 4.21.
4.2.14.4 Flow Arrangement
A simple crossflow layout is generally suitable for low to moderate duties. It is used extensively for
gas/liquid applications and is especially effective when handling a low pressure gas stream on one
side of the heat exchanger. For heavier duty tasks, where the mean effective temperature difference
in crossflow may be significantly reduced, the counterflow pattern offers an efficient solution.
The higher levels of efficiency achieved by counterflow units are essential to most low-temperature
applications.
A heat exchanger’s size, number of layers, type of fins, stacking arrangement, and stream circuit-
ing will vary depending on the application requirements. The basic components of a BAHX are as
follows [14].
• Fins
• Fins types
The herringbone and serrated fins provide the greatest surface area and the highest heat transfer per-
formance. They are particularly suitable for applications involving close temperature approaches.
D
C
B
C
D
A
1
2
3
4
5
6
7
3
2
1 Stub pipe
Cover plate
Side bar
Partition plate
Heat transfer fin
Distributor fin
Header tank
4
5
6
7
B
A
FIGURE 4.21 Brazed aluminum plate-fin heat exchanger structure. (Note: A, B, C, D are fluids.) (From
Linde AG, Engineering Division. With permission.)

Where there are critical pressure drop requirements, the plain and perforated fins can be used. Fins,
also known as secondary surface, provide an extended heat transfer surface. Fins provide a con-
necting structure between the parting sheets, thereby creating the essential structural and pressure
holding integrity of the heat exchanger. Various fin types are shown in Figures 4.22 through 4.24.
Typical fin height, thickness, and density are
• Fin height: 3.8–12 mm
• Fin thickness: 0.15–0.61 mm
• Fin pitch: 1.15–4.5 mm (i.e., fin density is 22–6 fpi)
• Surface area density, area/volume: 1500 m2/m3
• Design pressure up to a maximum of 110 bar (1600 psig)
• The size is available up to (W × H × L)—1.5 × 3.0 × 8.2 M
(a) (b)
FIGURE 4.22 Brazed aluminum plate-fin heat exchanger fin profiles—(a) perforated fin and (b) offset strip
fin (schematic). (From Linde AG, Engineering Division. With permission.)
(a) (b) (c)
FIGURE 4.23 Brazed aluminum plate-fin heat exchanger fin profiles—(a) serrated fins (b) OSF and
(c) perforated fins. (Courtesy of Fives Cryo, Golbey, France.)
(a) (b) (c) (d)
FIGURE 4.24 Brazed aluminum plate-fin heat exchanger fin profiles: (a) plain fin, (b) perforated fin, (c) herring-
bone fin, and (d) serrated fin. (Courtesy of Chart Industries Inc., Garfield Heights, OH.)

4.2.14.5 Rough Estimation of the Core Volume
To obtain a quick indication of the heat exchanger volume required for a certain duty, the following
simple relation as per ALPEMA standard may be used
V
Q
=
/MTD
Γ
where
V is the required volume of heat exchanger (without headers)
Q is the overall heat duty
MTD is the mean temperature difference between streams
Γ is the coefficient: 100,000 for hydrocarbon applications
50,000 for air separation application
The values of 100,000 and 50,000 represent the product, UAd, assuming an overall heat transfer
coefficient of 200 W/m2 and 100 W/m2 K, respectively, and a mean geometric heat transfer surface
density of 500 m2/m3.
The weight of a complete heat exchanger may be assumed to be 1000 kg per unit core volume
(m3). This value varies in practice between 650 and 1500 kg/m3.
Distributor fins: Distributor fins distribute the fluid between the port and the heat transfer
fins. The distributor fin used adjacent to a port is called a port fin. The distributor fin used
between a port fin and a heat transfer fin is called a turning fin. The typical distributor fin thick-
ness is 0.45 mm (0.016 in.).
Parting sheets: Parting sheets (sometimes referred to as separator sheets) contain the fluids
within individual layers in the exchanger and also serve as primary heat transfer surface. Their
selection is mainly based on design pressures. Parting sheets are normally clad on both sides
with a brazing alloy. However, unclad parting sheets are available, where brazing is performed
using brazing foils (filler material). Standard parting sheet thicknesses typically vary between
0.8 and 2.0 mm. Typical parting sheet thicknesses are 1.0, 2.0, and 3.0 mm (0.040, 0.080, and
0.125 in.).
Cap sheet or outside sheets: Cap sheets serve as the outside parting sheets. Standard cap sheet
thicknesses are typically 5 or 6 mm. However, thicknesses from 2 to 10 mm are also used for special
applications.
Side and end bars: Side and end bars enclose individual layers and form the protective perimeter
of the exchanger. Solid extruded forms are used. Side bar heights are the same as the fin heights, and
width is selected by the manufacturer according to the design pressure and typically varies between
10 and 25 mm.
Permissible temperature differences between adjacent streams: Aluminum PFHEs are
produced by brazing. To maintain the thermal stresses within the acceptable limits for the
material used, the maximum permissible temperature difference between streams shall be
about 50°C.
Support angles: Support angles are typically 90° extruded aluminum angles welded to the
exchanger bar face for the purpose of supporting or securing an exchanger in its installed position.
Other support configurations, such as pedestal bases, are also available.
Lifting lugs: Lifting lugs (aluminum) are lift attachment points strategically welded to the
exchanger block assembly for the specific purpose of lifting the exchanger into its installed
position.
Header/nozzle configurations: Streams to and from the heat exchanger enter and leave by means
of various header/nozzle configurations. Nozzles are the pipe sections used to connect the heat

exchanger headers to the customer piping. Headers are the half cylinders which provide for the
distribution of fluid from the nozzles to or from the ports of each appropriate layer within the heat
exchanger.
Ports: Ports are the openings in either the side bar or the end bar, located under the headers,
through which the fluids enter or leave individual layers.
Materials of construction: Typical materials of construction for the BAHX components are
hereunder.
Cap sheets—AA 3003 Headers and nozzles, flanges-AA
Parting sheets—AA 3003 5083/5454
Side and end bars—AA 3003 Support angles—AA 6061-T6
Heat transfer fins—AA 3003 Lifting lugs—AA 5083
Distributor fins—AA 3003
Life: A design life similar to tubular heat exchangers can be expected from them.
Construction code: The design, construction, and testing of BAHXs are governed by the existing
national rules applying to pressure vessels.
Modular exchanger assembly: A modular exchanger assembly consists of two or more exchanger
blocks, welded together prior to attaching the headers, to form a single piece exchanger. This form
of construction is used when the customer’s heat exchange requirements exceed the maximum block
size which can be furnace brazed. Modular construction eliminates the need for costly piping to
interconnect separate, individual exchangers.
Cold box: The installation of different exchangers in a steel containment (cold box), usually rect-
angular in shape. Interconnecting piping, vessels, valves, and instrumentation are included in this
packaged unit to form, after filling with insulation material, a ready-to-operate unit.
Block-in-shell: One or more heat exchanger blocks installed in a shell instead of a tube bundle.
This is a highly efficient and economical alternative to standard shell and tube heat exchangers. The
benefits include tighter approach temperatures, smaller in size and weight, lower capital costs, and
lower operating costs. A typical block-in-shell is shown in Figure 4.25.
Transition joint: A transition joint is a bimetallic coupling used to make the transition from alu-
minum to stainless steel piping. Transition joints are available in various configurations.
FIGURE 4.25 Brazed aluminum heat exchanger: block-in-shell. (From Linde AG, Engineering Division.
With permission.)

4.2.14.6 Provisions for Thermal Expansion and Contraction
Provisions for thermal expansion and contraction of the heat exchanger in the horizontal plane at the
support location must be provided. The expected thermal movement should be calculated in both
horizontal directions by the following equation:
∆ ∆L L T= × × ×−
12 6 1 in in FPS units6
. . ( )0
∆ ∆L L T= × × ×−
97 1 1 m in SI units6
. ( )0
where
L is the distance in m/in. between extreme bolts in the direction under consideration
∆T is the change in temperature in °C(°F) at the support location from the installed (ambient)
temperature to the coldest possible operating temperature
∆L is the expected thermal movement in m/in. which will result from this calculation
If the expected thermal movement in both directions is 12.7 mm (0.5″) or less, the bolt hole
diameters in the aluminum support angles should be oversized by adding the maximum expected
thermal movement to the bolt diameter. If the expected thermal movement exceeds 12.7 mm
(0.5 in.) in one of the horizontal directions, a slotted hole should be used with a slot length equal
to the bolt diameter plus the maximum expected thermal movement.
4.2.14.7 Mechanical Design of Brazed Aluminum Plate-Fin Heat Exchangers
The design of a brazed aluminum PFHEs is the result of the mechanical strength analysis of
• The plate-fin structure under pressure
• The influence of headers on the plate-fin structure
• The header/nozzle assembly
Pressure vessel codes generally do not contain formulae for the fins. The calculation methods used
by manufacturers have been approved by the applicable Code Authority. The calculated stresses are
compared with the maximum allowable stress as per the code.
4.2.14.8 Codes
BAHXs are normally designed and manufactured in accordance with Section VIII, Division I
of the ASME Pressure Vessel Code, carry the “U” stamp, and are registered with the National
Board of Boiler and Pressure Vessel Inspectors. Manufactures can manufacture to other interna-
tional standards, such as PED European Pressure Equipment Directive, AD-Merkblatter, Australian
Standard, British Standard, Chinese Standard, CODAP, Japanese Industrial Standards, Raccolta/
VSR, Stoomwezen Grondslagen, Swedish Pressure Vessel Code, Russian Gost, etc.
Associated piping is normally designed and manufactured in accordance with the ASME
B31.3 Piping Code. The ASME pressure vessel and piping code boundaries are indicated on the
drawing. Heat exchangers and piping are sometimes designed and manufactured to other national
codes. The governing national code is specified on the drawing and exchanger nameplate.
4.2.14.9 Materials of Construction
Typical materials for use on the construction of brazed aluminum PFHEs are (1) core matrix
(fins, plates, side bars) is aluminum alloy AA 3003 and (2) headers/nozzles is aluminum alloy
AA 5083 and their mean metal temperature limitations as per ASME code are alloy AA 3003 is
−269/+204°C and that of AA 5083 is −269/+65°C.

4.2.14.10 Manufacture
After forming, cutting, and cleaning of the single parts, the block is stacked and prepared for high
vacuum brazing at about 600°C. For welding of headers and nozzles to the core, proven welding
procedures, such as GTAW and GMAW, are used.
4.2.14.11 Quality Assurance Program and Third Party Inspection
Quality management is an essential part of all manufacturers’ strategy. The companies are certi-
fied to various national and international standards. Acceptance inspection is carried out by firm’s
own specialists and further by experts from various international inspection organizations/agencies,
such as TÜV, Lloyd’s Register, Stoomwezen, ISPESL, Bureau Veritas, Det Norske Veritas, etc.
4.2.14.12 Testing of BAHX
Extensive test procedures are carried out on the completely assembled heat exchangers. These
include radiographic and dye penetrant testing of weld seams, pressure test, and helium leak
tests and if requested, flow tests. A BAHX is first structurally tested. For hydrostatic test meth-
ods, each stream is pressurized, with the other streams at zero pressure, to 1.3 times the design
pressure as per the requirements of ASME. The unit remains pressurized for stipulated period as
per the code. Pneumatic test methods can be used with the pressure level being adjusted to 1.1 times
design pressure. Leak testing is performed after the structural test has been successfully per-
formed. Internal leak testing is performed by pressurizing each stream individually and moni-
toring small nozzle valves on the unpressurized streams using soap film solution. External leak
testing is performed using soap solution on the exchanger external joints. For critical applica-
tions, helium vacuum leak testing may also be used to validate the leak tightness of an exchanger.
4.2.14.13 Guarantees
Manufacturers shall offer a thermal performance guarantee and a mechanical guarantee. Details
shall be agreed upon by the purchaser and the manufacturer.
4.2.14.14 ALEX: Brazed ALuminum EXchanger
ALEX is the trade name of a BAHX developed independently by Kobe Steel in 1963 for use as the
regenerator in air separation plants. Core tube is steel with aluminum coated in flat shape with par-
allel sides and smooth fins having a reduced tendency for fouling. Kobe Steel is one of the members
of ALPEMA standards and is the top user of ALEX for cold box for LNG applications, core-in-
drum type heat exchangers, etc. A small ALEX core is shown in Figure 4.26a, and an air-cooled
condenser made of ALEX core is shown in Figure 4.26b.
(a) (b)
FIGURE 4.26 Aluminum Exchanger (ALEX) core—(a) mini core and (b) aircooled heat exchanger with
single row type with steel tubes and ALEX core. (Courtesy of GEA Power Cooling, Inc., Lakewood, CO.)

4.2.15 Comparison of Salient Features of Plate-Fin Heat
Exchangers and Coil-Wound Heat Exchanger
Both the brazed aluminum PFHEs and coiled tube heat exchangers find application in liquefication
processes. Salient features of these two types of heat exchangers are compared in Table 4.2 for the
intended service.
4.2.16 Heat Exchanger Specification Sheet for Plate-Fin Heat Exchanger
Heat exchanger specification sheet for PFHE is shown in Figure 4.27.
4.3 SURFACE GEOMETRICAL RELATIONS
4.3.1 Surface Geometrical Parameters: General
The following are some of the basic relationships between the surface and core geometries on one
side of the compact heat exchangers.
4.3.1.1 Hydraulic Diameter, Dh
The generalized relation for hydraulic diameter is given by

hD
A L
A
=
4 o

(4.1)
where
A is the total heat transfer area
Ao is the free flow area
L is the flow length
The hydraulic radius rh is given by Dh/4.
TABLE 4.2
Comparison of Salient Features of Plate-Fin Heat Exchangers and Coil-Wound Heat
Exchangers
Plate-Fin Heat Exchangers Coil-Wound Heat Exchangers
Characteristics Extremely compact, multiple streams,
single- and two-phase streams
Compact, multiple streams, single and
two-phase streams
Fluid To be very clean To be clean
Flow types Counterflow, crossflow Cross counterflow
Heating surface compactness 300–1400 m2/m3 20–300 m2/m3
Materials Aluminum Aluminum, stainless steel (SS), carbon
steel (CS), special alloys
Temperature −269°C to +65°C (150°F) All
Pressure Up to 115 bar (1660 psi) Up to 250 bar (3625 psi)
Applications Cryogenic plants, noncorrosive fluids.
Very limited installation space
Also for corrosive fluids and thermal
shocks
Source: Linde AG, Engineering Division, Germany. With permission.

FIGURE 4.27 PFHE specification sheet N°. (Courtesy of Fives Cryo, Golbey, France.)

4.3.1.2 Surface Area Density α and σ
For a compact heat exchanger with secondary surface on one side, it is customary to designate
the ratio of the total heat transfer surface area on one side of the exchanger to total volume of the
exchanger by α, and the ratio of the free flow area to the frontal area by σ. Thus,

α α1
1 2
= =
A
V
A
V
and 2

(4.2)

σ1
0 1
1
14 4
= =



 =
A
A
AD
A L
AD
V
. ( )
fr,1
h
fr
h/ /

(4.3a)

σ2 = =



 =
A
A
AD
A L
AD
V
h0 2
2 2
24 4. ( )
fr, fr
h/ /

(4.3b)
From the definition of hydraulic diameter Dh, the relation between hydraulic diameter, surface area
density α, and σ is given by

D
L
A
A L
h o
4 1 1 1



 =



 =




σ
α

(4.4a)

D
L
A
A L
h o
4 2 2 2



 =



 =




σ
α

(4.4b)
and

D Dh,
1
h,21
1 2
2
4 4= =
σ
α
σ
α
,

(4.5)
4.3.2 Tubular Heat Exchangers
Geometrical relations are derived for the inline and staggered tube arrangements with bare
tubes, individually finned circular tubes, and circular tubes with plain continuous fins. The
header dimensions for the tube bank is L2 × L3, the core length for flow normal to the tube bank
is L2, and the no-flow dimension is L3. The lateral pitch is given by Pt, and longitudinal pitch
by Pl. Flow is idealized as being normal to the tube bank on the outside. Surface geometrical
relations for tube-fin heat exchangers are derived from first principles by Shah [20,21], and for
individually finned tubes by Idem et al. [22]. The surface geometrical relations given here are
based on Shah [21].
4.3.2.1 Tube Inside
Tubes have inside diameter di, length between headers L1, header thickness Th, and total length
including header plates thickness as L1 + 2Th. The total number of tubes, Nt, is given by

N
L L
PP
t
t l
= 2 3

(4.6)

The geometrical properties of interest for analysis are
Total heat transfer area i 1 tA d L N= π (4.7)

Minimum free flow area o i tA d N=




π
4
2

(4.8)

Hydraulic diameter =h iD d

(4.9)

Tube length for heat transfer = 1L
(4.10)

Tube length for pressure drop = +2 hL T1

(4.11)
The geometrical properties given by Equations 4.7 through 4.11 also hold good for other types of
arrangements discussed next.
4.3.2.2 Tube Outside
4.3.2.2.1 Bare Tube Bank
Inline arrangement: The geometrical properties of the inline tube bank as shown in Figure 4.28 are
summarized here. The number of tubes in one row (in the flow direction) is

N
L
P
l
t
= 3

(4.12)
The total heat transfer area consists of the area associated with the tube outside surface given by
A d L N= π o t1 (4.13)
The minimum free flow area Ao, frontal area Afr, the ratio of free flow area to frontal area σ, and
hydraulic diameter Dh are given by
A P d N Lo t t= − ′( )ο 1 (4.14)
A L LFr = 1 3 (4.15)
Pl/2
Pl
Flow
Pt/2
Pt
do
L3
Th
L2 L1
di
do
FIGURE 4.28 Inline tube bank geometry (bare tube).


σ =
−( )P d
P
t o
t
(4.16)

D
A L
A
h
o
=
4 2

(4.17)

Flow length for pressure drop calculation
Heat exchanger
= L2
volume V L L L= 1 2 3

(4.18)
It must be emphasized that the foregoing definition of the hydraulic diameter is used by Kays and London
[17] for tube banks. However, many correlations use the tube outside diameter or fin root diameter as the
characteristic dimension in the heat transfer and pressure-drop correlations. So it is essential to find out
first the specific definition of the characteristic length before using a particular correlation.
The geometrical properties given by Equations 4.14 through 4.18 also hold good for other types
of arrangements discussed later.
Staggered arrangement: A staggered tube bank layout and its unit cell are shown in Figure 4.29.
The total number of tubes with half tubes in the alternate row is given by Equation 4.6. If the half tubes
are eliminated from the alternate intermediate tube rows, then the number of tubes in the first row
will be L3/Xt, and in the second row L3/Xt − 1. The minimum free flow area occurs either at the front
or through the diagonals (refer to Figure 4.29b). The minimum free flow area is then given by [20,21]

A
L
P
z P d Lo
t
t o= −



 + −






3
11 ( )

(4.19a)
Pl/2
Pl
Pl
Pt
do
2x
y
y
Pt/2Pt
L2
(a)
(b)
L1
L3
do
Th
do
di
Flow
FIGURE 4.29 Staggered tube bank (bare tube): (a) layout and (b) unit cell.

where

z x x y= 2 2 2if

(4.19b)

z y y x= 2 if 2 2

(4.19c)
in which 2x and y are defined as
2x P d= −( )t o (4.20a)

y
P
P d=



 +








−t
t o
2
2
2
0 5
( )
.

(4.20b)
In Equation 4.19a, the last term (Pt − do)L1 corresponds to the free flow area between the last tube at
each end in the first row and the exchanger wall.
4.3.2.2.2 Circular Fins on Circular Tubes
The basic core geometry of an idealized single-pass crossflow exchanger for an inline arrangement
is shown in Figure 4.30. The total number of tubes in this exchanger is given by Equation 4.6. It is
idealized that the root of a circular fin has an effective diameter dr and the fin tip has a diameter df.
Depending upon the manufacturing techniques, dr may be the tube outside diameter or tube outside
diameter plus two fin collar thickness. The total heat transfer area consists of the area associated
Pt
Amin
(b)
tf
df
dr
Pt/2
Pl/2 Pl
df
di
do
Pt
L3
L2
L1
Th
(a)
Flow
FIGURE 4.30 Individually finned circular fin tube. (a) Inline layout and (b) diagram showing frontal area
(dotted lines) and free flow area (hatched area).

with the exposed tubes (primary area) and fins (secondary area). The primary area, Ap, is the tube
surface area minus the area blocked by the fins. It is given by

A d L t N L Np r f f t= −π ( )1 1

(4.21)
where
tf is the fin thickness
Nf is the number of fins per unit length
The fin surface area, Af, is given by

A
d d
d t N L Nf
f r
f f f t=
−( )+








2
4
2 2
1
π
π

(4.22)
and therefore, the total heat transfer surface area A is equal to Ap + Af, given by

A d L t N L N
d d
d t N L N= − +
−( )+








π
π
πr 1 f f t
f r
f f f t( )1
2 2
1
2
4

(4.23)
Minimum free flow area: Inline arrangement: The minimum free flow area for the inline arrange-
ment is that area for a tube bank, Equation 4.13, minus the area blocked by the fins:

A P d L d d t N L
L
P
ο = − − −[ ]



( ) ( )t r f r f f
t
1 1
3

(4.24)
Minimum free flow: Staggered arrangement: The basic core geometry of an idealized single-pass
crossflow exchanger for staggered arrangement is given in Figure 4.31. The total number of tubes in
this exchanger is given by Equation 4.6. For the staggered tube arrangement, the minimum free flow
area could occur either through the transverse pitch or through the diagonals similar to those of the
unit cell shown in Figure 4.31b. The minimum free flow area is given by [19,20]

A
L
P
z P d d d t N Lo
t
t r f r f f= −



 ′ + − − −






3
11 ( ) ( )

(4.25)
where
′ = ′ ′ ′z x x y2 2 2if
(4.26a)
′ = ′ ′ ′z y y x2 2 2if
(4.26b)
in which 2x′ and y′ are given by
2 ′ = − − −x P d d d t N( ) ( )t r f r f f
(4.27a)

′ =



 +








− − −y
P
P d d d t Nt
r f r f f
2
2
1
2
0 5
( ) ( )
.

(4.27b)
Dimensions 2x′ and y′ cannot be depicted in the figure.

4.3.2.2.3 Continuous Plain Fins on Circular Tubes
The tube-fin arrangement is shown in Figure 4.32. The total heat transfer area consists of the area associ-
ated with the exposed tubes (primary area) and the fins (secondary area). The primary area is the same
as that given by Equation 4.13, minus the area blocked by the fins. Therefore, Ap is given by [14,20]

A d L t N L Np = −π r f f t( )1 1

(4.28)
The total fin surface area, Af, consists of (1) the fin surface area, and (2) the area with leading and
trailing edges, given by

A L L d N N L L t N Lf r f f f f= − +2 4 22 3
2
1 3 1[( )/ ]π

(4.29)
and

Total heat transfer surface area p fA A A= +

(4.30)
Minimum free flow area for the inline arrangement: The minimum free flow area for an inline
arrangement is that area for a tube, Equation 4.13, minus the area blocked by the fins [14,20]

A P d L P d t N L
L
P
ο = − − −[ ]



( ) ( )t r t r f r
t
1 1
3

(4.31)
Pt
2x΄
Pl
(b)
dr
y΄
y΄
Pl/2
Pt/2Pt
L3
L2
(a)
L1
df
dr
di
Flow
Pl
FIGURE 4.31 Individually finned tube staggered arrangement. (a) Geometry and (b) unit cell. (After Shah,
R.K., Compact heat exchangers, in Handbook of Heat Transfer Applications, W.M. Rohsenow, J.P. Harnett,
and E.N. Ganic, eds., McGraw-Hill, New York, 1985, pp. 4-176–4-312.)

Minimum free flow area for the staggered arrangement: For the staggered tube arrangement as
shown in Figure 4.32b, the minimum free flow area could occur either through the transverse pitch
or through the diagonals. The minimum free flow area is given by [20,21] as follows:

A L P z P d P d t N Lo t t r t o f f= −( ) ′′ + − − −[ ]{ }3 11/ ( ) ( )

(4.32)
In Equation 4.32, z″ is defined as
′′ = ′′ ′′ ′′z x x y2 2 2if (4.33a)
′′ = ′′ ′′ ′′z y y x2 2 2if
(4.33b)
where 2x″ and y″ are given by
2 ′′ = − − −x P d P d t N( ) ( )t r l r f f
(4.34a)

′′ =



 +








− − −y
P
P d P d t Nt
r t r f f
2
2
1
2
0 5
( ) ( )
.

(4.34b)
Pl/2
Pl/2
Pt/2
Pt/2Pt
Pt
Th
Th
Pl
Pl
Flow
Flow
di
do
L3
L2 L1
(a)
(b)
L2
L1
di
dr
do
L3
dr
FIGURE 4.32 Continuous flat fin-tube heat exchanger: (a) inline layout and (b) staggered layout.

Minimum free flow area for pressure drop: For the determination of entrance and exit pressure
losses, the area contraction and expansion ratio σ′ is needed at the leading and trailing fin edges. It
is given by [14,20] as follows:

′ =
−
σ
L L L t N L
L L
3 1 3 1
3 1
f f

(4.35)
4.3.3 Compact Plate-Fin Exchangers
The following geometrical properties on each side are needed for the heat transfer and pressure-
drop analysis of a PFHE:
1. The primary and secondary surface area (if any) Ap and As, respectively
2. Minimum free flow area Ao
3. Frontal area Afr
4. Hydraulic diameter Dh
5. Flow length L
6. Fin dimensions—thickness and length (height)
4.3.3.1 Heat Transfer Area
The total heat transfer area consists of sum of the primary and secondary heat transfer areas and
their calculation method is given later. The primary heat transfer surface within the heat exchanger
consists of the bare parting sheet and the fin base directly brazed to the parting sheet and the sec-
ondary heat transfer surface is provided by the fins. The cross-sectional view of fin and parting
sheet is shown in Figure 4.33. The effectiveness of the secondary surface to transfer heat is given by
the fin efficiency. Per unit area of the each parting sheet is given by
a. Primary surface area, Ap is given by 2(1 − ntf)
b. Secondary surface, As is given by 2n (lf − 1)
where
n is the fin density (m−1), i.e. number of fins per unit length
tf is the fin thickness (m)
lf is the fin height (m)
The effective heat transfer surface area for a passage can be estimated by the following equation:

A A A= +p sηφ

(4.36)
Primary
surface
Secondary
surface
Fin
thickness
Finheight
FIGURE 4.33 Primary and secondary heat transfer area for a unit flow passage.

single blanking (Figure 4.33) and fin efficiency, η is given by

η
β
β
=
/
tan ( /2)
2
h

(4.37a)
where
Ap is the primary heat transfer surface of a stream (Figure 4.33)
As is the secondary heat transfer surface of a stream (Figure 4.33)
η is the passage fin efficiency for single banking
lf is the fin height
n is the fin density

β
α
=



h
k t
2
0 5
f f
.

(4.37b)
α is the effective heat transfer coefficient of a stream
ϕ is the unperforated fraction (1 − ratio of perforated area to the total fin area)/100
kf is the thermal conductivity of fin material
The thermal length of a brazed aluminum PFHE is defined as the effective length of the finned
region between, but not including, the distributors.
The information not specified directly is computed based on the specified surface geometries
and core dimensions. Consider a PFHE as shown in Figure 4.34 in which L1 and L2 are the flow
lengths, Np and Np + 1 are the number of flow passages on sides 1 and 2, respectively, and V is the
total core volume. The following formulas define some of the geometrical properties on any one side
of the PFHE. These geometrical relations are derived in Refs. [17,23,24].
The volume between plates on each side is given by

V L L b N V L L b Np 1 p p,2 p, ( ) ( )1 1 2 1 2 2 1= = +

(4.38)
Heat transfer area on each side is given by

A V A V1 1 2 2= =β βp,1 p,2

(4.39)
where β1 and β2 are the surface area density on each side per unit volume between plates.
Fluid 1
Fluid 2
Np+1
b2
Np
b1
L3
L2
L1
FIGURE 4.34 Plate-fin heat exchanger core to calculate surface geometrical parameters.

The ratio of minimum free flow area to frontal area (σ) on side 1 is given by

σ
β
1
0 1
1
0 1 1
1 1
1 14 4
= = = =
A
A
A L
A L
A D
V
V D
V
,
,
,
,fr fr
h,1 p,1 h,1/ /

(4.40a)

/ /p h,1
p p p
h,1
=
+ + + +
≈
+ +
b N D
b N b N a N
b D
b b a
1 1
1 2
1 1
1 2
4
1 2 1
4
2
β β
( ) ( )

(4.40b)

σ
β β
2
2 2
1 2
2 2
1 2
1 4
1 2 1
4
=
+
+ + + +
≈
+ +
b N D
b N b N a N
b D
b b
( )
( ) ( )
p h,2
p p p
h,2/ /
22a

(4.40c)
where a is the thickness of parting plates. The ratio is given similarly for side 2. Here, the last
approximate equality is for the case when Np is very large or the numbers of passages on the two
sides are the same.
The heat transfer surface area on one side divided by the total volume V of the exchanger, des-
ignated as α1, is

α
σ β
1
1 1 1 1
1 2
4
2
= = =
+ +
A
V D
b
b b ah,1

(4.41a)
Similarly, α2 is given by

α
σ β
2
2 2 2 2
1 2
4
2
= = =
+ +
A
V D
b
b b ah,2

(4.41b)
4.3.3.2 Components of Pressure Loss
The individual pressure losses within a heat exchanger typically consist of [12]
1. Expansion loss into the inlet header
2. Contraction loss at the entry to the core
3. Loss across the inlet distributor
4. Loss across the heat transfer length
5. Loss across the outlet distributor
6. Expansion loss into the outlet header
7. Contraction loss into the outlet nozzle
4.3.3.2.1 Single-Phase Pressure Loss
The frictional pressure loss across a plate-fin passage and at any associated entry, exit, and turning
losses can be expressed by [12]

∆p f
L
D
G
K
G
=







 +



4
2 2
2 2
h
m m
ρ ρ

(4.42)
where
f is the fanning friction factor
L is the passage length
Dh is the hydraulic diameter of passage
Gm is the mass velocity (mass flux) of stream
ρ is the density of a stream
K is the expansion, contraction, or turning loss coefficient
∆p is the overall pressure drop

4.4 FACTORS INFLUENCING TUBE-FIN HEAT EXCHANGER PERFORMANCE
Important factors that influence the heat transfer performance of tube-fin heat exchangers include
the following:
1. Tube layout (staggered vs. inline arrangement)
2. Equilateral layout versus equivelocity layout
3. Number of rows
4. Tube pitch
5. Finned tube variables (fin height, spacing, thickness)
6. Fin tubes with surface modifications
7. Side leakage
8. Boundary-layer disturbances and characteristic flow length
9. Contact resistance in finned tube heat exchangers
10. Induced draft versus forced draft
Johnson [25] and Rabas and Taborek [7] discuss the effect of various tube-fin parameters on ther-
mohydraulic performance.
4.4.1 Tube Layout
The two basic arrangements of the tubes in a tube bank are (1) staggered arrangement with equilat-
eral triangular pitch and (2) inline arrangement. The extent of transverse flow in the inline layout
is small in comparison to the staggered arrangement. The most commonly used is the staggered
layout. There are very few applications of low-finned tubes with the inline arrangement. It may be
used when airside fouling problems are encountered. For identical operating conditions, the inline
arrangement has low heat transfer, of the order of 70%, and pressure drop is also of this order.
4.4.2 Equilateral Layout versus Equivelocity Layout
In the conventional equilateral staggered layout, the area available for airflow in the transverse
direction is half of that available in the diagonal direction; therefore, energy is lost in accelerating
and decelerating the air stream as it flows through the bank. In the equivelocity layout, these two
areas are made equal by adjusting the transverse (Pt) and longitudinal (Pl) pitches, thus minimiz-
ing these losses. In general, for applications where horsepower is evaluated at a high premium and
a reduced pressure drop is attractive, even at the expense of some loss of thermal performance, an
expanded pitch layout type should be strongly considered.
4.4.3 Number of Tube Rows
The addition of tube rows in the crossflow direction is the common way of increasing heat transfer
area when the frontal area of the tube bank is fixed. Such an addition of tube rows increases the
flow length for the air and may affect the fluid dynamics with a possible effect on heat transfer and
pressure drop. Pressure drop through the tube bundle increases with the number of tube rows. The
temperature drop through the tube bundle also increases with the number of tube rows, though the
effect is very large with the first few tube rows and for a very large number of tube rows the effect
is small. Temperature drop through a multirow tube bank is shown schematically in Figure 4.35.
The row effect on heat transfer coefficient is discussed by Johnson [25]. A basic difference exists
between the row effects for the inline and the staggered arrangements. For an inline arrangement,
the heat transfer coefficient decreases with an increase in the number of rows. Brauer [27] shows
that the one-row tube bank heat transfer coefficient is approximately 50%–80% higher than the
average for four rows, whereas for a staggered arrangement the four-row tube bank has approxi-
mately 30% higher heat transfer coefficient (average) than a one-row tube bank.

4.4.4 Tube Pitch
Tube pitch is commonly used in heat-exchanger design to affect compactness of the core and flow
conditions. The hydraulic diameter increases with the pitch. Based on comparable air velocities, the
pitch has no effect on the heat transfer coefficient. However, increasing the pitch strongly affects the
pressure drop, as it decreases the pressure drop through the bundle [25].
4.4.5 Tube-Fin Variables
The tube-fin variables that affect the thermal performance include fin height, fin spacing, and thickness
and thermal conductivity of the fin material. Surface area of the tube bank can be increased by employ-
ing fin tubes with high (longer) fins and denser spacing. However, increasing the fin height will decrease
the fin effectiveness, and may lower heat transfer compared with the short fins. Denser fins may lower
the heat transfer because of laminarization of the flow conditions between the fins [25]. Fin efficiency
increases with a reduction in fin height and an increase in fin thickness. Thermal conductivity is usually
not a problem in selecting the material of a primary surface, but it is important in extended surfaces
because of the relatively long and narrow heat flow path, which affects their heat transfer performance [6].
4.4.5.1 Fin Height and Fin Pitch
The fin height and fin pitch that can be used effectively are fundamentally related to the boundary-
layer thickness [6]. Wen-Jei Yang [6] states the rule of thumb: (1) For large thermal boundary-layer
thickness, the heat transfer coefficient, h, is low and thus high fins are employed; (2) low fins are
employed in the case of a thin boundary layer where h is high; and (3) if the fin spacing is too small,
the main stream cannot penetrate the spaces between the fins, resulting in no increase in thermal
boundary area and an excessive pressure drop.
4.4.6 Finned Tubes with Surface Modifications
The term “surface modification” refers to fin tubes that have extended surfaces that are mechani-
cally deformed to various shapes by crimping, corrugating, cutting, slotting, or serrating the fins;
for continuous plate-fins, surface interruptions constitute surface modification [25]. Any surface
modification will increase the heat transfer and pressure drop as compared with the identical
smooth fin. Common surface modifications for circular fins are discussed further in Chapter 8.
Cooling water temperature
Number of tube rows
1
75
100
125
150
175
2 3 4 5 6 7 8 9 10 11 12
Airtemperature°C
FIGURE 4.35 Temperature drop through a multi-tube row heat exchanger—schematic (for a typical case).

4.4.7 Side Leakage
The heat transfer and pressure-drop performance of a tube bank is affected by the leakage flow
between the outermost tube and the side walls. This is equivalent to the bundle-to-shell bypass
stream (C-stream) leakage in a shell and tube exchanger. The effect of bypass flow can be mini-
mized by attaching side seals to the exchanger in every even row as shown in Figure 4.36. Clearance
between the core and the housing can be minimized by welding metal strips to the housing or
attaching metal strips to the header as shown in Figure 4.36b.
4.4.8 Boundary-Layer Disturbances and Characteristic Flow Length
Periodic interruption of the boundary layer is achieved by breaking the total flow length into many
characteristic lengths by means of OSFs, louvered fins, wavy fins, etc. [28]. The characteristic flow
length, Lf, is illustrated in Figure 4.37. The characteristic flow length and the hydraulic diameter, Dh,
are responsible for the numerical merits of a surface geometry. The representative length of finned
heat exchangers as parameters to represent their performance suggests that it would be possible
Core
(a)
(b)
FIGURE 4.36 Sealing strips to arrest bypass flow: (a) between the core and the housing and (b) between the
tubes and side sheets.
Lf
Lf
Lf
(e)(d) Louvered fins Wavy fins Offset strip fins(f)
Lf Lf
Lf
(a) Bare tubes
and pin fins
Tubes with
circular fins
Straight continuous fins(b) (c)
FIGURE 4.37 Characteristic flow length between major boundarylayer disturbance for various heat
exchanger surfaces. (Adapted from LaHaye, P.G. et al., Trans. ASME, J. Heat Transfer, 96, 511, 1974.)

to enhance their performance by shortening the representative length of the fin and using finer
segmentation than the regions of louvered or OSFs [29]. The application of the pin finned surface
can be considered one of the best candidates.
4.4.9 Contact Resistance in Finned Tube Heat Exchangers
4.4.9.1 Continuous Finned Tube Exchanger
In the design of finned tube heat exchangers, the contribution of contact resistance at the interface
between the tube and fin collar is not always negligible compared with the total heat transfer resistance,
Figure 4.38 [29]. This is particularly true for mechanically bonded tube-fin exchangers used in low-
pressure applications such as air-conditioning industries and air coolers for supercharged engine intake
air. In the heat exchanger assembly process, the initial interference, the microhardness of the softer mate-
rial at the interface, contact area, and contact pressure are parameters that determine the contact resis-
tance [30]. Selection of the proper bullet size can optimize the degree of contact at the interface. During
the last three decades, many researchers have developed experimental methods to measure thermal
contact resistance accurately. An experimental method to measure contact resistance in a vacuum envi-
ronment is described by Nho et al. [30]. In a typical experimental setup, they found that the contact resis-
tance at the tube and fin interface was 17.6%–31.5% of the overall resistance in a vacuum environment.
4.4.9.2 Tension-Wound Fins on Circular Tubes
For round-fin tubes with aluminum fins wrapped on steel tubes under tension, the contact resistance
increases quickly with the operating temperature so that their application is limited to temperatures
of 100°C or less [31]. Otherwise, the tension would be reduced, leading to fin loosening, due to the
higher thermal expansion of aluminum.
4.4.9.3 Integral Finned Tube
With an integral finned tube, there is no concern at the fin bond about heat transfer resistance and
the integrity of tubing, regardless of temperature and pressure levels. However, only certain fin
geometries can be obtained with an extrusion process.
Tube
Fin
Fin
collar
FIGURE 4.38 Metal-to-metal contact between the tube and the fin.

4.4.10 Induced Draft versus Forced Draft
The heat transfer and pressure drop depend on the method used to generate the flow on the tube bank,
namely, induced draft or forced draft. When a fluid enters the tube bank, the level of turbulence can
change with penetration into the bundle. The tube bundle heat transfer coefficient and pressure-drop
performance vary for each additional row for a shallow exchanger, and become independent of the
number of rows only for the deep bundles with a very large number of tube rows [7]. Common practice
is to apply a row correction multiplier to the deep bundle correlations (ideal bundle) to account for
these variations. Recommendations by Rabas et al. [7] for the mode of flow are discussed next.
4.4.10.1 Induced Draft
For induced draft, the recommended approach is to use the heat transfer row correction for plain
tube banks. For the plain tube, bundle row corrections refer to Giedt [32] and ESDU [33]. The
value varies from 0.65 for a single row to about 0.98–1.0 for an eight tube rows bundle. The bundle
pressure-drop variation with row number is smaller than the heat transfer coefficient variation and
hence the row effect is usually ignored.
4.4.10.2 Forced Draft
A conservative approach suggested is to neglect the row correction for the forced draft mode of
operation for low-finned tube banks [7].
4.5 THERMOHYDRAULIC FUNDAMENTALS OF FINNED TUBE
HEAT EXCHANGERS
It is a common practice to use the Colburn j factor to characterize the heat transfer performance
and the Fanning friction factor f to characterize the pressure drop of the tube banks as functions of
Reynolds number. This section provides empirical correlations for j and f factors. With these cor-
relations, the performance of geometrically similar heat exchangers can be predicted, within the
parameter range of the correlations.
4.5.1 Heat Transfer and Friction Factor Correlations for Crossflow
over Staggered Finned Tube Banks
During the last 50 years, many investigations have been carried out to determine the heat transfer
and pressure drop over the tube banks. One of the first correlations was established by Grimson [34]
for bare tube banks. A standard reference for the heat transfer and fraction data of PFHE surfaces is
the book by Kays and London [17]. This book presents j and f versus Reynolds number plots for tube
banks, tube-fin heat exchangers, and 52 different plate-fin surface geometries. Some of these data
were published in Transactions of the ASME. Shah and Bhatti [35] summarize important theoreti-
cal solutions and correlations for simple geometries that are common in compact heat exchangers.
Most of the experimental data have been obtained with air as the test fluid. The j factor and fanning
f factor are defined rather consistently in the literature by the following equations:

j
h
Gc
=
(Pr)
P
2 3/

(4.43a)
P
P
=




h
Gc
c
k
µ
2 3/

(4.43b)


h jGc
c
k
h
k
Dh
=



 =
−
P
P
or
Nuµ
2 3/

(4.43c)

∆p f
L
D
G
g
=



4
2
2
h c
max
ρ

(4.44)
where Gmax is given by

G U
A
A
max =



ρ f
fr
o

(4.45)
and is based on the minimum free flow area within the tube bundle. This minimum free flow area
includes the gaps between the outermost tubes and the side walls of the tube bundle. In Equation 4.44,
contraction and expansion losses and momentum losses are neglected; only flow friction effect is
taken into account.
The Reynolds number is defined as

Re Re Re= = =
Gd Gd GDr o h
or or
µ µ µ
(4.46)
where
dr is the fin root diameter or the tube outside diameter, which depends on the tube manufacturing
techniques
Dh is the hydraulic diameter
The j factor is related to Stanton number and Prandtl number by

j = St(Pr) /2 3

(4.47)
where the Stanton number is given by

St
Nu
=
Re(Pr)
(4.48)
From Equations 4.47 and 4.48, the expression for j is given by

j =
Nu
Re(Pr) /1 3

(4.49)
4.5.2 The j and f Factors
4.5.2.1 Bare Tube Bank
Experimental heat transfer and fluid friction data for six staggered circular tube patterns and one inline
arrangement are given in Ref. [36]. The results of Ref. [36] have been presented in Kays and London [17].
The Giedt [32] correlation states that the thermal performance of a bare tube bank is given by

j =
0 376
0 4
.
Re .

(4.50)

4.5.2.1.1 Inline Tube Bank
For a 10-row-deep inline tube bank, the correlation for j is given by [37]

j =
0 33
0 4
.
Re
.

(4.51)
This correlation is valid for tube diameter from 1/4 to 2 in., and Reynolds number range 100–80,000.
4.5.2.2 Circular Tube-Fin Arrangement
The basic geometry is shown in Figure 4.39.
Experimental heat transfer and fluid friction data for three circular finned tube surfaces are
given in London et al. [38]. The results of Ref. [38] have been presented in Kays and London [17].
4.5.2.2.1 Briggs and Young Correlations [39]
For low-fin tube banks, the correlation based on experimental heat transfer data is

Nu d
0.667
f f
=







0 1507 1 3
0 164 0 075
. Re Pr /
. .
s
l
s
t

(4.52)
where [s = (l − Nftf)/Nf] with a standard deviation of 3.1%. This is applicable for a circular finned tube
with low-fin height and high-fin density, Red (based on tube outer diameter) = 1000–20,000, Nr ≥ 6,
and equilateral triangular pitch.
For high-fin tube banks, the correlation based on experimental heat transfer data is

Nu Red
0.718
f
=



0 1378 1 3
0 296
. Pr /
.
s
l

(4.53)
with a standard deviation of 5.1%.
df
dr
tf
S
lf
FIGURE 4.39 Tube-fin details.

For all tube banks, the correlation based on regression analysis is

Nu
f f
=







0 134 0 681 1 3
. Re Prd
. /
0.200 0.1134
s
l
s
t

(4.54)

j
s
l
s
t
=








−
0 134 0 319
0 200 0 1134
. Re .
. .
d
f f

(4.55)
with a standard deviation of 5.1%.
4.5.2.2.2 Robinson and Briggs Correlations [40]
For equilateral triangular pitch with high-finned tubes,

f
P
d
t
=



9.465Re
0.927
d
0.316−
−
ο

(4.56)
with a standard deviation of 7.8%. This is applicable for the following parameter definitions:
Red = 2000–50,000
df = 1.562–2.750
Pt = 1.687–4.50
For isosceles triangular layout,

f
P
d
P
P
=








−
−
9 465 0 316
0 927 0 515
. Re .
. .
d
t
r
t
l

(4.57)
This is applicable for
do mm 18 6 4 9( ) . .= − 0
l df o 35 56/ . .= 0 0−
l sf 4 5 5 3/ . .= −
σ = 13 3 17 4. .−
P dt o/ 18 4 6= . .−
P dl o/ 18 4 6= . .−
Nr 6≥
4.5.2.2.3 Rabas, Eckels, and Sabatino Correlation [41]
For tube banks arranged on an equilateral triangular pitch with low-finned tubes,

j R
s
d
s
l
t
s
=











0 292. e
1.116 0.257 0.666
d
m
f f
f−
f
r
f
f
h n×








d
d
d
t
0.473 .0 7717
α α

(4.58a)


m
d
s
= −



0 415 0 0346. . ln f

(4.58b)

f Re
s
d
l
s
d
d
=








×


−
3 805 0 234
0 251 0 759
. d
.
. .
f
f
r
f










0 729 0 709 0 379. . .
d
P
P
P
r
t
t
l

(4.59)
where αh and αn are a temperature-dependent fluid properties correction factor and a row correc-
tion factor, respectively. The row correction factor has been covered earlier. Rabas and Taborek [7]
recommend the following correlations for αh:

αh
b
w
=
+
+




T
T
273
273
0 25.

(4.60a)

αh
0.26
( )
( )
=




Pr T
Pr T
b
w

(4.60b)
Equation 4.60a is from Weierman [42], and Equation 4.60b is from ESDU [33]. However, the Prandtl
number format is recommended by Rabas and Taborek [7] for liquids and there is no fluid property
correction term for the friction factor f. These are applicable for lf 6.35 mm, 1000 Red 25,000,
4.76 mm ≤ d ≤ 31.75 mm, 246 ≤ Nf ≤ 1181 fins/m, 15.08 mm ≤ Pt ≤ 111 mm, 10.32 mm ≤ P1 ≤
96.11 mm, P1 ≤ Pt, df/s 40, and Nr 6.
4.5.2.2.4 ESDU Correlation [33]

j
s
l
l
d
P
d
=












+
0.183Re Pr. 0.027
. .
d
f
f
f
t
f
0 3
0 36 0 11 00 06.
α αh n

(4.61a)

f
X
d
l
s
X d
X d
= −








−
−
−
−
4.71Re 1d
( 0.286) t
r
( 0.36)
f
0.51
t r
1 rr
0.536





(4.61b)
This is applicable for 1000 Red 80,000 or 100,000 and Nt 10.
4.5.2.2.5 Ganguly et al. [43] Correlation

j
d
s
=




−
−
0 255 0 3
0 3
. Re .
.
d
f

(4.62)

f F f= s p

(4.63a)
where

F A As p= +  
−
2 5
3
0 5 51
. tan . ( / )
π
−

(4.63b)


fp d= ( )−
0 25 0 25
. Re .
β

(4.63c)

β = + − + −



 − −




−
2.5 1.2( 0.85) 0.4 1 0.01 1t
1.06 l
t
3
t
l
3
X
X
X
X
X

(4.63d)
For both j and f factors, 95% of the data correlated within 15% and 100% of the data correlated within
20%. This is applicable for lf ≤ 6.35 mm, 800 ≤ Red ≤ 800,000, 20 ≤ θ ≤ 40, Xt ≤ 4, and Nr ≥ 4.
4.5.2.2.6 Elmahdy and Biggs Correlation [44]
For a multirow staggered circular or continuous fin-tube arrangement,

j C= 1 Reh
C2
(4.64a)
where

C
t
l
D
t
1
0 141 0 065
0 159=







.
. .
f
f
h
f

(4.64b)

C
t
l
s
t
2
0 049 0 077
0 323= −







.
. .
f
f f

(4.64c)
This correlation is also valid for circular fin-tube arrangement. The experimentally determined j
factor is 3%–5% lower than that predicted analytically.
This correlation is applicable for the following:
Re 2 2d = 00 000−
D th f 3 33/ . .= 00 0−
t lf f 1 45/ . .= 0 0 0−
d Pf l 87 127/ . .= 0 −
s t/ . .f 2 25= 00 0−
d Ptf 76 14/ . .= 0 0−
d d/ . .f 37 85= 0 0−
σ = 0 0. .35 62−
4.5.2.3 Continuous Fin on Circular Tube
4.5.2.3.1 Gray and Webb Correlation [45]
Four-row array:

j
P
P
s
d
4
0 328
0 502 0 0312
0 14=








−
−
. Re .
. .
d
t
l o

(4.65)
For this form, 89% of data were correlated within ±10%.

Up to three rows:

j
j
NN
d
0.092 r
Nr
4
0 031
0 607 4
0 991 2 24
4
=












−
−
. . Re
.
. ( )
−

(4.66)
This is used for Nr = 1–3 (for Nr 4, the row effect is negligible). The standard deviation is −4% to +8%.
Pressure drop correlation: Gray and Webb correlation is based on a superposition model that
was initially proposed by Rich [46]. The basic model is written as

∆ ∆ ∆p tp p= +f

(4.67)
where
∆pt, is the pressure-drop component due to the drag force on the tubes
∆pf is the pressure-drop component due to the friction factor on the fins
Accordingly, the expressions for ∆pt and ∆pf are given by

∆p f
A
A
G
g
f f
f
c c
=
2
2 ρ
(4.68a)

∆p f
A
A
G
g
t t
t
c,t c
=
2
2 ρ

(4.68b)

f f
A
A
f
A
A
t
s
= + −



 −



f
f
t
f f
1 1

(4.69a)

f Re
P
d
f d
0.521 t
1.318
0.508=




−
ο

(4.69b)
The mass velocity G used in Equations 4.68a and 4.68b is evaluated as the same G that exists in the
finned-tube exchanger. Several correlations are available for the friction factor of flow normal to
tube banks [32,36,47]. Parameters are
Nr 1 8 or more= –
Re 5 24 7d = 00 00– ,
P dt 197 2 55/ . .ο = −
P dl 17 2 58/ . .ο = 0−
s d/ 8 64ο = 0 0 0. .−
Re o= Gd /µ

4.5.2.3.2 McQuistion Correlation [48]
Continuous-fin tube heat exchanger with four rows:

j
A
A
4
0 4
0 15
0 0014 0 2618= +




−
−
. . Re .
.
d
t

(4.70)
where A/At is the ratio of the total surface area to the area of the bone tube. Here, 90% of data were
correlated within ±10%.
Less than four rows:

j
j
NN r L
L4
1 2
1 2
1 0 128
1 0 5120
=
−
−
−
−
. Re
. Re
.
.

(4.71)
for Nr = 1–3 with a standard deviation of −9% to +18%.

f = × +−
4 904 10 1 3823 2
. . α

(4.72a)

α =




−
−





 −−
−
Re
*
( )
( ) *
.
. .
d
a f
f f
t0 25
0 25 0 4
2
4 1 2
1
R
R
X R N
n t
P
R




−0 5.

(4.72b)

R
R
A A
R nt
*
( )





 =
− +
/
P
t
f2 1

(4.72c)

A
A
P
D
P
dt
l
h
t
o
=
4
π
σ

(4.72d)
R
d
= o
2
Parameters are
P P
d
N
l t
f
in.
in.
= 1 in.
,
. .
Tube spacing
= −
= −
= −
−
1 2
0 08 0 24
3
8
5
8
2
α
ο
== −
= −
4 14
0 006 0 010
fin/in.
in.ft . .
4.5.2.4 Continuous Fin on Flat Tube Array
Performance figures for three geometries are given in Kays and London [17]. New data are pre-
sented for two new types of rippled fin by Maltson et al. [49]. For these types of layouts, fin length
for calculating fin efficiency is half the spanwise length of fin between tubes. Kroger [50] presented

performance characteristics for a six rows deep (3 × 2) core geometry given in Figure 4.40, whose
j and f factors are given by

j f= =
0 174 0 3778.
Re
,
.
Reh
0.387
h
0.3565

(4.73)
These equations were also found to correlate the data for having eight rows deep (4 × 2).
4.6 CORRELATIONS FOR j AND f FACTORS OF PLATE-FIN HEAT EXCHANGERS
4.6.1 Offset Strip Fin Heat Exchanger
Wieting correlations [51] consist of power-law curve fits of the j and f values for 22 heat exchanger
surface geometries over two Reynolds number ranges: Reh ≤ 1000, which is primarily laminar, and
Reh ≥ 2000, which is primarily turbulent.
For Reh ≤ 1000,

j
l
D
=




−
− −
0 483
0 162
0 184 0 536
. Re
.
. .f
h
hξ

(4.74)

f
l
D
=




−
− −
7 661
0 384
0 092 0 712
. Re
.
. .f
h
hξ

(4.75)
For Reh ≥ 2000,

j
l
D
t
D
=








−
−
0 242
0 322 0 089
0 368
. Re
. .
.f
h
f
h
h

(4.76)

f
l
D
t
D
=








−
−
1 136
0 781 0 534
0 198
. Re
. .
.f
h
f
h
h

(4.77)
where Reh is the Reynolds number based on hydraulic diameter Dh given by

D
sh
s h
h
f
f
=
+
2

(4.78)
and α is the aspect ratio, s/hf (Figure 4.41).
18.35
25.4 2.82
Fin thickness 0.2
2
19.18.75
FIGURE 4.40 Geometrical details of a flat tube-fin radiator to calculate j and f factors as per Equation 4.73.
(Parameters are in mm.)

Joshi and Webb [16] have developed a more sophisticated theoretical model to predict the char-
acteristics of j and f versus Reynolds number for the OSF. This model preferably includes all geo-
metrical factors of the array (s/d, tf/lf, tf/s) and heat transfer to the base surface area to which the fins
are attached.
Manglik and Bergles [52] reviewed the available j and f data and developed improved correla-
tions for j and f, with a single predictive equation representing the data continuously from laminar
to turbulent flow. Their correlations for j and f are as follows:

j =
× + ×
− − −
−
0 6522
1 5 269 10
0 5403 0 1541 0 1499 0 0678
5 1
. Re
. Re
. . . .
h
h
ξ δ η
.. . . .
.
340 0 504 0 456 1 055
0 1
ξ δ η−
{ }
(4.79)
and

f =
× + ×
− −
−
9 6243
1 7 6669 10
0 7422 0 1856 0 3053 0 2659
8 4
. Re
. Re
. . . .
h
h
ξ δ η
.. . . .
.
429 0 92 3 767 0 236
0 1
ξ δ η{ }
(4.80)
where ξ is the aspect ratio = s/hs; δ = tf/lf; η = tf/s; and Reh is based on the hydraulic diameter Dh
given by the following equation:

D
sh l
sl h l t h t s
h
f f
f f f f f f
=
+ + +
4
2( )
(4.81)
These equations correlate the experimental data for the 18 cores within ±20%.
4.6.2 Louvered Fin
Based on tests of 32 louvered-fin geometries, Davenport [19] developed multiple regression correla-
tions for j and f versus Re as follows:

j l H
l
H
=



 −
0 249 300 40000 42
1
0 26
1 1
. Re Re. .
.
lp h
0.33 l
l

(4.82)
Partition sheet Partition sheet
Partition sheet
Fin
tf
tf
lf
hf
hf
Partition sheet
(a) (b)
s
Fin
FIGURE 4.41 Details of offset strip fin. (a) Rectangular fin and (b) triangular fin.


f l H l
l
H
=



 5 47 70 10000 72 0 23 0 2
0 89
. Re Re. . .
.
lp h
0.37
l p
l
l
−

(4.83a)

f H
l
H
l
H
=







 −
0 494 1000 40 39 0 46
0 33 1 1
. Re Re. .
. .
1p l
h
l
l
l
0000

(4.83b)
where
Re1p is the Reynolds number based on louver pitch
lh is the louver height
ll is the louver length
lp is the louver pitch
Hl is the fin height
Here, 95% of the data could be correlated within ±6% for heat transfer, and within ±10% for the
friction factor. The required dimensions are millimeters. Figure 4.17 defines the terms in the
equations. The characteristic dimension in the Reynolds number is louver pitch, lp and not Dh.
4.6.3 Pin Fin Heat Exchangers
For the heat transfer characteristics of pin-finned surfaces, refer to Kays [53], Norris et al. [54] and
Kanzaka et al. [55], among others. The results of Ref. [53] were presented in Kays and London
[17]. The works of Kays [53] and Norris [54] are limited to the heat transfer characteristics of pin
fins having their representative length comparable to those of louvered or offset fins currently used
[55]. To materialize a heat exchanger that has thermal performance superior to those of offset or
louvered fins requires a more finely segmented surface of less than 1 mm at maximum. Kanzaka et
al. [55] studied the heat transfer and fluid dynamic characteristics of pin-finned surfaces of various
profiles, namely, circular, square, and rectangular, and both inline and staggered arrangements.
Staggered arrangements: For their test element, the expression for the Nusselt number is

Nuφ φ= 0 662 0 5 1 3
. Re Pr. /

(4.84)
Inline arrangements: The expression for the Nusselt number is

Nuφ φ= 0 440 0 5 1 3
. Re Pr. /

(4.85)
where ϕ is the characteristic length. The expressions for Nusselt number and dϕ are

Nuφ
φ
φ
φ
µ
= =
hd
k
Gd
Re

(4.86)

d
d
φ
π
= p
for circular fins
2
(4.87a)

d
a b
φ =
+p p
for rectangular fins
2
(4.87b)
where
ap and bp are the rectangular pin fin dimensions (i.e., cross section is ap × bp)
dp is the circular fin diameter

4.7 FIN EFFICIENCY
Fins are primarily used to increase the surface area and consequently to enhance the total heat
transfer rate. Both conduction through the fin cross section and convection from the surface area
take place. Hence, the fin surface temperature is generally lower than the base (prime surface)
temperature if the fin convects heat to the fluid. Due to this, the fin transfers less heat than if it
had been at the base temperature. This is described by the fin temperature effectiveness or fin
efficiency ηf. The fin temperature effectiveness is defined as the ratio of the actual heat transfer,
q, through the fin to that which would be obtained, qi, if the entire fin were at the base metal
temperature:

ηf
i
=
q
q
(4.88)
The fin efficiency for plate-fin surfaces in heat exchanger design can be determined from Gardner
[56], Kern and Kraus [57], Scott and Goldschmidt [58], Schmidt [59], Zabronsky [60], Lin and
Sparrow [61], Shah [19,62], and others. Fin efficiency of a plain rectangular profile cross section is
discussed in this section.
4.7.1 Fin Length for Some Plate-Fin Heat Exchanger Fin Configurations
The two most commonly used plate-fin geometries are rectangular and triangular passages, shown
in Figure 4.41. From a review of Figure 4.41, the fin length lf for a rectangular passage is

l
h t h
f
f f f
=
−
2 2
≈

(4.89)
Note that no effect of the fin inclination is taken into account in Equation 4.89 for the triangular fin.
Numerous fin geometries and corresponding fin lengths for various flow passage configuration are
presented by Shah [24].
4.7.2 Fin Efficiency
4.7.2.1 Circular Fin
Kern and Kraus [57] formula for rectangular-profile circular fin: For circular fins (Figure 4.42), the
fin efficiency is given by

ηf
o
c
2
o
2
l e l o l e l o
o o l e
=
−
−2r
m r r
I mr K mr K mr I mr
I mr K mr( )
( ) ( ) ( ) ( )
( ) ( )) ( ) ( )+





I mr K mrl e o o

(4.90)
where
m = (2h/kftf)0.5
In is the modified Bessel function of the first kind (nth order)
Kn is the modified Bessel function of the second kind (nth order)
kf is the fin material thermal conductivity
re is the fin radius
ro is the tube outer radius

The fin efficiency expressed by Equation 4.90 does not lend itself to comparison with the effi-
ciencies of fins of other radial profiles but can be adjusted by expressing the efficiency in terms of
the radius ratio ro/re and a parameter ϕ:

ρ =
r
r
o
e
(4.91)

φ = −





( ) /
.
r r
h
k A
e o
f p
3 2
0 5
2

(4.92)
where Ap is the profile area of the fin

A t r rp f e o= −( )

(4.93)
Substituting the values of ρ and ϕ in Equation 4.90, the resulting formula for fin efficiency is given by

η
ρ
φ ρ
φ ρ ρφ ρ φ ρ ρφ ρ
f
2
(1 )
[ ( )] [ ( )] [ )] [ ( )]
=
+
− − − − −I K K Il l l/ 1 / /( /1 1 1 1
II K I Ko l o/ / / /[ ( )] [ ( )] [ ( )] [ ( )]ρφ ρ φ ρ φ ρ ρφ ρ1 1 1 11− − + − −







(4.94)
Scott and Goldschmidt: An excellent approximation of Equation 4.94 has been provided by Scott
and Goldschmidt [58] as follows:

η φf e
y
= +− −
x ml r( ) for . . ( *) .
0 6 2 257 0 445

(4.95a)

η
φ
φ
φf
tanh
= +
−( )
for . . ( *)
.
≤ 0 6 2 257
0 445
r

(4.95b)
where
x r1
0 246
= −
( *) .
(4.96)

φ = −
ml re
ml
( *)exp( . . )0 13 1 3863e

(4.97)

y r r1 0 9107 0 0893 2= +. . * *for ≤

(4.98a)
re–ro
tf
re
ro
FIGURE 4.42 Circular fin details to calculate fin efficiency as per Equations 4.90, 4.94, and 4.95.


= + 0 0 0. . * *97 6 17125 ln for 2r r

(4.98b)

r
r
r
* ,= e
o
(4.99)

l l
t
e f
f
= +
2
(4.100)
Schmidt method: The Schmidt [59] formula for the efficiency of a plane circular fin is given by

η =
tanh *ml
ml*
(4.101)
where l* is given by

l r r
t
r r
* ( )
)
[ .= − +
−





 +e o
f
e o2(
ln( )]1 1 0 35 ρ

(4.102)
in which ρ = re/ro. It was shown that for 0.5 ≤ ρ ≤ 1 and 1 ≤ ρ ≤ 8, the error using Equation 4.101 is
less than 1% of the exact value of the fin efficiency. Because the fin efficiency is very close to unity
for typical low-finned tube geometries, Rabas and Taborek [7] do not recommend any corrections
to this method to account for departure from a rectangular profile and for the nonuniformity of the
heat transfer coefficient over the height of the fin.
4.7.2.2 Plain Continuous Fin on Circular Tubes
A recurring arrangement of extended surface is that of a single sheet of metal pierced by round
tubes in either a square or equilateral triangular array. For polygonal fins, methods suggested in
Refs. [19,59–61] can be used.
Schmidt method: Schmidt [59] extended the circular fin efficiency formula expressed in Equation
4.101 to rectangular and hexagonal layout fin surfaces as shown in Figure 4.43. The extension was
made by analyzing these surfaces on the basis of equivalent circular fins. The expression for the
ratio of the equivalent fin radius to the tube radius, ρe, is expressed as follows:
For rectangular fins,

ρ λ βe = −1 28 0 21 1
0 5
. ( . ) .

(4.103)
L
(a) (b)
ro
ro
M
M
L
FIGURE 4.43 Geometrical details of continuous fin-tube heat exchanger layouts. (a) Rectangular tube array
and (b) hexagonal tube array.

For hexagonal fins,

ρ λ βe l l= −1 27 0 3 0 5
. ( . ) .

(4.104)
where

λl
o
=
M
r
(4.105)

βl =
L
M
(4.106)
and where L and M are defined in Figure 4.43. Of these two, L must always be the larger dimension.
The fin efficiencies calculated in this way always fall within the known upper and lower limits defined
by the inner and outer circumscribing circles and are very close to that of a circular fin of equal area.
The accuracy of this method is especially good for square or regular hexagonal fins, where L = M.
Sparrow and Lin method: The Sparrow and Lin method [61] considered both the square fin and
hexagonal fin formed by tubes on equilateral triangular pitch as shown in Figure 4.44. For the fins
shown in Figure 4.44, the fin efficiency is obtained from the numerical temperature solution and is
2s
ro
ro2s
ro
re
S
ro
r
re
S
Square fin
Hexagonal fin
Pt
Pl
FIGURE 4.44 Fictitious edge radius for unit fin surface of continuous fin with circular tube. (a) Square lay-
out (i.e., square fin) and (b) staggered layout (60°) (i.e., hexagonal fin).

conveniently represented in terms of a fictitious edge radius re
* that corresponds to a radial fin having
the same surface area as the square and hexagonal fins under consideration. This fictitious edge
radius for the square fin is given by

r se* =




2
π
(4.107)
and for the hexagonal fin

r se* =






2 3
1 2
π
/

(4.108)
The Sparrow and Lin method satisfies exactly the isothermal boundary condition at the fin base and
fulfills approximately to any desired accuracy the adiabatic boundary condition at the fin edge.
Sector method: The fin efficiency of the polygonal fin is obtained by an approximate method referred
to as the “sector method” [24]. The flat fin is broken down into n sectors bounded by idealized adiabatic
planes as indicated by the dotted lines for the inline and staggered tube arrangements in Figure 4.45.
The radius of each circular sector is determined by the length of a construction line originating from
the tube center and passing through the midpoint of each line segment. The fin efficiency of each sector
is then determined by use of Equations 4.94, 4.95, or 4.101. The fin efficiency for the entire surface can
then be determined by the summation as [24]

η
η
f
i=1 f i
i=1 f,i
f i
=
Σ
Σ
n
n
A
A
, ,

(4.109)
where Af,i is the area of each fin sector. The approximation improves as n becomes very large, but for
practical purposes, only a few segments will suffice to provide ηf within a desired accuracy of 0.1%.
The fin efficiency calculated by the sector method is lower than that for the actual flat fin, whereas
the equivalent annulus method yields ηf values that are higher than those by the sector method for
highly rectangular fin geometry around the tubes [24].
4.8 RATING OF A COMPACT EXCHANGER
The rating problems for a two-fluid direct transfer type compact crossflow and counterflow exchanger
with gas as a working fluid at least on one side is discussed in this section. The surface employed on the gas
side of this exchanger has a high surface area density and low hydraulic diameter. Customarily, the ε-NTU
Pt
(a) (b) (c) (d)
Pt
Pl
Pl
ro ro
ro
re,n
re,1
re,1
ro
re,n
FIGURE 4.45 Fin sectors to determine fin efficiency of continuous finned-tube heat exchanger. (a) Inline
layout, (b) staggered layout, (c) fin sectors for inline layout, and (d) fin sectors for staggered layout.

method is employed for compact heat exchangers. Hence, the solution procedure is outlined using the
ε-NTU method. The rating procedure given here is as in Refs. [24,63].
4.8.1 Rating of Single-Pass Counterflow and Crossflow Exchangers
The basic steps of the rating problem are shown in Figure 4.46 and involve the determination of the
following parameters.
1. Surface geometrical properties. These include
Ao minimum free flow area
A heat transfer surface area (total of primary surface area, Ap, and secondary surface area, Af)
L flow length
Establish heat balance
Calculate primary and secondary
heat transfer surface area and
surface geometrical properties;
A, Ao, Afr, Dh, α, β and σ
Calculate thermophysical
fluid properties
Calculate Re and Nu
Determine j and f factors
Calculate convective film
coefficients
Calculate fin efficiency and
overall surface effectiveness
Assume fouling factors and calculate
overall heat transfer coefficient, U
Calculate C*, NTU and hence
thermal effectiveness
Calculate pressure drop
FIGURE 4.46 Flowchart for rating of a compact heat exchanger. (Note: Wherever applicable the calculation
is to be done for both fluid 1 and fluid 2.)

Dh hydraulic diameter
β heat transfer surface area density
σ ratio of minimum free flow area to frontal area
lf fin length
tf fin thickness
Alsoincludedarespecializeddimensionsusedforheattransferandpressure-dropcorrelations.
2. Fluid physical properties. Determine the thermophysical properties at bulk mean tem-
perature for each fluid, namely, hot and cold fluids. The properties needed for the rating
problem are μ, cp, k, and Pr. Since the outlet temperatures are not known for the rating
problem, they are guessed initially. Unless it is known from the past experience, assume
an exchanger effectiveness as 60%–75% for most single-pass crossflow exchangers, and
80%–85% for single-pass counterflow and two-pass cross-counterflow exchangers. For the
assumed effectiveness, calculate the fluid outlet temperatures by

t t
C t t
C
h,o h,j
h,i c,i
h
= −
−
ε min ( )

(4.110)

t t
C
C
t tc,o c,i
c
h,i c,i= + −ε min
( )

(4.111)
Initially, assume Cc/Ch ≈ Mc/Mh for a gas-to-gas exchangers, or C C Mc Mcc h p c p h/ /= ( ) ( )
for a gas-to-liquid exchanger with approximate values of cp. For exchangers with C* ≥ 0.5
(usually gas-to-gas exchangers), the bulk mean temperature on each side will be the arith-
metic mean of the inlet and outlet temperatures on each side. For exchangers with C* 0.5
(usually gas-to-liquid exchangers), the bulk mean temperature for Cmax as the hot fluid is
th,m = (th,i + th,o)/2, tc,m = th,m − LMTD and for Cmax as the cold fluid tc,m = (tc,i + tc,o)/2, th,m =
tc,m + LMTD [24,63].
Once the bulk mean temperatures are obtained on each side, obtain the fluid properties
from thermophysical property tables or from standard thermal engineering books.
3. Reynolds numbers. Calculate the Reynolds number and/or any other pertinent dimension-
less groups needed to determine j or Nu and f of heat transfer surfaces on each side of the
exchanger.
4. Compute j or Nu and f factors.
5. Correct Nu (or j) and f for variable fluid property effects in the second and subsequent iterations.
6. From Nu or j, determine heat transfer coefficient for both the fluid streams.

h
k
D
=
Nu
h
(4.112a)
or

h jG C Pr= −
p
2/3

(4.112b)
7. Determine the fin efficiency ηf and the overall surface efficiency ηo given by

ηf
tanh
=
ml
ml
(4.113)
where l is the fin length.

η ηo
f
f= − −1 1
A
A
( )

(4.114)

8. Overall conductance. Calculate the wall thermal resistance, RW. Knowing the fouling
resistances Rf,h and Rf,c on the hot and cold fluid sides, respectively, calculate the overall
thermal conductance UA from

1 1 1
UA hA
R
A
R
hA
R
A
= + + + +
( ) ( ) ( ) ( )η η η ηo h
f,h
o h
w
o c
f,c
o c
(4.115a)
h w c= + + + +R R R R R1 2 (4.115b)
9. Calculate NTU, C*, and exchanger effectiveness, ε. If the thermal effectiveness is above
80%, correct for wall longitudinal conduction effect.
10. Compute the outlet temperature from Equations 4.110 and 4.111. If these outlet temperatures
differ significantly from those assumed in step 2, use these outlet temperatures in step 2 and
continue iterating steps 2–9 until the assumed and computed outlet temperatures converge
within the desired degree of accuracy. For a gas-to-gas exchanger, probably one or two
iterations will be sufficient.
11. Compute the heat duty from

q C t t= −ε min h,i c,i( )

(4.116)
12. Calculate the core pressure drop. The friction factor f on each side is corrected for the
variable fluid properties as discussed in Chapter 3. The wall temperature Tw is com-
puted from

T t q R Rw,h m,h h= − +( )1

(4.117)

T t q R Rw,c m,c c= − +( )2

(4.118)
4.8.2 Shah’s Method for Rating of Multipass Counterflow
and Crossflow Heat Exchangers
The rating procedure for multipass crossflow exchangers with fluids mixed between passes is
described by Shah [63]. The solution procedure for rating problem for the two-pass crossflow
exchangers with flows unmixed in the passes but mixed between passes is also very similar to the
sizing of single-pass crossflow. Only some of the calculations on the two pass side need to be modi-
fied, and only those points are summarized here.
1. In order to compute fluid bulk mean temperature and thermophysical properties of fluids,
first guess the overall thermal effectiveness, εN. Assume it to be 80%–85% unless it is
known from the past experience. Assume that the NTU per pass is same. The individ-
ual pass effectiveness εp is related to overall effectiveness εN for the case of fluids mixed
between passes. Compute approximate values of Cc and Ch since we don’t know yet the
accurate values of the specific heats.
2. Determine the intermediate and outlet temperature by solving the following individual
pass effectiveness and overall effectiveness equations:

εp1
c c,o c,int
h,i c,int
=
−
−
C t t
C t t
( )
( )min

(4.119)


εp2
c c, c,i
h,int c,i
=
−
−
C t t
C t t
( )
( )
int
min

(4.120)

ε =
−
−
C t t
C t t
c c,o c,i
h,i c,i
( )
( )min

(4.121)
In the foregoing three equations, there are three unknowns: tc,o, tc,int, and th,int. Hence, they
can be evaluated exactly and then from the overall energy balance th,o is calculated.

C t t C t tc c,o c,i h h,i h,o( ) ( )− = −

(4.122)
Since we know all terminal temperatures for each pass, we can determine the bulk mean tempera-
ture for each fluid in each pass and subsequently the fluid properties separately for each pass.
4.9 SIZING OF A COMPACT HEAT EXCHANGER
The basis of sizing involves coupling of heat transfer and flow friction in the derivation of the core
mass velocity G on each side of a two-fluid exchanger. Subsequently, the sizing problem is carried
out in a manner similar to the rating problem.
4.9.1 Core Mass Velocity Equation*
The dominant term in the expression for the pressure drop is the core friction term. The entrance and
exit effects are generally relatively small and are of the opposite sign. Similarly, the flow acceleration
term is relatively small in most heat exchangers, being generally less than 10% of the core friction
term [24], so their elimination is usually warranted in a first approximation. With these approxima-
tions and L/rh = A/Ao, the expression for pressure drop may be written after rearrangement as

G
g p
p
p
A
A f
2
2
1
1
1
c i i i
o
i m)ρ ρ ρ
=
∆
( /
(4.123)
In the absence of fouling resistances, the overall NTU is related to NTUh, NTUc, and the wall resis-
tance, Rw, by

1 1 1
NTU NTU / NTU /h h
w
c c
= + +
( ) ( )min
min
minC C
C R
C C
(4.124)
The wall resistance term is generally small and hence neglected in the first-approximation calcula-
tion. Hence, the number of transfer units on one side of interest (either hot or cold), designated as
NTU1, may be estimated from the known overall NTU as given next.
If both fluids are gases, one can start with the estimate that the design is “balanced” by a
selection of the hot and cold side surfaces so that Rh = Rc = Ro/2, that is, NTUh = NTUc = 2NTU.
Then
NTU NTU 2NTU1 2= =
(4.125)
For a gas–liquid heat exchanger, one might estimate

NTU 11 NTUgas side = . ( )

(4.126)
* After Shah, R.K., Compact heat exchanger design procedures, in Heat Exchangers: Thermal-Hydraulic Fundamentals
and Design, Kakac, S., Bergles, A.E., and Mayinger, F., eds., Hemisphere, Washington, DC, pp. 495–536, 1981.

The term NTU1 is related to the Colburn factor j on side 1 by

NTU o
o
o
o
op p
1
1 1
2 3
1
=





 =





 =




−η
η η
hA
MC
hA
GC A
jPr
A
A
/

(4.127)
Eliminating (A/Ao) from Equations 4.123 and 4.127, and simplifying the expression, we get the core
mass velocity G for one side:

G
g
Pr
p j
f
=


















2
1 2 3
0 5
c o
m/ ) NTU
η
ρ( /
.
∆

(4.128)
The feature that makes this equation so useful is that the ratio j/f is a relatively flat function of the
Reynolds number. Thus, one can readily estimate an accurate magnitude of j/f based on a “ballpark”
estimate of Re. If there are no fins, overall surface efficiency ηo = 1. For a “good design,” the fin
geometry is chosen such that ηo is in the range 70%–90%. Therefore, ηo = 0.8 is suggested as a first
approximation to determine G from Equation 4.128.
4.9.2 Procedure for Sizing a Compact Heat Exchanger
The procedure for sizing any of the compact heat exchangers (Figure 4.47) is almost inevitably an
iterative one and thus lends itself very conveniently to computer calculations. Kays and London [17]
illustrate the procedure for sizing a crossflow heat exchanger. To illustrate this, a simple crossflow heat
exchanger is considered as shown in Figure 4.34. It is assumed that each fluid is unmixed throughout.
The two fluids are designated by h and c. The problem is to determine the three dimensions L1, L2, and
L3. The first step after choosing the two surfaces is to assemble the geometric characteristics of the
surface—Dh,σ, α, β, Af /A, and Aw/A for the hot side and cold fluids side. A first estimate of Gh and Gc
can be made using Equation 4.128. After the determination of mass velocity, carry out the calculations
similar to a rating problem. The sequence of parameters to be calculated after determination of mass
velocity include Re, ηf, ηo, j, f, h, UA, Ao, Af, flow length, Kc, Ke, and (∆p/p), both on the hot side and
cold side. The pressure drop results are then compared with those specified for the design, and the
procedure is repeated until the two pressure drops are within the specified value.
4.9.3 Optimization of Plate-Fin Exchangers and Constraints
on Weight Minimization [64]
Minimizing the material volume, or weight, of the PFHE core does not necessarily represent the
optimum solution, even for weight-sensitive aerospace applications; size and shape can be important
design considerations [64]. Minimum weight core could be longer than is desirable because of the
low-fin efficiency implied. If the fin is too thin, its efficiency will be low, and to compensate both
core length and flow area will be high, giving an excessively high weight. On the other hand, a very
thick fin giving high-fin efficiency will yield a low core length but with low porosity (free flow area)
and weight. Minimizing the components’ thickness can also contribute to low weight. But there are
limitations in reducing components beyond certain limits as follows:
The thicknesses of fin material and separating plates have lower limits set by pressure-retain-
ing capability.
Plate-fin cores are usually made from sheet stock of a fixed range of thickness; rolling finstock
to a special “optimum” thickness could be uneconomic.
It may not be possible to form fins of sufficient dimensional accuracy if they are too thin; if
they can be made, they might deform unsatisfactorily on brazing.
There may also be lower thickness limits set by erosion and corrosion problems.

4.10 EFFECT OF LONGITUDINAL HEAT CONDUCTION
ON THERMAL EFFECTIVENESS
The ε-NTU and LMTD methods discussed are based on the idealization of zero longitudinal heat
conduction in the wall in the fluid flow direction. If a temperature gradient is established in the
wall in the fluid flow direction, heat transfer by conduction takes place from the hotter to the colder
region of the wall in the longitudinal direction. This longitudinal conduction in the wall flattens
the temperature distributions, reduces the mean outlet temperature of the cold fluid, increases the
mean outlet temperature of the hot fluid, and thus reduces the thermal effectiveness [63,65]. The
reduction in the effectiveness at a specified NTU may be quite significant for a compact exchanger
Input: NTU, C*, ε, Δp1 and Δp2
Calculate thermophysical fluid properties
Calculate the surface geometrical properties
on both sides A, Ao, Dh, α, β and σ
Select (j/f)n
Calculate mass velocity, Gn
Evaluate these variables: Re, j, f, h, ηf, ηo,
kc, ke, on both sides
Compute (UA)n
Compute frontal area and hence determine
flow length on both sides
Calculate (Δp)n; (Δp)n≤specified
complete the design:
Else assume new G1 and G2,
and itereate till convergence
n =1, 2
n=1, 2
n=1, 2
n=1, 2
Assume an overall exchanger size and
configuration–frontal area, core length,
number of flow passages and
surface geometry
FIGURE 4.47 Flowchart for sizing of a compact heat exchanger. (Note: 1, 2 are both sides fluids designation.)

designed for high thermal effectiveness (above ∼80%) and a short flow length, L. The shell and
tube exchangers and plate exchangers are usually designed for effectiveness of 60% or less per
pass. Therefore, the influence of heat conduction in the wall in the flow direction is negligible for
these effectiveness levels. The presence of longitudinal heat conduction in the wall is incorporated
into the thermal effectiveness formula by an additional parameter, λ, referred to as the longitudinal
conduction parameter. Another parameter that influences the longitudinal wall heat conduction is
the convection conduction ratio, ηohA. Thus, in the presence of longitudinal heat conduction in the
wall, the exchanger thermal effectiveness is expressed in a functional form [65]:

ε φ η λο= { }NTU, *, ,C hA

(4.129)
4.10.1 Longitudinal Conduction Influence on Various Flow Arrangements
The influence of longitudinal conduction in the case of parallelflow is not discussed because high-
performance exchangers are not designed as for parallelflow arrangements. For high-performance
exchangers, the effect is discussed in Chapter 7. In a crossflow arrangement, the wall temperature
distributions are different in the two perpendicular flow directions. This results in a two-dimen-
sional longitudinal conduction effect, and is accounted for by the cold-side and hot-side parameters
defined as [65]:

λ λc
w k
c
h
w k
h
=



 =




k A
LC
k A
LC
and

(4.130)
Note that the flow lengths Lc and Lh are independent in a crossflow exchanger. If the separating wall
thickness is a, and the total number of parting sheets is Np, then the transfer area for longitudinal
conduction is given by [65] as follows:

A N L a A N L ak,c p n k,h p cand= =2 2

(4.131)
Chiou [66] analyzed the problem for a single-pass crossflow heat exchanger with both fluid unmixed
and tabulated values for the reduction in thermal effectiveness due to longitudinal wall heat
conduction.
4.10.2 Comparison of Thermal Performance of Compact Heat Exchangers
Among the three types of compact heat exchangers, viz., tube-fin, continuous fin, and PFHE, PFHE
has maximum heat transfer capacity compared to the other two types of heat exchangers. Figure 4.48
shows comparison of thermal performance of PFHEs, flat tube heat exchangers (oil coolers), and
tube-fin heat exchangers. Performance is shown as Q/ITD, the heat load divided by the difference in
incoming temperature of the liquid and air.
4.11 AIR-COOLED HEAT EXCHANGER (ACHE)
Air-cooled heat exchangers (ACHEs), or “fin-fans,” are an alternate heat rejection method that
is used frequently in place of the conventional water-cooled shell and tube heat exchanger to
cool a process fluid. They can be used in all climates. ACHE are increasingly found in a wide
spectrum of applications including chemical, process, petroleum refining, and other industries.
A fan located below the tube bundle forces air up through the bundle, or a fan above draws the
air through the bundle. The fans are axial low fans varying from 4 to 12 ft diameter and having

four to six blades. The fan blades may be of aluminum, plastic, or, in the case of corrosive
atmospheres, stainless steel. The drive can be an electric motor with gears or V-belts. Before
discussing the construction details and design aspects, the factors that favor air cooling over
water cooling are discussed. For generic/specific details on design, manufacture, and operation of
ACHEs, refer to references [67–86]. An important guide book for design of ACHEs is American
Petroleum Institute Standard 661 [70]. The principle of ACHE is shown in Figure 4.49 and a
forced draft ACHE is shown in Figure 4.50.
4.11.1 Air versus Water Cooling
Two primary methods of process cooling are (1) water cooling and (2) air cooling. The choice
between air or water as coolant depends on many factors like (1) cooler location; (2) space for cool-
ing system; (3) effect of weather; (4) design pressure and temperature; (5) danger of contamination;
(6) fouling, cleaning, and maintenance; and (7) capital costs. Environmental concerns such as short-
age of makeup water, blowdown disposal, and thermal pollution have become an additional factor
in cooling system selection.
Performance(Q/ITD)
Water flow
Tube fin
Plate fin
Oil coolers (flat tube fin)
FIGURE 4.48 Chart for comparison of thermal performance of PFHEs, flat tube heat exchangers (oil
coolers), and tube-fin heat exchangers performance is shown as Q/ITD, the heat load divided by the dif-
ference in incoming temperature of the liquid and air. (Courtesy of Lytron Inc., Woburn, MA.)
Warm air out
Hot
Cold air in
Process fluid Cold
FIGURE 4.49 Principle of ACHE.

4.11.1.1 Air Cooling
Air cooling is increasing in use, particularly where water is in short supply. Factors that favor air
cooling include the following:
1. Air is available free in abundant quantity with no preparation costs.
2. ACHE design is well established, and can perform well with a reasonable degree of
reliability.
3. Water is corrosive and requires treatment to control both scaling and deposition of dirt,
whereas air is mostly noncorrosive. Therefore, material selection is governed by process
fluids routed through the tubeside.
4. Mechanical design problems are eased with ACHEs since the process fluid is always on the
tubeside.
5. Danger of process fluid contamination is much greater with water-cooled system.
6. Air-side fouling can be periodically cleaned by air blowing, and chemical cleaning can be
carried out either during half-yearly or yearly attention. Water-cooled systems may require fre-
quent cleaning.
7. Maintenance costs for ACHEs are about 20%–30% of those for water-cooled system [68].
Operating costs for water coolers are higher, because of higher cooling water circulation
pump horsepower and water treatment costs.
8. Air cooling eliminates the environmental problems like heating up of lakes, rivers, etc.,
blowdown, and washout.
Air cooling has the following disadvantages:
1. ACHEs require large surfaces because of their low heat transfer coefficient on the airside and the
low specific heat of air. Water coolers require much less heat transfer surface.
2. ACHEs cannot be located next to large obstructions if air recirculation is to be avoided.
3. Because of air’s low specific heat, and dependence on the dry-bulb temperature, air cannot
usually cool a process fluid to low temperatures. Water can usually cool a process fluid
from 10°F to 5°F lower than air, and recycled water can be cooled to near the wet-bulb
temperature of the site in a cooling tower [68].
FIGURE 4.50 A bank of ACHEs. (Courtesy of GEA Iberica S.A., Vizcaya, Spain.)

4. The seasonal variation in air temperatures can affect performance and make temperature
control more difficult. Low winter temperatures may cause process fluids to freeze.
5. ACHEs are affected by hailstorms and may be affected by cyclonic winds.
6. Noise is a factor with ACHEs. Low noise fans can reduce this problem but at the cost of fan
efficiency and higher energy costs.
7. May need special controls for cold weather protection.
8. Cannot cool the process fluid to the same low temperature as cooling water
4.11.2 Construction of ACHE
A typical ACHE consists of the following components:
1. Tube bundle.
2. An air pumping device, such as an axial flow fan or blower driven by an electric motor and
power transmission device such as belt (up to 50 hp) or gear (above 50 hp) to mechanically
rotate the air moving device.
3. The moving of air across the tube bundle may be either forced draft (fan is located below
the tube bundle and air is forced through the fin tubes) or induced draft (fan is located
above the bundle and air is induced or pulled through the fin tubes).
4. A support structure high enough to allow air to enter beneath the ACHE at a reasonable flow rate.
5. Optional features like (i) header and fan maintenance walkways with ladders to climb
(Figure 4.51), (ii) louvers for process outlet temperature control, (iii) recirculation ducts
and chambers for protection against freezing or solidification of high pour point fluids in
cold weather, and (iv) variable pitch fan hub or frequency drive for temperature control.
4.11.2.1 Tube Bundle Construction
An ACHE tube bundle consists of a series of finned tubes set between side frames, passing between
header boxes at either end. The number of passes on the tubeside (the process fluid side) is made
possible by internal baffling of the header boxes. For horizontal bundles, vertical baffles result
in a side-by-side crossflow arrangement, whereas horizontal baffles result in a counter-crossflow
arrangement relative to airflow. Inlet and outlet nozzles may or may not be on the same header box.
Tubes are attached to the tubesheet by expansion or welding.
4.11.2.1.1 Tube Bundle Fin Geometry
The tube-fin geometries, viz., attachment of fins to the tubes, include extruded, embedded, and
welded—single footed or double footed (Figure 4.52). These fins can be solid or serrated, tension
wound or welded, and of a variety of metals. For higher process temperatures, most customers
Motor
Fan
Header
Walkway Walkway
Plenum chamber
Finned tube bundle
FIGURE 4.51 Layout of ACHE showing tube bank with walkways. (Note: Induced draft design.)

prefer either embedded 400°C (750°F) or extruded fins 310°C (590°F). Extruded fins are made by
putting an aluminum sleeve (sometimes called a muff) over the tube, then passing the tube through
a machine which has rollers which squish the aluminum to form fins. The process is similar to a
thread-rolling. This results in a fin tube which has extremely good metal-to-metal contact between
the tube and fin sleeve. Extruded fins are often used in coastal regions or on offshore platforms for
this reason. Extruded fins typically have the maximum ability to transfer heat due to absence of
contact resistance at the fin and tube base. High finned (extruded) monometallic fin-tube and bime-
tallic fin-tubes are shown in Figure 4.53. Serrations or slitting the fin tips help to increase the airside
heat transfer coefficient. However, this improvement is accompanied by higher airside pressure drop
and hence will require higher motor power and depending on the physical location of the ACHE,
(a) (b) (c) (d) (e)
FIGURE 4.52 Tube-fin geometry—(a) welded single L footed, (b) welded double L footed, (c) extruded,
(d) serrated, and (e) embedded.
tf
hf
di
Do
Df
p
1
L
(a)
(b)
2
tf
hf
Dw
Df
p
1
L
2
FIGURE 4.53 High finned tube—(a) extruded monometallic fin tube and (b) bimetallic fin tube. Note:
Sections 1 and 2 are unfinned sections. di is tube inner diameter, Do or Dw is tube outer diameter, Df is fin
diameter, L is tube length and hf is fin height, p is fin pitch and tf is fin thickness..

serrated fins will have a greater propensity for fouling. To check the adequacy of bonding between
the fin and tube, manufacturers subject the fin to a tensile test by pulling the fin using a spring bal-
ance. Other tests involve such aspects as fin spacing, diameter, and thickness.
The fin most commonly used for ACHEs is aluminum, tension wound and footed. These are
used where the process temperatures are below about 177°C (350°F). The API 661 specification
calls for cast zinc bands at the ends of the tubes to prevent the fins from unwrapping. It is cheaper
but susceptible to damage due to thermal upsets and airside corrosion. The embedded fins have the
highest temperature capabilities. They are made by a process which cuts a helical groove in the
outer diameter of the tube, wraps the fin into the groove, then rolls the upset metal from the tube
back against the fin to lock it into place. Embedded fins have less contact resistance to heat transfer
than do tension-wound fins, but corrosion is likely to be induced at the groove between fin and tube.
Additionally, embedded fin tubes require tubes that are nominally one gauge heaver in wall thick-
ness to account for the mechanical attachment of fin in to the groove [68].
The tubes are usually 1 in. (25.4 mm) diameter; fin density varies from 7 to 16 fins/in. (276–630
fins/m), fin height from 3/8 to 5/8 in. (9.53–15.88 mm), and fin thickness from 0.012 to 0.02 in.
(0.3–0.51 mm). The tubes are arranged in standard bundles ranging from 4 to 40 ft (1.22–12.20 m)
long and from 4 to 20 ft (1.22–6.10 m) wide, but usually limited to 9.90–10.8 ft (3.2–3.5 m).
4.11.2.1.2 Fin Materials
Aluminum fins are used because of high thermal conductivity, light weight, and formability, but
their use is limited to low-temperature applications. Either SO2-containing or marine atmospheres
may corrode aluminum fins, so carbon steel might be preferred for such conditions. As the base tube
is usually carbon or low-alloy steel, galvanic corrosion at the fin/tube junction is expected. Hence,
finned tubes of carbon steel can be hot-dip galvanized to protect against galvanic corrosion and also
to provide a metallic bond between the fin and the bare tube [68]. Carbon steel tubes with carbon
steel or alloy steel fins are used in boiler and fired heater applications.
4.11.2.1.3 Header
Headers are the boxes at the ends of the tubes which distribute the fluid from the piping to the
tubes. Tube-to-header joints are either welded or expanded depending on header design. A wide
range of header designs has been developed for different applications and requirements. Almost all
headers on air-cooled exchangers are welded rectangular boxes. Headers are usually constructed of
carbon steel or stainless steel, but sometimes more exotic alloys are used for corrosion resistance.
The selection of materials is usually made by the customer. Standard header configurations are pre-
sented next. Major types of headers with finned tube bundle are shown in Figure 4.54. Cross section
of commonly used headers are shown in Figures 4.55 and 4.56 shows finned tubes positioned with
the header for welding.
4.11.2.1.3.1 Cover Plate Header Either with removable cover or with bonnet, a cover plate
header is typically used in chemical applications or services with severe fouling conditions. This
design is available for low to medium pressure (300 psi) installations and where fouling is a poten-
tial problem and hence the tube bundle may require internal cleaning. As the name implies, these
have a removable plate on the back side of the header opposite the tubes. The cover plate is attached
to the header by a set of studs or through-bolts to a flange around the perimeter of the header. A bon-
net header is similar, but opposite in construction. The whole header or bonnet bolts to the tubesheet
end comes off. Bonnet headers are sometimes used where the process fluid is very highly corrosive
and the tubesheet material is exotic alloy, such as titanium.
4.11.2.1.3.2 Cover Plate Header (with Stud Bolts) The cover plate header with stud bolts fea-
tures top or bottom nozzles to allow cover removal without disassembly of the piping (Figure 4.54a).
Nozzles may alternatively be integrated in the cover. The header is fit for a maximum pressure of

50 bar depending on fluid temperature and the type of sealing. A nonstandard header design is
required for higher pressures. Tubes may be weld connected or expanded.
4.11.2.1.3.3 Welded Header (D-Type) The welded header is mainly used for clean products or
vacuum pressure conditions. The tubes are welded into tube sheets to which the bonnet-type header
with the necessary nozzles is welded (Figure 4.54b).
4.11.2.1.3.4 Cover Plate Header (with Through-Bolts) The header features a removable cover
plate with through-bolts for easy inspection and tube cleaning (Figure 4.54c). It is normally suf-
ficient to remove a pipe bend for inspection, since the removal of the bend allows the examination
of part of the tube array. Tubes may be weld connected or expanded.
4.11.2.1.3.5 Plug Header A vast majority of the headers are of the plug type. The design consists
of a shoulder plug opposite each tube which allows access for inspection and cleaning of individual
tube (Figure 4.54d). This general purpose design is used for most refinery and power processes with
(a)
(c)
(b)
(d)
FIGURE 4.54 ACHE header types—(a) cover plate header with stud bolts, (b) welded header (D type),
(c) cover plate header with through-bolts, and (d) plug type header. (Courtesy of GEA Luftkühler GmbH,
Bochum, Germany.)

low to moderately high pressures. They can also be used to plug a leaking tube. The plug holes are
used in the manufacturing process for access to roller expand the tubes into the headers.
4.11.2.1.3.6 Pipe Manifold or Billet Header Pipe manifold headers are common for all pres-
sures, including full vacuum. Billet headers, machined from a solid piece of material, are used in
extremely high pressure (10,000 psig) applications.
4.11.2.1.3.7 High-Pressure Header with Return Segments A threaded plug with a soft iron gasket
is located opposite each tube. The plug may be removed for further tube expansion or for tube cleaning.
Number of passes on the tubeside: On the tubeside, ACHEs can be designed with up to 10 or
more passes. But normally, the number of passes adopted is up to four. Figure 4.57 shows front and
rear headers with three passes arrangement on the tubside. Figure 4.58 shows a four pass rectangu-
lar tubeplate.
Plug
Removable
Tubular D-type Box
FIGURE 4.55 Cross section of commonly used headers.
FIGURE 4.56 Finnedtubespositionedwiththeheaderforwelding.(CourtesyofPolysoudeS.A.S,Cedex,France.)

Number of tube rows: A minimum of three rows is used in the tube bank. The usual maximum
limit is eight rows, though occasionally up to 12 rows are used.
4.11.2.1.4 Orientation of Tube Bundle
ACHE bundles can be installed either vertically or horizontally. Various orientations of ACHEs are
shown in Figure 4.59. The most common orientation is in the horizontal plane. A considerable reduc-
tion in ground area can be made if bundles are vertically mounted, but the performance of the unit is
greatly influenced by the prevailing wind direction. In general, the use of vertically mounted bundles
is confined to small, packaged units. A compromise, which requires about half the ground area of
the horizontal unit, is the A- or V-frame unit. In this type, two bundles sloped at 45°–60° from the
horizontal are joined by their headers at top or bottom to form the sloping side of the A (i.e., roof type)
or V, respectively. The A-frame type with forced draft fans below (Figure 4.60) is the more common
and is used in steam condensing applications. Specification sheet for ACHE is shown in Figure 4.61.
4.11.2.1.4.1 Fan Ring Design Fan ring design varies among manufacturers. The common
configurations for fan rings are [83] the following: (1) eased inlet, (2) taper fan ring, (3) straight
inlet, (4) flanged inlet, and (5) channel rings, and they are indicated in Figure 4.62. Due to the cost
of manufacture, the eased or taper fan rings are generally not utilized in standard products; however,
they are available when required for special applications.
Inlet
header
(a) (b)
Exit
header
FIGURE 4.57 ACHE: (a) inlet or front header and (b) exit or rear headers with three passes arrangement on
the tubeside.
FIGURE 4.58 Four pass rectangular tube plate of an energy recuperator. (From Thermofin, www.thermofin.net)

(b)(a)
Inlet
manifold
Outlet
manifold
(d)(c)
FIGURE 4.59 Orientation of ACHE tube bundle—(a) horizontal, forced draft, (b) horizontal, induced draft,
(c) vertical, and (d) A-frame.
(a) (b)
FIGURE 4.60 Air-cooled condensers (A-type orientation)—(a) two tube row design with hot dip galvanized
elliptical fin tubes with rectangular fins and (b) hot dip galvanized elliptical fin tube. (Courtesy of GEA
Iberica S.A., Vizcaya, Spain.)

Air-Cooled Heat Exchanger Specification Sheet
Customer: Equip. Tag No:
Plant Location: Manufacturer
Service: Size:
Job Number: Surface area per bundle
Model No: Type: Forced or Induced Draft
Heat duty Orientation: A- or V-frame
Process Data
Fluid Circulated: Tubeside
In Out In Out
Fluid quantity, total
Molecular Weight,
Vapor
Liquid
Molecular Weight, Non
condensable
Vapor Viscosity
Non condensable Thermal Conductivity
Steam /water Latent heat
Temperature
Inlet Pressure (specify
gauge or absolute)
Dew Point Outlet Pressure
Freezing point
−Bubble point
Maximum Allowable
Pressure Drop
Pour point Calculated pressure drop
Density Fouling resistance (min.)
Specific heat
Air Side Data
Air quantity Altitude
Air quantity/fan Temperature in
Static Fouling resistance: Pressure: Temperature out
Mass Velocity Face velocity Min. ambient temp.
Design pressure Test pressure Design Temperature
Tube bundle Headers Tubes details
Size Type Material
No./bay Material ASTM: Seamless/Welded
Arrangement: Passes: O.D./Min. Thk.
Bundles in Parallel Plug design Tubes/bundle
Bays in Parallel Material Tube pitch
Bundle Frame Gasket material Fin Type
Miscellaneous Corrosion Allow. Fin Material
Structure Inlet nozzle(s) Fin O.D.
Surface Prep.:
Galvanised/Painted
Outlet nozzle(s) Fin Thickness
Louvers Auto/Manual Nozzle Rating/Type Fin density(Fins/inch):
Standards/Code API-661/ASME Code
FIGURE 4.61 ACHE specification sheet.
(continued)

Tapered or eased rings: The tapered inlet and eased rings both allow for a more uniform exit
of the air from the fan ring. Most fan design programs will indicate slightly less airside pressure
drop and less horsepower required for this configuration. In addition, these fan rings allow for
better air dispersion since the air is directed when it leaves the ring. In most ACHEs, the cost
of producing this configuration outweighs the increased savings in horsepower, or in airflow
efficiency.
Straight, flanged inlet or channel rings: These are the most common fan rings utilized by
manufacturers. This ring is easily produced, and provides good air movement if close tip clear-
ance between the ring and the fan is maintained. The depth of this ring will vary with the fan
selected.
4.11.3 American Petroleum Institute Standard API 661/ISO 13706
American Petroleum Institute Standard 661/ISO 13706 [70] is meant for ACHEs for general refinery
service. The scope of the standard includes minimum requirements for design, materials selection,
Mechanical Drive Equipment
Fan -Constant- or
Variable pitch
Drive Speed Reducer
Mfg/Model Type: Belt/Gear Type
No./bay No./bay No./bay
HP/fan HP/Drive motor Model
Fan Diameter/RPM RPM HP rating
No. blades Enclosure Speed ratio
Pitch: Adjustable or
Auto
Volt/Ph/Cycles Manufacturer
Blade/Hub Material Manufacturer Coupling Model
Vibration switch Louvers Control: Open/Closed
Noise: dB Motor- Constant- or
variable freq.
Fan- Install Inlet bells- and Fan seal disc
Remarks: 1. Recirculation ducts and chambers-
2. Support structure height-
3. Maintenance walkways-
FIGURE 4.61 (continued) ACHE specification sheet.
Tapered inlet Eased inlet
Flanged inletStraight inlet
Channel
FIGURE 4.62 Fan ring design.

fabrication, inspection, testing, and preparation for shipment of refinery process ACHEs. The stan-
dard specifies that the pressure parts shall be designed in accordance with ASME Code, Section
VIII, Division 1 [71]. API Standard 661 should be specified and used as a guide in preparing the
requisition/specification. When the customer’s requirements deviate from API 661, the exceptions
or special requirements should be listed as “Specific Requirements” [72].
4.11.4 Problems with Heat Exchangers in Low-Temperature Environments
ACHEs are designed to perform at ambient temperatures ranging from 130°F to −60°F. In
extremely cold environments, overcooling of the process fluid may cause freezing. This may lead
to tube burst, and hence freeze protection is required to prevent plugging or damage to the tubes.
The minimum temperature also affects material selection for construction of the cooler.
4.11.4.1 Temperature Control
Several methods are used to control the performance of ACHEs to meet variations in weather
and process requirements. The current practice for ACHE design in cold climates for problem
services include (1) recirculation of hot air through the tube bundle; (2) steam coils provided
to preheat air for start-up conditions—these may be mounted at the cooler base to warm up the
inlet air, and according to the recommendation of API 661, this steam coil should be separate
from the main cooler bundle; (3) control devices that enable part of the process fluid to bypass
the unit; (4) for some units, particularly viscous oil coolers, concurrent design is appropriate,
where the hot fluid enters nearest the cold ambient wall, and the outlet where wall temperature
is critical is in the warm air stream [69]; and (5) in certain cases, simply controlling the process
outlet temperature with fan switching, two-speed fan drives, variable-speed motor automatic
louvers, variable pitch fans, or autovariable-pitch fans is sufficient. Each case must be consid-
ered on its merits to decide on the best method of control.
4.11.5 Forced Draft versus Induced Draft
One of the design criteria affecting the performance of ACHEs is the type of draft: forced draft or
induced draft. Both these arrangements are shown in Figure 4.59.
4.11.5.1 Forced Draft
The majority of air-cooled exchangers is of forced draft construction. A common problem with
forced draft coolers is accidental warm air recirculation. Forced draft fans have the advantage of
handling cold air entering the exchanger, requiring smaller volumes of air and less horsepower.
They generally offer better arrangements for maintenance and they are easily accessible. They are
best adapted for cold-climate operation with warm air recirculation. Also, forced draft fans afford a
higher heat transfer coefficient relative to induced draft, because forced draft fans cause turbulence
across the tube bundle [68].
4.11.5.2 Induced Draft
Compared with the forced draft design, induced draft design has the following advantages:
1. Easier to shop assemble, ship, and install
2. The hoods offer protection from weather and hailstone protection
3. Easier to clean the underside when covered with lint, bugs, and debris
4. Better air distribution over the tube bundle
5. Less likely to be affected by hot air recirculation

The disadvantages of induced draft design are
1. More difficult to remove bundles for maintenance
2. High-temperature service limited due to effect of hot air on the fans
3. More difficult to work on the fan assembly, due to heat from the bundle and due to their location
4.11.6 Recirculation
Recirculation of hot plume air occurs in most forced draft ACHEs. The resultant increase in inlet
cooling air reduces the effectiveness of the heat exchanger. To reduce the amount of recirculation,
wind walls may be erected along the periphery of the heat exchanger. This problem has been ana-
lyzed experimentally and numerically by Kroger [67].
4.11.7 Design Aspects
Proper design of ACHEs for cold climate service requires a well-balanced consideration of fluid
flow, heat transfer, structural design, air movement, wind effects, temperature control in cold cli-
mate, and economics [73].
4.11.7.1 Design Variables
Modern ACHEs are designed thermally by computers, which are capable of examining all design
variables to produce the optimum unit. In view of the increased size and cost of these units in large
plants and the competitive nature of the industry, improved and more sophisticated designs are
essential to satisfy the needs of the industry and the society [67]. Important design variables per-
taining to the tube bundle include
Tube (diameter, length and wall thickness, number of tube rows)
Fins (height, spacing, thickness)
Space (length, width, and depth)
Number of tube rows
Number of passes
Face area
Horsepower availability
Plot area
Designers usually optimize criteria such as [78]
Capital versus running cost
Forced versus induced draft fan
Type and spacing of fins
Number of tube rows
Fan design and noise level
Some of the governing factors in the design of the ACHE and hence the thermal design pro-
gram structure is shown in Table 4.3
4.11.7.1.1 Air Velocity
If the airflow rate is known, the tentative air velocity may be chosen, which establishes the cooler
face area. In air-cooled heat exchanges, face velocity is usually in the range of 1.5–4 m/s [75].
Face velocity is based on the gross cross-sectional area for airflow (face area), as though the tubes
were absent.

4.11.7.1.2 Airside Pressure Losses, Fan Power, and Noise
The total air-side pressure loss is the sum of pressure loss through the finned-tube bundle and the pressure
loss due to the fan and plenum. Bundle pressure loss is calculated from makers’ test data or correlations.
4.11.7.1.3 Capital versus Running Cost
A total cost evaluation usually consists of the following four elements [79]:
1. Project equipment cost
2. Field installation cost
3. Electrical distribution cost
4. Operating cost
ACHE costs are influenced by the type of airside flow and the temperature control requirements. Those
process fluids that do not require controlled outlet temperature and do not have freeze problems require
minimal airflow control [77]. Consider the preferred drive and cost of horsepower, and the payback
time for balancing capital investment for adding surface area, against operating costs of fan horsepower.
4.11.7.2 Design Air Temperature
The following data are needed for realistic estimates of the design air temperature [68]:
An annual temperature probability curve
Typical daily temperature curves
Duration frequency curves for the occurrence of the maximum dry-bulb temperature
TABLE 4.3
Program Structure for Design of Air-Cooled Heat Exchanger
Input Parameters
Heat Duty, Process Parameters, Fouling Resistances,
Allowable Pressure Drop, Minimum Ambient Temperature
Code ASME Code, Section VIII, Div. 1
Standard API 661
Header types Plug, studded cover, flanged confined cover, flanged full face cover,
bonnet, U-tube, pipe(dished), header gasket type
Tube parameters Diameter (internal, outer), length and wall thickness and material
Bundle parameters Size (length, width, and depth)
Tubes per row, tube rows per pass, passes per bundle, bundle
connection and bay connection
Tube layout pattern Triangular, rotated triangular, square, diamond
Fin size High- fin (fin height, spacing/fin density, thickness, diameter of fin)
Fin configuration Circular, tension wound
Fin attachment Extruded, L-type weld, L-type tension, embedded, sleeve, metal
coated, etc.
Nozzle details Number of inlet and outlet nozzles, inlet and outlet nozzle diameter
Type of flange Slip-on, weld neck, lap joint, ring type joint, long weld neck
Bundle orientation Horizontal, vertical or inclined
Fan Horse power rating, size, number of blades, rpm, fan pitch control,
noise level and type of drive
Draft type Forced, induced draft
Others Recirculation, operation of louvers, controls for winter operation

4.11.8 Design Tips
A list of points to help to create the most economical design of ACHE for process industries as sug-
gested by GEA Heat Exchangers/GEA Rainey Corporation, Catoosa, OK, are as follows:
a. Maximize tube length while maintaining 40% or more fan coverage.
b. Design aircooler with a 1:3 ratio (width to core length ratio) which helps reduce the header
size, the most expensive portion of an aircooler, and maintain proper fan coverage.
c. Minimize tube rows to increase heat transfer effectiveness of area, minimize header thickness.
Typically between four and six tube rows (maximum).
d. Try to use 25.4 mm (1 in.) tube diameter, depending on service. Even high viscosity services
that appear to benefit from larger diameter tubes can typically be designed cheaper with
more 25.4 mm (1 in.) diameter tubes. Minimum thickness of tubeplate shall be 20 mm for
carbon and low alloy steel tubes and 15 mm for high alloy steel or other material [70].
e. Utilize allowable pressure drop. This allows more passes in the bundle reducing the cooler size.
Other design tips are as follows [83]:
i. A general rule of thumb for the airside face velocity through the coils is as follows:
ii. Three row coil 800–850 fpm, four row coil 500–700 fpm, five row coil 450–600 fpm, and
six row coil 350–500 fpm.
iii. On new construction, good design practice would normally restrict the number of tube rows to 4.
iv. This allows for some modification, if need later, to allow for higher heat load applications.
Normally, on gas compressor applications, the air is at such a high temperature after the
four rows, that additional cooling from additional rows in minimal.
v. A minimum fan to coil face area of 40%.
vi. Air dispersion angle of 45° should not be exceeded, without compensating for this in the design.
vii. Fans should be operated in the mid range of the fan performance, this should be applied to
tip speed, ability to handle the static pressure, and blade angle.
viii. The fan tip speed shall not exceed the maximum value specified by the fan manufacturer
for the selected fan type. Fan tip speed shall not exceed 60 m/s (12,000 ft/min) unless
approved by the purchaser. The radial clearance between the fan tip and the fan orifice ring
shall be as specified by the design.
xi. More surface area is always better than more airflow.
4.11.8.1 Air-Cooled Heat Exchanger Design Procedure
Preliminary sizing by Brown’s method: Once the inlet temperature is known, a reliable first approxi-
mation of the cooler design may be obtained. There are several short-cut manual methods available
in the literature. One such method is that of Brown [74]. Brown considers his method will establish
a size within 25% of optimum. The method can be stated by the following simple steps:
First, an overall heat transfer coefficient is assumed, depending on the process fluid and its tem-
perature range. Approximate overall heat transfer coefficient, for ACHEs are tabulated in Ref. [74].
Second, the air temperature rise (t2 − t1) is calculated by the following empirical formula:

t t U
T T
t2 1
1 2
10 005
2
− =
+
−



.

(4.132)
where T1 and T2 are hot process fluid terminal temperatures.
Third, the estimate is based on bare tubes, with a layout and fan horsepower estimated from
that, so as to avoid the complexity of fin types. Approximate bare tube surface versus unit sizes are
tabulated in Ref. [74].

Sizing: The procedure to follow in ACHE design includes the following steps:
1. Specify process data and identify site data.
2. Assume the layout of the tube bundle (from preliminary sizing), fin geometry, and air
temperature rise.
3. Calculate film coefficients and overall heat transfer coefficient, mean temperature differ-
ence and correction F, and surface area. Check this surface against the assumed layout.
4. If the required surface matches with the assumed layout, calculate the tubeside pressure
drop and verify with the specified value.
5. If the surface area and tubeside pressure drop are verified, calculate the airside pressure
drop and fan horsepower.
4.11.8.2 Air-Cooled Heat Exchanger Data/Specification Sheet
An ACHE data/specification sheet is shown in Figure 4.61. It should be submitted to the vendor along
with the job “specific requirements” as follows [72]:
1. Location of the plant and elevation above sea level
2. Location of the unit in the plant
3. Temperature variation due to weather conditions
4. Seismic and wind loads
5. Variations in operation
6. Process control instrumentation
7. Fire protection
8. Pumping power. The fan power (Pp) required is given by
P
p
p =
Μ∆
ρ
(4.133a)

or
pP
GA p
=
min ∆
ρ
(4.133b)
9. Special surface finish
The condition for dispersion angle of the fan is shown in Figure 4.63. Each fan shall be located such
that its dispersion angle shall not exceed 45° at the bundle centerline [70].
Plenum
45°
45° 45°
45°
Induced draft
Center line of bundle
Forced draft
Typ. max.
dispersion angle
Typ. max.
dispersion angle
FIGURE 4.63 Condition for dispersion angle of the fan.

4.11.8.3 Performance Control of ACHEs
In addition to the fact that the process flow rate, composition, and inlet temperature of the fluid may
vary from the design conditions, the ambient air temperature varies throughout a 24 h day and from
day to day. Since ACHEs are designed for maximum conditions, some form of control is necessary
when overcooling of the process fluid is detrimental, or when saving fan power is desired. Although
control could be accomplished using by-passing of process fluid, this is rarely done, and the usual
method is airflow control [79].
4.11.8.3.1 Varying Airflow
Varying airflow can be accomplished by [79]
• Adjustable louvers on top of the bundles
• Two-speed fan motors
• Fan shut-off in sequence for multifan units
• AUTO-VARIABLE® fans
• Variable frequency fan motor control
4.11.8.3.1.1 Holtec’s HI-MAX™ All Stainless Steel All Welded Fin Tube HI-MAX’s stainless
steel fin tubes (Figure 4.64) eliminate the thermal stresses associated with aluminized carbon steel
tubes and aluminum fins (used in peer systems), thus extending the performance life of the air-
cooled condenser. The stainless steel bundles also provide a superior internal and external corrosion
protection, which mitigates two significant problems with today’s ACHE’s—(1) flow accelerated
corrosion and (2) iron carryover into the condensate. The HI-MAX fin-to-tube bond is made by
laser welding and hence stronger in construction. HI-MAX do not have a galvanic coating to combat
against corrosion.
NOMENCLATURE
A total heat transfer area, m2 (ft2)
Af fin surface area, m2 (ft2)
Afr frontal area, m2 (ft2)
Ao minimum free flow area, m2 (ft2)
Ap primary heat transfer surface area, m2 (ft2)
As secondary heat transfer surface area, m2 (ft2)
C, cp specific heat, J/kg °C (Btu/lbm.°F)
FIGURE 4.64 HI-MAX™ all stainless steel all welded fin tube. (Courtesy of Holtec International, Marlton, NJ.)

Cc specific heat of cold fluid, J/kg °C (Btu/lbm.°F)
Ch specific heat of hold fluid, J/kg °C (Btu/lbm.°F)
C* heat capacity rate ratio for a compact exchanger= (mcp)min/(mcp)max
di inside diameter of the tueb, m (ft)
df fin diameter of circular fin, m (ft)
do outside diameter of the tube, m (ft)
dr effective fin diameter at the collar, m (ft)
F LMTD correction factor
ff friction factor on the fin surfaces
ft friction factor due to drag force on the tubes
G, Gm mass velocity, kg/m2·s (lbm/h·ft2)
Gmax mass velocity based on free flow area, kg/m2·s (lbm/h·ft2)
gc acceleration due to gravity or proportionality constant 9.81 m/s2 (32.17 ft/s2)
= 1 and dimensionless in SI units
h convective heat transfer coefficient, W/m2·°C (Btu/ft2 h·°F)
j Colburn heat transfer factor
jN Colburn heat transfer factor for N number of tube rows
K fluid entrance contraction or exit expansion coefficient
k thermal conductivity of the fluid, W/m°C (Btu/h·ft·°F)
kf thermal conductivity of the fin material, W/m°C (Btu/h·ft·°F)
L length in the fluid flow direction, m (ft)
Lf characteristic fin length, m (ft)
lf fin length, m (ft)
L1, L2, L3 heat exchanger core dimensions of a tube bank, m (ft)
M mass flow rate of the fluid, kg/s (lbm/h)
N1 number of tubes in one row
Nt total number of tubes
Nf fin density of a tubular exchanger
Np Number of flow passages on side 1 of PFHE
Np + 1 Number of flow passages on side 2 of PFHE
NTU number of transfer units,
Nu Nusselt number
Nr number of tube rows,
n fin density of PFHE
Pp fluid pumping power
Pl longitudinal pitch, m2 (ft2)
PT, Pt lateral pitch, m2 (ft2)
Pr Prandtl number
Q total heat duty of the exchanger, W·s (Btu)
R heat capacity rate ratio of shell and tube heat exchanger fluids
Re Reynolds number
Red Reynolds number based on tube outer diameter
Reh Reynolds number based on hydraulic diameter
St Stanton number
s gap between two fins, m (ft)
tf thickness, m (ft)

T Temperature, °C (°F)
t Temperature, °C (°F)
Th header plate thickness, m (ft)
Uf upstream fluid velocity on the fin side, m/s (ft/s)
U overall heat transfer coefficient, W/m2·°C (Btu/h·fr2·°F)
VP volume between plates on one side, m3(ft3)
α Surface area density of PFHE, m2/m3 (ft2/ft3)
α the effective heat transfer coefficient of a stream (Eq. 4.37b), W/m2·°C (Btu/ft2 h·°F)
∆p pressure drop, Pa (lbf/ft2)
μ viscosity of the fliud, kg/m·s or Pa·s (lbm/h·ft)
ρ fluid density, kg/m3 (lbm/ft3)
β surface area density, m2/m3 (ft2/ft3)
ηf fin efficiency
ηo overall surface efficiency
σ = the ratio of minimum free flow area to frontal area
Subscripts
ave average
b bulk mean temperature
c cold
h hot
e exit
i inlet
lm log mean
m mean
n nozzle
o outlet
w wall temperature conditions
1 side 1 or inlet of the exchanger
2 side 2 or outlet of the exchanger
min minimum
max maxim
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Ward, D. J. andYoung, E. H., Heat transfer and pressure drop of air in forced convection across triangular pitch
banks of finned tubes, Chem. Eng. Prog. Symp. Ser., 55, 37 (1959).
Ward, D. J. andYoung, E. H., Heat transfer and pressure drop of air in forced convection across triangular pitch
banks of finned tubes, Chem. Eng. Prog. Symp. Ser. 59, 37–44 (1963).
Webb, R. L., Air side heat transfer in finned tube heat exchangers, Heat Transfer Eng., 1, 33–49 (1980).
Webb, R. L., Compact heat exchangers, in Heat Exchanger Design Handbook (E. U. Schlunder, editor-in-
chief), Vol. 3, Hemisphere, Washington, DC, 1983, Section 3.9.
Zukauskas, A., Heat transfer from tubes in cross flow, in Advances in Heat Transfer (J. P. Hartnett and T. Irvine,
Jr., eds.), Vol. 8, Academic Press, New York, 1972, pp. 93–160.

237
5 Shell and Tube Heat
Exchanger Design
The most commonly used heat exchanger is the shell and tube type. It is the “workhorse” of indus-
trial process heat transfer. It has many applications in the power generation, petroleum refinery,
chemical industries, and process industries. They are used as oil cooler, condenser, feedwater
heater, etc. Other types of heat exchangers are used when economical. Though the application of
other types of heat exchangers is increasing, the shell and tube heat exchanger will continue its
popularity for a long time, largely because of its versatility [1].
5.1 CONSTRUCTION DETAILS FOR SHELL AND TUBE EXCHANGERS
The major components of a shell and tube exchanger are tubes, baffles, shell, front head, rear
head, and nozzles. Expansion joint is an important component in the case of fixed tubesheet
exchanger for certain design conditions. Other components include tie-rods and spacers, impinge-
ment plates, sealing strips, supports, and lugs. The selection criteria for a proper combination of
these components are dependent upon the operating pressures, temperatures, thermal stresses,
corrosion characteristics of fluids, fouling, cleanability, and cost. Expansion joints, nozzles, and
supports are discussed in detail in Chapter 11. A large number of geometrical variables are asso-
ciated with each component, and they are discussed in detail in this chapter. Major components
of shell and tube heat exchangers and a cut section of a heat exchanger are shown in Figure 5.1.
5.1.1 Design Standards
5.1.1.1 TEMA Standard
TEMA standards [2] are followed in most countries of the world for the design of shell and tube heat
exchangers. The TEMA standards are applicable to unfired shell and tube heat exchangers with inside
diameters not exceeding 60 in. (1524 mm). Each section is identified by an uppercase letter symbol, which
precedes the paragraph numbers of the section and identifies the subject matter. TEMA classes R, C, and
B have been combined into one section titled class RCB. The differences in design practices among the
classes have been to some extent simplified. Details of R, C, and B classification are as follows:
1. TEMA B—generally for chemical process services, more stringent than TEMA C, but not
as stringent as R
2. TEMA C—for generally moderate commercial and process application requirements, the
most commonly used in industries
3. TEMA R—the highest integrity design
5.1.1.2 ANSI/API Standard 660
ANSI/API Standard 660 [3] is the national adoption of ISO 16812:2002—Petroleum and natural
gas industries—Shell and tube heat exchangers. This International Standard specifies requirements
and gives recommendations for the mechanical design, material selection, fabrication, inspection,
testing, and preparation for the shipment of shell and tube heat exchangers for the petroleum and
natural gas industries.

5.2 TUBES
Tubes of circular cross section are exclusively used in exchangers. Since the desired heat transfer
in the exchanger takes place across the tube surface, the selection of tube geometrical variables is
important from the performance point of view [4]. Important tube geometrical variables include
tube outside diameter, tube wall thickness, tube pitch, and tube layout patterns (Figure 5.2). Tubes
should be able to withstand the following:
1. Operating temperature and pressure on both sides
2. Thermal stresses due to the differential thermal expansion between the shell and the tube
bundle
3. Corrosive nature of both the shellside and the tubeside fluids
There are two types of tubes: straight tubes and U-tubes. The tubes are further classified as
1. Plain tubes
2. Finned tubes
3. Duplex or bimetallic tubes
4. Enhanced surface tubes
Tubesheet
Shell plate/shell
Tube
Expansion joint
Nozzle
ChannelDished end
Flange
End cover
(a)
Baffle
(b)
FIGURE 5.1 (a) Major components of a shell and tube heat exchanger. (b) Cut section of a shell and tube heat
exchanger. (Courtesy of API Heat Transfer Inc., Buffalo, NY.)

239Shell and Tube Heat Exchanger Design
Extended or enhanced surface tubes are used when one fluid has a substantially lower heat transfer
coefficient than the other fluid. Doubly enhanced tubes with enhancement both on inside and outside of
the tubes are available that can reduce the size and cost of the exchanger. Extended surfaces of finned
tubes types can provide 2–4 times as much heat transfer area on the outside as the corresponding bare
tube, and this enhanced area helps to offset a lower outside heat transfer coefficient. More recent devel-
opments include corrugated tube, which has both inside and outside heat transfer enhancement, a finned
tube, which has integral inside turbulators as well as extended outside surface, and tubing, which has
outside surfaces designed to promote nucleate boiling [5].
5.2.1 Tube Diameter
Tube size is specified by outside diameter and wall thickness. From the heat transfer point of view,
smaller diameter tubes yield higher heat transfer coefficients and result in a compact exchanger.
However, larger diameter tubes are easier to clean, more rugged, and they are necessary when the
allowable tubeside pressure drop is small. Almost all heat exchanger tubes fall within the range of
1
4 in. (6.35 mm) to 2 in. (5.8 mm) outside diameter. TEMA tube sizes in terms of outside diameter
are 1
4
3
8
1
2
5
8
3
4
7
9, , , , , ,1,1.25,1.5, and 2 in. (6.35, 9.53, 12.70, 15.88, 19.05, 22.23, 25.40, 31.75, 38.10,
and 50.80 mm). Standard tube sizes and gauges for various metals are given in TEMA Table RCB-
2.21. These sizes give the best performance and are most economical in many applications. Most
popular are the 3
8 -in. and 3
4 -in. sizes, and these sizes give the best all-around performance and are
most economical in most applications [6]. Use 1
4 in. (6.35 mm) diameter tubes for clean fluids. For
mechanical cleaning, the smallest practical size is 3
4
in. (19.05 mm). Tubes of diameter 1 in. are
normally used when fouling is expected because smaller ones are not suitable for mechanical clean-
ing, and falling film exchangers and vaporizers generally are supplied with 1.5- and 2-in. tubes [7].
5.2.2 Tube Wall Thickness
The tube wall thickness is generally identified by the Birmingham wire gauge. Standard tube
sizes and tube wall thickness in inches are presented in TEMA Table RCB-2.21. Tube wall
thickness must be checked against the internal and external pressures separately, or maximum
pressure differential across the wall. However, in many cases, the pressure is not the governing
factor in determining the wall thickness. Except when pressure governs, the wall thickness
is selected on these bases [8]: (1) providing an adequate margin against corrosion, (2) fretting
Square pitch
p–d
p
d
(e)
Flow
p–d
d
p
Triangular pitch(f)
Flow
Triangular
(30°)
Flow
(a)
Rotated triangular
(60°)
Flow
(b)
Square
(90°)
Flow
(c) (d)
Flow
Rotated square
(45°)
FIGURE 5.2 Tube layout patterns: (a) 30°; (b) 60°; (c) 90°; (d) 45°; (e) flow area for square pitch; and (f) flow
area for triangular pitch.

and wear due to flow-induced vibration, (3) axial strength, particularly in fixed exchangers,
(4) standardized dimensions, and (5) cost.
5.2.3 Low-Finned Tubes
Shell and tube exchangers employ low-finned tubes (Figure 5.3) to increase the surface area on the
shellside when the shellside heat transfer coefficient is low compared to the tubeside coefficient—
e.g., when shellside fluid is highly viscous liquids, gases, or condensing vapors. The low-finned
tubes are generally helical or annular fins on individual tubes.
Fin tubes for a shell and tube exchanger are generally “low-fin” type with fin height slightly less
than 1
16 in. (1.59 mm). The most common fin density range is 19–40 fins/in. (748–1575 fins/m). The
surface area of such a fin tube is about 2.5–3.5 times that of a bare tube [4]. The finned tube has bare
ends having conventional diameters of bare tubing; the diameter of the fin is either slightly lower
than or the same as the diameter of the bare ends, depending upon the manufacturer. In addition to
the geometrical variables associated with bare tubes, the additional geometrical dimensions associ-
ated with a fin tube are root diameter, fin height, and fin pitch.
5.2.4 Tube Length
For a given surface area, the most economical exchanger is possible with a small shell diameter
and long tubes, consistent with the space and the availability of handling facilities at site and in the
fabricator’s shop [8]. Therefore, minimum restrictions on length should be observed. However, for
offshore applications, long exchangers, especially with removable bundles, are often very difficult
to install and maintain economically because of space limitations [9]. In this case, shorter and larger
shells are preferred despite their higher price per unit heat transfer surface. Standard lengths as per
TEMA standard RCB-2.1 are 96, 120, 144, 196, and 240 in. Other lengths may be used.
5.2.5 Means of Fabricating Tubes
Tubing used for heat exchanger service may be either welded or seamless. The welded tube is rolled
into cylindrical shape from strip material and is welded automatically by a precise joining process.
A seamless tube may be extruded or hot pierced and drawn. Copper and copper alloys are available
only as seamless products, whereas most commercial metals are offered in both welded and seam-
less. More details on tubing are given in Chapters 8 and 13.
5.2.6 Duplex or Bimetallic Tubes
Duplex or bimetallic tubes are available to meet the specific process problem pertaining to either the
shellside or the tubeside. For example, if the tube material is compatible with the shellside fluid, but not
compatible with the tubeside fluid, a bimetallic tube allows it to satisfy both the corrosive conditions.
Wall thickness of
unfinned section
Root dia. Internal dia. Dia. over fins
Dia. of
unfinned section
FIGURE 5.3 Low-finned tube.

5.2.7 Number of Tubes
The number of tubes depends upon the fluid flow rate and the available pressure drop. The number
of tubes is selected such that the tubeside velocity for water and similar liquids ranges from 3 to
8 ft/s (0.9–2.4 m/s) and the shellside velocity from 2 to 5 ft/s (0.6–1.5 m/s) [4]. The lower velocity
limit is desired to limit fouling; the higher velocity is limited to avoid erosion–corrosion on the
tubeside, and impingement attack and flow-induced vibration on the shellside. When sand, silt, and
particulates are present, the velocity is kept high enough to prevent settling down.
5.2.8 Tube Count
To design a shell and tube exchanger, one must know the total number of tubes that can fit into the
shell of a given inside diameter. This is known as tube count. Factors on which the tube count depends
are discussed in Ref. [8] and in Phadke [10] and Whitley et al. [11]. Such factors include the following:
• Shell diameter
• Outside diameter of the tubes
• Tube pitch
• Tube layout pattern—square, triangular, rotated square, or rotated triangular
• Clearance between the shell inside diameter and the tube bundle diameter
• Type of exchanger, i.e., fixed tubesheet, floating head, or U-tube
• Number of tubeside passes
• Design pressure
• Nozzle diameter
• Tie-rods and sealing devices that block space
• Type of channel baffle, i.e., ribbon, pie shape, vertical, etc. [11]
The conventional method of obtaining tube count by plotting the layout and counting the tubes
(thus the tube count) is cumbersome, time-consuming, and prone to error. Tables of tube count are
available in references like Ref. [10,12], and others, which often cover only certain standard com-
binations of pitch, tube diameter, and layout parameters. A mathematical approach using number
theory is suggested by Phadke [10] to predict the tube count and presented tube count for various
combinations of tube layout parameters. His method eliminates the disadvantages of drawing the
tube layout pattern and can accommodate any configuration.
5.2.9 U-Tube
5.2.9.1 U-Tube U-Bend Requirements as per TEMA
When U-bends are formed, it is normal for the tube wall at the outer radius to thin. As per TEMA
section RCB-2.33, the minimum tube wall thickness in the bent portion before bending shall be [2]

t t
d
R
o
b
= +



1 1
4

(5.1)
where
to is the original tube wall thickness
t1 the minimum tube wall thickness calculated by code rules for a straight tube subjected to the
same pressure and metal temperature
d the tube outer diameter
Rb the mean radius of bend

5.3 TUBE ARRANGEMENT
5.3.1 Tube Pitch
The selection of tube pitch is a compromise between a close pitch for increased shellside heat trans-
fer and surface compactness, and a larger pitch for decreased shellside pressure drop and fouling,
and ease in cleaning. In most shell and tube exchangers, the minimum ratio of tube pitch to tube
outside diameter (pitch ratio) is 1.25. The minimum value is restricted to 1.25 because the ligament
(a ligament is the portion of material between two neighboring tube holes) may become too weak for
proper rolling of the tubes into the tubesheet. The ligament width is defined as the tube pitch minus
the tube hole diameter; this is shown in Figure 5.4.
5.3.2 Tube Layout
Tube layout arrangements (Figure 5.2) are designed so as to include as many tubes as possible
within the shell to achieve maximum heat transfer area. Sometimes a layout is selected that also per-
mits access to the tubes for cleaning as required by process conditions. Four standard types of tube
layout patterns are triangular (30°), rotated triangular (60°), square (90°), and rotated square (45°).
(Note that the tube layout angle is defined in relation to the flow direction and is not related to the
horizontal or vertical reference line arrangement, and that the 30°, 60°, and 45° arrangements are
“staggered,” and 90° is “in-line.”) For identical tube pitch and flow rates, the tube layouts in decreas-
ing order of shellside heat transfer coefficient and pressure drop are 30°, 45°, 60°, and 90°. Thus, the
90° layout will have the lowest heat transfer coefficient and pressure drop. The selection of the tube
layout pattern depends on the following parameters, which influence the shellside performance and
hence the overall performance:
1. Compactness
2. Heat transfer
3. Pressure drop
4. Accessibility for mechanical cleaning
5. Phase change if any on the shellside
5.3.2.1 Triangular and Rotated Triangular Arrangements
Triangular and rotated triangular layouts (30° and 60°) provide a compact arrangement, better
shellside heat transfer coefficients, and stronger tubesheets for a specified shellside flow area.
For a given tube pitch/outside diameter ratio, about 15% more tubes can be accommodated within
a given shell diameter using these layouts [8]. These layout patterns are satisfactory for clean
services, but have the disadvantage of making the lanes between tubes rather inaccessible for
mechanical cleaning. It is difficult to insert a rigid tool between the tubes. Only chemical cleaning
or water jet cleaning is possible.
p
d
d
FIGURE 5.4 Tube pitch and ligament width (p – d).

5.3.2.2 Square and Rotated Square Arrangements
When mechanical cleaning is necessary on the shellside, 45° and 90° layouts must be used with a
minimum gap between tubes of 6.35 mm. There is no theoretical limit to tube outer diameter for
mechanical cleaning, but the 6.35 mm clearance limits the tubes to a minimum of 5
8
or 3
4
in outer
diameter in practice [9]. The square pitch is generally not used in the fixed design because of no
need of mechanical cleaning on the shellside. These layout patterns offer lower pressure drops and
lower heat transfer coefficients than triangular pitch. The 45° layout is preferred for single-phase
laminar flow or fouling service, and for condensing fluid on the shellside. Shah [4] suggests a square
layout for the following applications:
1. If the pressure drop is a constraint on the shellside, the 90° layout is used for turbulent flow,
since in turbulent flow, the 90° has superior heat transfer rate and less pressure drop.
2. For reboilers, a square layout will be preferred for stability reasons. The 90° layout pro-
vides vapor escape lanes.
5.4 BAFFLES
Baffles must generally be employed on the shellside to support the tubes, to maintain the tube spac-
ing, and to direct the shellside fluid across or along the tube bundle in a specified manner. There are
a number of different types of baffles, and these may be installed in different ways to provide the
flow pattern required for a given application.
5.4.1 Classification of Baffles
Baffles are either normal or parallel to the tubes. Accordingly, baffles may be classified as
transverse or longitudinal. The transverse baffles direct the shellside fluid into the tube bundle
at approximately right angles to the tubes and increase the turbulence of the shell fluid. Every
shell and tube exchanger has transverse baffles except the X and K shells, which have only
support plates. The longitudinal baffles are used to control the direction of the shellside flow.
For example, F, G, and H shells have longitudinal baffles. In the F shell, an overall counterflow
is achieved.
5.4.2 Transverse Baffles
Transverse baffles are of two types: (1) plate baffles and (2) rod baffles. Three types of plate baffles
are (1) segmental, (2) disk and doughnut, and (3) orifice baffles.
5.4.2.1 Segmental Baffles
The segmental baffle is a circular disk (with baffle holes) having a segment removed.
Predominantly, a large number of shell and tube exchangers employ segmental baffles. This
cutting is denoted as the baffle cut, and it is commonly expressed as a percentage of the shell
inside diameter as shown in Figure 5.5. Here the percent baffle cut is the height, H, given as a
percentage of the shell inside diameter, Ds. The segmental baffle is also referred to as a single
segmental baffle. The heat transfer and pressure drop of crossflow bundles are greatly affected
by the baffle cut. The baffle cuts vary from 20% to 49% with the most common being 20%–25%,
and the optimum baffle cut is generally 20%, as it affords the highest heat transfer for a given
pressure drop. Baffle cuts smaller than 20% can result in high pressure (HP) drop. As the baffle
cut increases beyond 20%, the flow pattern deviates more and more from crossflow [7] and can
result in stagnant regions or areas with lower flow velocities; both of these reduce the thermal
effectiveness of the bundle [1].

Baffle spacing: The practical range of single segmental baffle spacing is 1
5 –1 shell diameter [1],
though optimum could be 40%–50% [1]. TEMA Table RCB-4.52 [2] provides maximum baffle
spacing for various tube outer diameters, tube materials, and the corresponding maximum allow-
able temperature limit. The baffles are generally spaced between the nozzles. The inlet and outlet
baffle spacings are in general larger than the “central” baffle spacing to accommodate the nozzles,
since the nozzle dimensions frequently require that the nozzle should be located far enough from
the tubesheets.
Baffle thickness: TEMA Tables R-4.41 and CB-4.41 [2] provide the minimum thickness of trans-
verse baffles applying to all materials for various shell diameters and plate spacings.
Shellside flow distribution: Segmental baffles have a tendency to poor flow distribution if spac-
ing or baffle cut ratio is not in correct proportion, as shown in Figure 5.6 [13]. Too low or too high
a ratio results in maldistribution and produces inefficient heat transfer and also favors fouling. For
low-pressure (LP)-drop designs, choose baffles that ensure a more uniform flow such as multiseg-
mental, disk and doughnuts, and rod baffles.
Orientation of baffles: Alternate segmental baffles are arranged at 180° to each other, which cause
shellside flow to approach crossflow through the bundle and axial flow in the baffle window zone. All
segmental baffles have horizontal baffle cuts as shown in Figure 5.7a. Unless the shellside fluid is con-
densed, the horizontal baffle cut should be used for single-phase application, to reduce accumulation of
deposits on the bottom of the shell and to prevent stratification of the shellside fluid [7]. The direction
of the baffle cut is selected as vertical (Figure 5.7b) for the following shellside applications [8]:
θb
A B
Bc
Ds
FIGURE 5.5 Baffle cut.
Baffle
Baffle
Ideal baffle cut
and baffle spacing
Baffle
Small baffle cut
Shelldia.
Baffle
Eddies
Main flow
Baffle
Large baffle cut
Main flow
FIGURE 5.6 Shellside flow distribution influenced by baffle cut.

(1) for condensation, to allow the condensate to flow freely to the outlet without covering an excessive
amount of tubes [4,7]; (2) for boiling or condensing fluids, to promote more uniform flow; and (3) for
solids entrained in liquid (to provide least interference for the solids to fall out).
5.4.2.1.1 Double Segmental and Multiple Segmental Baffles
Various multi-segmental baffles can be used to reduce baffle spacing or to reduce crossflow because
of pressure limitations. The multi-segmental baffles are characterized by large open areas and some
allow the fluid to flow nearly parallel to the tubes, offering a much lower pressure drop [14].
Double and triple segmental baffle layout are shown in Figure 5.8a, Figure 5.8b shows design
requirement to ensure adequate tube support [5], idealized fluid flow fraction through the baffles is
shown in Figure 5.8c, and fluid flow stream pattern is shown in Figure 5.8d. In an exchanger with
(a) (b) (c)
FIGURE 5.7 Baffle cut orientation: (a) horizontal; (b) vertical; and (c) rotated.
(a)
Edge of baffle–2
Edge of baffle–1
1
(b)
2
2
2
1 1
This overlap must include
at least one full row
to ensure full tube field support
Each overlap must include
at least one full tube row
1U
1L
1L
1U
2
FIGURE 5.8 Segmental baffles layout. (a) Double and triple segmental baffles with end view flow pattern,
(b) design requirement to ensure adequate tube support with double and triple segmental baffles.
(continued)

single segmental baffles the total flow, except for leakages and bypass streams, passes through the
tube bank between baffles in crossflow, whereas with double segmental baffles barring the leakages,
the flow divides into two streams on either side of the baffle, and in triple segmental baffles, the flow
divides into three streams as shown in Figure 5.8c and d. Due to this, heat exchangers with double
or multiple segmental baffles can handle larger fluid flows on the shellside. Other features of double
segmental or multiple segmental baffles are as follows [4]:
1. The flow on the shellside is split into two or more streams as per the number of baffle seg-
ments, namely, double, triple, multiple, etc.; hence, the danger of shellside flow-induced
vibration is minimal.
2. The baffle spacing should not be too small; otherwise, it results in a more parallel (longi-
tudinal) flow with significant low stagnant areas.
Double segmental and triple segmental baffle heat exchanger units under fabrication are shown in
Figure 5.9a and b, respectively.
(c)
Segmental baffle Double segmental baffle
Triple segmental baffle(d)
FIGURE 5.8 (continued) Segmental baffles layout. (c) idealized flow fraction with segmental baffles, and
(d) stream flow distribution with segmental baffles.

5.4.2.1.2 Window Baffles
These are considered when crossflow is not practical because of pressure-drop limitations. Window
baffles allow the fluid to flow parallel to the tubes, offering much lower pressure drop [7].
5.4.3 Disk and Doughnut Baffle
The disk and doughnut baffle is made up of alternate “disks” and “doughnut” baffles as shown in
Figure 5.10. Disk and doughnut baffle heat exchangers are primarily used in nuclear heat exchangers [4].
(a) (i) (ii)
(b)
FIGURE 5.9 (a) Heat exchanger with double segmental baffles. (i) Cage assembly (Courtesy of Brembana
Costruzioni Industriali S.p.A., Milan, Italy), and (ii) tube bundle under assembly. (Courtesy of Peerless
Mfg. Co. of Dallas, TX, Makers of Alco and Bos-Hatten brands of heat exchangers.) (b) Shell and tube
heat exchanger tube bundle cage with triple segmental baffles. (Courtesy of Heat Exchanger Design, Inc.,
Indianapolis, IN.)
Disk
Disk
Disk
Doughnut
Doughnut
Doughnut
Doughnut
FIGURE 5.10 Disk and doughnut baffles.

This baffle design provides a lower pressure drop compared to a single segmental baffle for the same
unsupported tube span and eliminates the tube bundle to shell bypass stream.
5.4.4 Orifice Baffle
In an orifice baffle, the tube-to-baffle hole clearance is large so that it acts as an orifice for the
shellside flow (Figure 5.11). These baffles do not provide support to tubes, and, due to fouling, the
annular orifices plug easily and cannot be cleaned. This baffle design is rarely used.
5.4.5 No Tubes in Window
The baffle cut area, or baffle window region, is generally filled with tubes. Since the tubes in the window
zone are supported at a distance of two times the central baffle spacing, they are most susceptible to
vibration. To eliminate the susceptibility of tube vibrations, the tubes in the window zone are removed
and therefore all tubes pass through all baffles. Additional support plates are introduced between main
baffles to reduce the unsupported span of the tubes as shown in Figure 5.12, thus providing an increase
in the natural frequency of the tubes. The resultant design is referred to as the segmental baffle with no-
tubes-in-window (NTIW) design. NTIW design has the following characteristics [15]:
1. Pressure drop about one-third that of single segmental baffle design
2. Uniform shellside flow pattern resembling that of an ideal tube bank, which offers high
shellside heat transfer coefficient and low fouling tendency
3. The baffle cut and the number of tubes removed vary from 15% to 25%
4. Very LP drop in the window and correspondingly lower bypass and leakage streams
Since the loss in heat transfer surface is considerable in an NTIW design, this can be minimized
by having small baffle cuts and possibly by an increase in the shellside fluid velocity or larger shell
Orifice baffles
FIGURE 5.11 Orifice baffle.
Baffle plates
Segmental baffle Tube
FIGURE 5.12 NTIW design.

diameter to contain the same number of tubes. It may be noted that the design of tubesheet of NTIW
does not fall within TEMA Standard.
5.4.6 Longitudinal Baffles
Longitudinal baffles divide the shell into two or more sections, providing multipass on the shellside. But
this type should not be used unless the baffle is welded to the shell and tubesheet. Nevertheless, several
sealing devices have been tried to seal the baffle and the shell, but none has been very effective [7].
Gupta [16] lists some sealing devices that are used to seal the baffle and shell. They are the following:
• Sealing strips or multiplex arrangement
• Packing arrangement
• Slide-in or tongue-and-groove arrangement
If the baffle is not welded, bypassing occurs from one side to the other, which adversely affects
the heat transfer coefficient and makes its accurate prediction rather difficult. Hence, it is better to
weld than to prefer this design. Common methods to weld the longitudinal baffle to the shellside
are shown in Figure 5.13 [17]. When multipass shells are required, it is economical to use a separate
shell, unless the shell diameter is large enough to easily weld a longitudinal baffle to the shell [7].
5.4.7 Rod Baffles
Phillips RODbaffle design uses alternate sets of rod grids instead of plate baffles, enabling the tubes
to be supported at shorter intervals without resulting in a large pressure drop. Flow-induced vibra-
tion is virtually eliminated by this design. The flow is essentially parallel to tube axis; as a result of
the longitudinal flow, it has LP drop to heat transfer conversion characteristics. The tube layout is
usually 45° or 90°. Design of rod baffle heat exchanger is covered separately in this chapter.
5.4.8 NEST Baffles and Egg-Crate Tube Support
NESTTM baffle: This is a patented design intended to overcome the danger of flow-induced vibra-
tion of tubes. In this design, each tube rests in a V-shaped cradle and is supported at line segments
(Figure 5.14a). These elements are preformed to the desired tube pitch and ligament size. The flow
is parallel to the tube bundle, and hence the vibration problem is greatly reduced [18]. It is claimed
that the pressure drop is lower for the same amount of heat transfer compared to a segmentally
baffled exchanger.
EGG-CRATE-GRID™ support (Figure 5.14b) is a simple and economical support for heat
exchanger tubes, which can droop or collapse under stress and elevated temperature. This support
is fabricated from commercial flat strip material, typically of stainless steel; strip ends are tack
welded to the heat exchanger shell and tubes are welded to strips at specified intervals. This design
eliminates conventional s, which requires tube insertion through drilled holes.
Figure 5.14c shows patented baffles similar to EGG-CRATE baffle but with a square tube layout.
Longitudinal
plate
(a) (b) (c)
FIGURE 5.13 Longitudinal baffle weld joint with shell. (a) Shell gouged and welded, (b) baffle passes
through shell and welded, and (c) baffle welded to inside of the shell.

5.4.8.1 Non-Segmental Baffles
The non-segmental baffle as shown in Figure 5.15 is a Holtec patented tube support system used to
promote axial flow in a tube bundle. Holtec’s non-segmental baffle eliminates the problems associ-
ated with high-volume shellside flows, since it provides total tube support while offering minimal
obstruction to the passing fluid. Furthermore, non-segmental baffles have been used by in a variety
of applications involving phase change (boiling or condensing), and thermosiphon flows. In addi-
tion, the use of these baffles virtually eliminates flow-induced vibrations and premature tube fail-
ure. These non-segmental baffles are made from a flat metal strip that emulates the surface quality
of typical heat exchanger tubing. Each strip is laser cut to ensure a precise lattice-like structure.
Typical materials of construction are 304 and 316 stainless steel; however, other material can be
used upon request. Tube hole clearances are within the TEMA and HEI limits.
Typ. for all
strip to ring
junctions
Tack
Shell
(a) (b)
(c)
FIGURE 5.14 Special types of plate baffles. (a) NEST™, (b) EGG-CRATE baffle support, and (c) patented
baffles with a square tube layout.
FIGURE 5.15 Non-segmental baffles. (Courtesy of Holetec International, Marlton, NJ.)

5.4.8.1.1 Low-Pressure Drop Baffles
Another type of non-segmental baffle made of rods (Figure 5.16) was developed by Koch Heat
Transfer, USA, and Holtec International, USA, and to ensure LP drop on the shellside since the
shellside flow is longitudinal in nature. This baffle type is different from Phillips RODbaffle heat
exchanger.
5.4.9 Grimmas Baffle
The Grimmas baffle is a patented version of the plate baffle, which ensures an axial flow and
improves heat transfer [19]. The design is shown in Figure 5.17.
5.4.10 Wavy Bar Baffle
Wavy bar baffle design, as shown in Figure 5.18, is similar to Grimmas baffle but made of
wavy bar. This design ensures axial flow and improves heat transfer and ensures LP drop on the
shellside.
5.4.11 Baffles for Steam Generator Tube Support
Figure 5.19 shows five types of baffles—four with plate baffles and one with lattice bars similar to
EGG-CRATE baffle used in applications of steam generators [20].
FIGURE 5.16 LP drop baffles. (Courtesy of Holtec International, Marlton, NJ.)
FIGURE 5.17 Grimmas baffle.

5.5 TUBESHEET AND ITS CONNECTION WITH SHELL AND CHANNEL
A tubesheet is an important component of a heat exchanger. It is the principal barrier between the shellside
andtubesidefluids.Properdesignofatubesheetisimportantforsafetyandreliabilityoftheheatexchanger.
Tubesheets are mostly circular with uniform pattern of drilled holes as shown in Figure 5.20. Tubesheets of
surface condensers are rectangular shape. Tubesheets are connected to the shell and the channels either by
welds (integral) or with bolts (gasketed joints) or with a combination thereof in six possible types:
1. Both shellside and tubeside are integral with tubesheet (Figure 11.2a)
2. Shellside integral and gasketed on tubeside, tubesheet extended as a flange (Figure 11.2b)
3. Shellside integral and tubeside gasketed construction (Figure 11.2c)
4. Both shellside and tubeside gasketed construction (Figure 11.2d)
5. Tubesheet gasketed on shellside and integral with channel, extended as a flange (Figure 11.2e)
6. Shellside gasketed and tubeside integral construction (Figure 11.2f)
FIGURE 5.18 Wavy bar baffle design. (Courtesy of Peerless Mfg. Co. of Dallas, TX, Makers of Alco and
Bos-Hatten brands of heat exchangers.)
(a) Drilled-
(conventional design)
(b) Drilled (with flow holes)-
(Westinghouse design)
(c) Broached trefoil-
(Babcock Wilcox design)
(d) Broached quatrefoil
(concave contact lands)-
(Westinghouse design)
(e) Egg crate (lattice bars)-
(combustion engineering design)
FIGURE 5.19 Types of baffle plates for a steam generator. (a) Drilled, (b), drilled (with flow holes), (c) broached
trefoil, (d) broached quatrefoil (concave contact lands), and (e) egg crate (lattice bars).

5.5.1 Clad and Faced Tubesheets
As per TEMA RB 7.8, the nominal clad thickness on tubeside face of tubesheet shall be 5/16 in.
(7.8 mm) when tubes are expanded and minimum clad thickness of 1/8 in. (3.2 mm) when tubes are
welded to tubesheet. As per C 7.8, the nominal clad thickness on tubeside face of tubesheet shall be
3/16 in. (4.8 mm) when tubes are expanded and a minimum clad thickness of 1/8 in. (3.2 mm) when
tubes are welded to tubesheet.
5.5.2 Tube-to-Tubesheet Attachment
Tubes are attached to the tubesheet by (1) rolling, (2) welding, (3) rolling and welding, (4) explosive
welding, and (5) brazing. Schematic sketches of tube to tubesheet attachment are given in Chapter 15.
Expansion of the tubes into the tubesheet is most widely used and is satisfactory for many services.
However, when stresses are higher, or where pressures are such that significant leakage could occur, or
where contamination between fluids is not permitted, the tubes are welded to the tubesheet. Explosion
welding can be used instead of conventional welding where there is incompatibility between tube and
tubesheet materials and for tube plugging under hazardous conditions.
5.5.3 Double Tubesheets
No known method of making tube to tubesheet joints can completely eliminate the possibility of
mixing of shellside and tubeside fluids due to leakage. When the possibility of intermixing of the
shellside and tubeside fluids cannot be tolerated, double tubesheet construction will offer positive
assurance against one fluid leaking into the other at a tube to tubesheet joint.
5.5.3.1 Types of Double Tubesheet Designs
Two designs of double tubesheets are available: (1) the conventional double tubesheet design, which con-
sists of two individual tubesheets at each end of the tubes, and (2) the integral double tubesheet design [21].
5.5.3.1.1 Conventional Double Tubesheet Design
In a conventional double tubesheet design, the tubesheets are installed with a small space between
them. The space is usually open to the atmosphere. Sometimes a thin strip is welded to avoid ingress
of dusts and dirt, or an expansion joint is welded with vent at the top and a drain at the bottom.
FIGURE 5.20 Drilled titanium tubesheet. (Courtesy of TITAN Metal Fabricators Inc, Camarillo, CA.)

These patterns are shown schematically in Figure 5.21 and double tubesheet heat exchangers are
shown in Figure 5.22 through 5.24. While selecting material for double tubesheet design, the outer
should be compatible with the tubeside fluid and the inner should be compatible with the shellside
fluid. The most important consideration is the differential radial expansion of the two s, which will
stress the tubes. The double tubesheet can be installed only in the U-tube, fixed tubesheet, and
floating head, outside packed stuffing box exchangers. It is not feasible to use the double tubesheet
Tubesheets
(a)
Tubesheets
(b)
Vent above, drain below
Bellows
Tubesheets
(c)
FIGURE 5.21 Double tubesheet shell and tube heat exchanger—schematic. (a) Removable tube bundle
with light gauge shroud between two tubesheets, (b) fixed tubesheets with light gauge shroud, and (c) fixed
tubesheet with bellows.
Outer tubesheet
Inner tubesheet
Leak path
(a) (b)
FIGURE 5.22 Double tubesheet shell and tube heat exchanger. (a) Schematic and (b) heat exchanger.
(Courtesy of Allegheny Bradford Corporation, Bradford, PA.)

in heat exchanger types such as [6] (1) floating head, pull-through bundle, (2) floating head with
split backing ring, and (3) floating head, outside packed lantern ring exchangers. An expression for
the space between the s pairs, lg, which is widely used in the industry, is a special case of the more
complex analysis of Urgami et al. [22]. The expression is given by [21]

l
E d
S
g
t
t
1.5
=
δ

(5.2)
where δ is the free differential in-plane movement in inches (mm) given by

δ α α= − − −


0.5 ( ) ( )ambD T T T Totl h h amb c c

(5.3)
and where
d is the tube outer diameter, inches (mm)
Et is Young’s modulus for the tube, psi (Pa)
Dotl is the tube outer limit, inches (mm)
Tamb the ambient (assembly) temperature, °F (°C)
Tc the temperature of the colder tubesheet, °F (°C)
Th the temperature of the hotter tubesheet, °F (°C)
αc the coefficient of thermal expansion of the colder tubesheet between the assembly temperature
and temperature Tc, in./(in. °F) [mm/(mm °C)]
αh the coefficient of thermal expansion of the hotter tubesheet between the assembly temperature
and temperature Th, in./(in. °F) [mm/(mm °C)]
St the allowable stress in the tubes, psi (Pa)
FIGURE 5.23 Double tubesheet shell and tube heat exchanger. (Courtesy of GEA Heat Exchangers Ltd,
Brazil/GEA do Brasil Intercambiadores Ltd, Brazil.)
FIGURE 5.24 Double tubesheet shell and tube heat exchanger with real-time leak indicator (A). (Courtesy
of Alstrom Corporation, Bronx, NY.)

The provision of a double tubesheet has been mandatory for UK power-station condensers in
past years to eliminate any possibility of cooling water entering the steam space of the condenser
[23]. The tubesheet interspace is drained to a low-level vessel, which is maintained at the condenser
absolute pressure by means of a connection to the air pump suction line.
5.5.3.1.2 Integral Double Tubesheets
The patented integral double tubesheet design consists of a single tubesheet made from a single
plate or forging, drilled to the desired tube layout pattern. Then the annular grooves are machined
into the tube holes about midway between the faces to interconnect the adjacent tubes. This con-
struction in effect minimizes differential expansion problems, but it is expensive and not effective
like conventional double tubesheets to avoid fluid mixing [24].
5.5.4 Demerits of Double Tubesheets
If at all practical, double tubesheets should be avoided. However, some conditions dictate their use
along with the problems such as [24] the following:
1. Wasted tube surface.
2. Increased fabrication cost due to additional drilling and rolling requiring special equipment.
3. Differential radial expansion. This limits the length of the gap between the tubesheets to
prevent overstressing the tubes in bending or shear. Very short gaps can result in outer
tubes being sheared off at the face.
4. Differential longitudinal expansion. (This is a problem if the tubesheets are restrained
across the gap and increases as the gap increases.)
5. All conditions of start-up, shutdown, and steam out (in the case of condenser) must be
considered since they will generally be more severe on the double tubesheet section than
in the operating condition.
5.6 TUBE BUNDLE
A tube bundle is an assembly of tubes, baffles, tubesheets, spacers and tie-rods, and longitudinal
baffles, if any. Spacers and tie-rods are required for maintaining the space between baffles. Refer to
TEMA for details on the number of spacers and tie-rods. A straight tube bundle and a U-tube bindle
are shown in Figure 5.25.
5.6.1 Bundle Weight
The maximum bundle weight that can conveniently be pulled should be specified and should allow for
the buildup of fouling and scaling deposits. Offshore applications are particularly sensitive to weight.
5.6.2 Spacers, Tie-Rods, and Sealing Devices
The tube bundle is held together and the baffles are located in their correct positions by a number of
tie-rods and spacers. The tie-rods are screwed into the stationary tubesheet and extend the length of the
bundle up to the last baffle, where they are secured by locknuts (refer to Figure 5.25a). Between baffles,
tie-rods have spacers fitted over them. Tie-rods and spacers may also be used as a sealing device to
block bypass paths due to pass partition lanes or the clearance between the shell and the tube bundle.
A baffle cage assembly showing the tie-rods and spacers is shown schematically in Figure 5.26.
5.6.3 Outer Tube Limit
The outer tube limit (OTL) is the diameter of the largest circle, drawn around the tubesheet center,
beyond which no tube may encroach. OTL is shown schematically in Figure 5.27.

(a) (b)
FIGURE 5.25 Shell and tube heat exchanger tube bundle assembly. (a) Straight tube bundle (Courtesy of
Vermeer Eemhaven B.V., Rotterdam, the Netherlands) and (b) U-tube bundle. (Courtesy of Holtec International,
Marlton, NJ.)
Tie-rod
Spacer
Baffle Tubesheet
FIGURE 5.26 Baffle cage assembly.
Impingement plate Outer tube limit (OTL)
Tube bundle to
shell clearance
Shell OD
Tube pitch
Shell ID
FIGURE 5.27 Definition of OTL.

5.7 SHELLS
Heat exchanger shells are manufactured in a large range of standard sizes, materials, and thickness.
Smaller sizes are usually fabricated from standard size pipes. Larger sizes are fabricated from plate
by rolling. The cost of the shell is much more than the cost of the tubes; hence, a designer tries to
accommodate the required heat transfer surface in one shell. It is found that a more economical heat
exchanger can usually be designed by using a small diameter shell and the maximum shell length
permitted by such practical factors as plant layout, installation, servicing, etc. [6]. Up to six shorter
shells in series is common, and this arrangement results in countercurrent flow close to performance
as if one long single shell design was used. Nominal shell diameter and shell thickness are furnished
in TEMA Tables R-3.13 and CB-3.13 [2]. Roundness and consistent shell inner diameter are neces-
sary to minimize the space between the baffle edge and the shell as excessive space allows fluid
bypass and reduced performance.
5.8 PASS ARRANGEMENT
5.8.1 Tubeside Passes
The simplest flow pattern through the tubes is for the fluid to enter at one end and exit at the
other. This is a single-pass tube arrangement. To improve the heat transfer rate, higher veloci-
ties are preferred. This is achieved by increasing the number of tubeside passes. The improve-
ments achievable with multipass heat exchangers are sufficiently large, and hence they have
become common in industry than the counterflow designs. Tubeside multiple passes are nor-
mally designed to provide roughly equal number of tubes in each pass to ensure an even fluid
velocity and pressure drop throughout the bundle. In a two-tube-pass arrangement, the fluid
flows through only half of the total tubes, so that the Reynolds number is high. Increasing the
Reynolds number results in increased turbulence and Nusselt number and finally increase in
overall heat transfer coefficient.
5.8.1.1 Number of Tube Passes
The number of tubeside passes generally ranges from one to eight. The standard design has one,
two, or four tube passes. The practical upper limit is 16. Partitions built into heads known as par-
tition plates or pass ribs control tubeside passes. This is shown schematically in Figure 5.28. The
pass partitions may be straight or wavy rib design. The maximum number of tubeside passes is
limited by workers’ abilities to fit the pass partitions into the available space and the bolting and
flange design to avoid interpass leakages on the tubeside. In multipass designs, an even number
of passes is generally used; odd numbers of passes are uncommon and may result in mechanical
and thermal problems in fabrication and operation. The number of tube passes depends upon the
available pressure drop, since higher velocity in the tube results in higher heat transfer coefficient,
at the cost of increased pressure drop. Larowski et al. [9] suggest the following guidelines for
tubeside passes:
1. Two-phase flow on the tubeside, whether condensing or boiling, is best kept in a single
straight tube run or in a U-tube.
2. If the shellside heat transfer coefficient is significantly lower than that on the tubeside, it is
not advisable to increase the film coefficient on the tubeside at the cost of higher tubeside
pressure drop, since this situation will lead to a marginal improvement in overall heat
transfer coefficient.

A–A
A–A
A–AA–A
A–A B–B
B–B
6–Pass
10–Pass
2–Pass
8–Pass
4–Pass
B–B
(a)
B–B
B–B
1
2 3 6 7
2
2 2
3
3 3
6 7 2 3 6 7
102 3 6
2 3 6 2 3 6
7 10
4 5 8
1
1
2
1
2
1 1
4
4 4
5 8 1 4 5 8
91 4 5
1 4 5 1 4 5
8 9
A–A A–A
A–A
A–A B–B
A–A
A–A
B–B
B–B
B–B
B–B
B–B
4–Pass
6–Pass
8–Pass
6–Pass
8–Pass
10–Pass
1
1
1 1
3
4
7
8
6
5
2
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
1
1
1 1
1 2
3
6
2
3
6
4
5
1
4
5
5
6 7 8 9
10
4 3 2 5
6 7 8 9
10
4 3 2
23
4
2
2
4
4 5
6 6
54
3 2
3
3
3 2
5
6
8
4
7
(b)
FIGURE 5.28 Typical tubeside partitions for multipass arrangement. (a) U-tube and (b) straight tubes. Note:
A–A: Front view and B–B: Rear view.

There are some limitations on how the different types of heat exchangers can be partitioned to pro-
vide various numbers of passes. They are summarized here.
1. Fixed tubesheet exchanger—any practical number of passes, odd or even. For multipass
arrangements, partitions are built into both front and rear heads.
2. U-tube exchanger—minimum two passes; any practical even number of tube passes can be
obtained by building partition plates in the front head.
3. Floating head exchangers:
a. With pull-through floating head (T head) type and split backing ring exchanger (S head),
any practical even number of passes is possible. For single-pass operation, however, a
packed joint must be installed on the floating head.
b. With outside packed floating head type (P head), the number of passes is limited to one
or two.
c. With externally sealed floating (W head), no practical tube pass limitation.
4. Two-phase flow on the tubeside, whether condensing or boiling, is best kept within a
single-pass or in U-tubes to avoid uneven distribution and hence uneven heat transfer.
Figures 5.29 through 5.31 shows tube bundle assemblies with multipasses on the tubeside.
5.8.1.2 End Channel and Channel Cover
Tubeside enclosures are known as end channels or bonnets. They are typically fabricated or
cast. They are attached to the tubesheet the by bolting with a gasket between the two metal
surfaces. Cast heads are typically used up to 250 mm (14 in.) and are made from cast iron, steel,
bronze, or stainless steel. They typically have pipe thread connection. Fabricated heads can
be made in a wide variety of configurations. They can have metal cover that allows servicing
the tubes without disturbing the shell or tube piping. Heads can have axially or tangentially
oriented nozzles, which are typically ANSI flanges. Flanged nozzles or threaded bonnets are
used in smaller exchangers.
Channel covers: These are round plates that tend to be bolted to the channel flanges. Figure 5.32
shows heat exchanger with bonnet and channel cover.
(a) (b)
FIGURE 5.29 Shell and tube heat exchanger tube bundle assemblies. (a) Four-pass arrangement and (b)
eight-pass arrangement. (Courtesy of Allegheny Bradford Corporation, Bradford, PA.)

FIGURE 5.30 Multipass titanium tube bundle assemblies. (Courtesy of TITAN Metal Fabricators Inc,
Camarillo, CA.)
FIGURE 5.31 Eight-pass shell and tube heat exchanger tube bundle showing a few top rows of tubes not
incorporated to avoid erosion due to high impingement velocity. (Courtesy of Riggins Company, Hampton, VA.)
Shellside
Mat. SA 240-304 L
Pressure: 25 Bar
Temp: 120°C
Thk: 19 mm
Tubeside
Mat. SB 265 Gr 2
Pressure: 19 Bar
Temp: 120°C
Thk: 19 mm
FIGURE 5.32 U-tube shell and tube heat exchangers showing bonnet and channel cover plate. (Courtesy of
Brembana Costruzioni Industriali S.p.A., Milan, Italy.)

Pass divider or ribs: This is required in exchanger with two or more tubeside passes. The divider
is required in both bonnets and channels (Figures 5.33 and 5.34). Front and rear head pass ribs and
gaskets are matched. Pass ribs in cast heads are integrally cast and then machined to sizes; in fab-
ricated heads, they are welded in place. On the tubesheet, pass rib(s) requires either removing tubes
to allow a straight pass rib or machining the pass rib with curves around the tubes, which is costlier
to manufacture. Where a full bundle tube count is required to satisfy the thermal requirements, the
pass rib approach may lead to consider the next larger shell diameter.
5.8.2 Shellside Passes
For exchangers requiring high effectiveness, multipassing is the only alternative. Shellside passes could
be made by the use of longitudinal baffles. However, multipassing on the shell with longitudinal baffles
will reduce the flow area per pass compared to a single pass on the shellside. This drawback is overcome
by shells in series (Figures 5.35), which is also equivalent to multipassing on the shellside. For the case of
the overall direction of two fluids in counterflow, as the number of shellside passes is increased to infinity
Front head
Rear head
(a) (b) (c)
FIGURE 5.33 Four-pass partitions in front channel. (a) Pass partition plate is vertical, (b) pass partition plate
is inclined, and (c) horizontal and rear channel.
Pass partition plates
Nozzles Bolted flange
(a) (b)
FIGURE 5.34 Six-pass partitions in (a) front channel and (b) rear channel. (Courtesy of Festival City
Fabricators, div. of CSTI, Stratford, Ontario, Canada.)

(practically above four), its effectiveness approaches that of a pure counterflow exchanger. In heat recov-
ery trains and some other applications, up to six shells in series are commonly used.
5.8.2.1 Expansion Joint
Since the shellside fluid is at a different temperature than the tubeside fluid, there will be a cor-
responding difference in the expansion of shell and tube. If the temperature difference is high, the
differential thermal expansion will be excessive, and hence the thermal stresses induced in the shell
and the tube bundle will be high. This is particularly true for fixed tubesheet exchangers. In fixed
tubesheet exchangers, the differential thermal expansion problem is overcome by incorporating an
expansion joint into the shell. A heat exchanger with an expansion joint is shown in Figure 5.36.
Alternatively, an expansion bellow fitted on one end of the tube bundle as shown in Figure 5.37 can
be devised to overcome the thermal expansion problem [5]. For U-tube exchangers and floating
head exchangers, this is taken care of by the inherent design. Types of expansion joints, selection
procedure, and design aspects are discussed in Chapter 11.
5.8.2.2 Drains and Vents
All exchangers need to be drained and vented; therefore, care should be taken to properly locate and
size drains and vents. Additional openings may be required for instruments such as pressure gauges
and thermocouples.
5.8.2.3 Nozzles and Impingement Protection
Nozzles are used to convey fluids into and out of the exchanger. These nozzles are pipes of
constant cross section welded to the shell and the channels. The nozzles must be sized with the
understanding that the tube bundle will partially block the opening. Whenever a high-velocity
fluid is entering the shell, some type of impingement protection is required to avoid tube ero-
sion and vibration. As per TEMA standard, impingement protection is mandatory if the inlet
fluid is a gas with abrasive particles and in heat exchanger that receives liquid–vapor mixtures
or vapor with entrained liquid where the erosive effects are intense. For single-phase fluid,
(a) (b)
FIGURE 5.35 (a and b) Stack of two shells in series/shell and tube heat exchangers stack. (Photo a: Courtesy
of Allegheny Bradford Corporation, Bradford, PA and photo b: Courtesy of Brembana Costruzioni Industriali
S.p.A., Milan, Italy.)

Shell
inlet
Shell
outlet
Tube
outlet
Tube
inlet
(a)
Nozzles Shell Expansion joint
Vent/drainRear channelSupportsFront channel
(b)
FIGURE 5.36 (a) Cross-sectional view of a fixed tubesheet shell and tube heat exchanger with an expan-
sion joint (schematic). (b) Fixed tubesheet shell and tube heat exchanger with an expansion joint. (Courtesy of
Festival City Fabricators, div. of CSTI, Stratford, Ontario, Canada.)
Tubesheet
Tubeside bonnet
Bellows
Shellside exit nozzle
FIGURE 5.37 Shell and tube heat exchanger with an expansion bellow on one end of the tube bundle to
overcome thermal expansion problem. (Adapted from Bell, K.J. and Mueller, A.C. Wolverine Heat Transfer
Data Book II, Wolverine Division of UOP Inc., Decatur, AL, 1984.)

TEMA standards define when the installation of impingement protection is required, depend-
ing on the kinetic energy of the fluid entering the shell. For liquids with abrasive particles,
impingement protection is required if the inlet mass velocity ρV2 exceeds 744 kg/m2, and for
clean single-phase fluids, impingement protection is required if the inlet mass velocity ρV2
exceeds 2,230 kg/m2. Some forms of impingement protection include (1) impingement plate
(Figure 5.38a), (2) impingement rods (Figure 5.38b), and (3) annular distributors. Criteria for
the requirement of the impingement protection are covered in Chapter 12.
5.8.2.3.1 Minimum Nozzle Size
Gollin [25] presents a methodology for determining the minimum inside diameter of a nozzle for
various types of fluid entering or leaving the unit. The actual size of nozzle used will depend on the
pressure, material, corrosion allowance, and pipe schedule.
The minimum inside diameter, dmin, is calculated from

d
M
min
.
=
× ×
2
6
4
3 54 10 ∆pvρ

(5.4)
where
M is the mass flow rate of fluid through nozzle (lb/h)
ρ the density of fluid (lb/ft3)
Δpv the velocity head loss through the nozzle (psi)
Inlet nozzle Inlet nozzle
Impingement
protection rods
Impingement plate
(a) (b)
Impingement plate
Tubesheet
First
baffle(c) (d)
FIGURE 5.38 Impingement protection arrangement. (a) Rod arrangement, (b) plate arrangement, (c) and (d)
plate view in the inlet baffle zone.

5.9 FLUID PROPERTIES AND ALLOCATION
To determine which fluid should be routed through the shellside and which fluid on the tubeside,
consider the following factors. These factors are discussed in detail in Refs. [5,26,27].
Corrosion: Fewer corrosion-resistant alloys or clad components are needed if the corrosive
fluid is placed on the tubeside.
Fouling: This can be minimized by placing the fouling fluid in the tubes to allow better veloc-
ity control; increased velocities tend to reduce fouling.
Cleanability: The shellside is difficult to clean; chemical cleaning is usually not effective on
the shellside because of bypassing and requires the cleaner fluid. Straight tubes can be
physically cleaned without removing the tube bundle; chemical cleaning can usually be
done better on the tubeside.
Temperature: For high-temperature services requiring expensive alloy materials, fewer alloy
components are needed when the hot fluid is placed on the tubeside.
Pressure: Placing a HP fluid in the tubes will require fewer costly HP components and the
shell thickness will be less.
Pressure drop: If the pressure drop of one fluid is critical and must be accurately predicted,
then that fluid should generally be placed on the tubeside.
Viscosity: Higher heat transfer rates are generally obtained by placing a viscous fluid on the
shellside. The critical Reynolds number for turbulent flow in the shell is about 200; hence,
when the flow in the tubes is laminar, it may be turbulent if the same fluid is placed on
the shellside. However, if the flow is still laminar when in the shell, it is better to place the
viscous fluid only on the tubeside since it is somewhat easier to predict both heat transfer
and flow distribution [27].
Toxic and lethal fluids: Generally, the toxic fluid should be placed on the tubeside, using a
double tubesheet to minimize the possibility of leakage. Construction code requirements
for lethal service must be followed.
Flow rate: Placing the fluid with the lower flow rate on the shellside usually results in a more
economical design and a design safe from flow-induced vibration. Turbulence exists on the
shellside at much lower velocities than on the tubeside.
5.10 CLASSIFICATION OF SHELL AND TUBE HEAT EXCHANGERS
There are four basic considerations in choosing a mechanical arrangement that provides for efficient
heat transfer between the two fluids while taking care of such practical matters as preventing leak-
age from one into the other [6]:
1. Consideration for differential thermal expansion of tubes and shell
2. Means of directing fluid through the tubes
3. Means of controlling fluid flow through the shell
4. Consideration for ease of maintenance and servicing
Heat exchangers have been developed with different approaches to these four fundamental design
factors. Three principal types of heat exchangers—(1) fixed tubesheet exchangers, (2) U-tube
exchangers, and (3) floating head exchangers—satisfy these design requirements.
5.11 TEMA SYSTEM FOR DESCRIBING HEAT EXCHANGER TYPES
Major components of a shell and tube heat exchanger are the front head, shell section, and rear
head. Each of these components is available in a number of standard designs. In TEMA stan-
dards, they are identified by an alphabetic character. A heat exchanger unit is designated using

the designations of front head, shell, and rear head. It consists of three alphabetic characters, such
as AES, AKT, AJW, BEM, AEP, and CFU. Seven major types of shells, five types of front heads,
and eight types of rear heads known as heat exchanger nomenclature as per TEMA are shown in
Figure 5.39. In addition to these types, special types of shells and heads are also available depend-
ing upon the applications and customer needs. Figure 5.40a through f illustrates various types of
heat exchangers.
Front End
Stationary Head Types
A
B
C
N
D
E
F
G
H
J
K
X
L
M
N
P
S
T
W
U
Shell Types
Rear End
Head Types
Fixed tubesheet
like “A” stationary head
Fixed tubesheet
like “B” stationary head
Fixed tubesheet
like “N” stationary head
Outside packed floating head
Floating head
with backing device
Pull through floating head
U-tube bundle
Externally sealed
floating tubesheet
One pass shell
Two pass shell
with longitudinal baffle
Split flow
Double split flow
Divided flow
Kettle type reboiler
Cross flow
Channel
and removable cover
Bonnet (integral cover)
Channel integral with tube
sheet and removable cover
Channel integral with tube
sheet and removable cover
Special high pressure closure
Removable
tube
bundle
only
FIGURE 5.39 Nomenclature for heat exchanger components. (© Standards of Tubular Exchanger
Manufacturers Association, Inc., 9th edn., 2007.)

32 2 3 6 32 8 7 37 27 28 14 12 34 2
5
36333712345
(a)
(b)
36 4 3 34 34 12 8 30 28 27 7 32
33353534121065341
9315
36 34 5 3 10 8 7 28 12 34 27 2423 2426 23 15 1 36
4353412343535
36 4 3 5 34 31 12 34 29 27 28 8 7 32 15 23 24 25 22 36
212019123435353310635341
12346134
(c)
(d)
FIGURE 5.40 Heat exchanger types as per TEMA designation. (a) Fixed tubesheet heat exchanger, (b) U-tube
heat exchanger, (c) divided flow—externally sealed floating tubesheet heat exchanger, (d) floating head—outside
packed floating head heat exchanger.
(continued)

5.11.1 Fixed Tubesheet Exchangers
This is the most popular type of shell and tube heat exchanger. These units are constructed with the
tubesheets integral with the shell. The fixed tubesheet heat exchanger uses straight tubes secured
at both ends into tubesheets, which are firmly welded to the shell. Hence, gasketed joints are mini-
mized in this type, and thereby least maintenance is required. They may be used with A-, B-, or
N-type front head and L-, M-, or N-type rear head. A BEM-type fixed tubesheet heat exchanger is
shown in Figure 5.40a. Fixed tubesheet heat exchangers are used where [28]
1. It is desired to minimize the number of joints
2. Temperature conditions do not represent a problem for thermal stress
3. The shellside fluid is clean and tube bundle removal is not required
4. High degree of protection against contamination of streams
5. Double tubesheet is possible
6. Mechanical tubeside cleaning is possible
36 4 3 34 5 31
8 34 12 39
9
38361715
16
39341235728
(f)
2735123410633451
(e)
36 4 3 34 5 31 6 34 12 29 7 8 27 28 18 36 32
36
9
15
16
33171311341235351033451
FIGURE 5.40 (continued) Heat exchanger types as per TEMA designation. (e) floating head heat exchanger
with a backing device, and (f) Kettle reboiler—pull through floating head. Nomenclature of heat exchanger com-
ponents: (1) Stationary head—channel; (2) stationary head—bonnet; (3) stationary head flange—channel or bon-
net; (4) channel cover; (5) stationary head nozzle; (6) stationary; (7) tubes; (8) shell; (9) shell cover; (10) shell
flange—stationary head end; (11) shell flange—rear head end; (12) shell nozzle; (13) shell cover flange; (14) expan-
sion joint; (15) floating; (16) floating head cover; (17) floating head cover flange; (18) floating head backing device;
(19) split shear ring; (20) slip-on backing flange; (21) floating head cover—external; (22) floating skirt; (23) pack-
ing box; (24) packing; (25) packing gland; (26) lantern ring; (27) tie-rods and spacers; (28) transverse baffles or
support plates; (29) impingement plate; (30) longitudinal baffle; (31) pass partition; (32) vent connection; (33) drain
connection; (34) instrument connection; (35) support saddle; (36) lifting lug; (37) support bracket; (38) weir; and
(39) liquid level connection. (a) BEM, (b) CFU, (c) AJW, (d) AEP, (e) AES, and (f) AKT. (© Standards of Tubular
Exchanger Manufacturers Association, Inc., 9th edn., 2007.)

Provision is to be made to accommodate the differential thermal expansion of the shell and the
tubes when the thermal expansion is excessive. Fixed tubesheet exchangers can be designed
with removable channel covers, “bonnet”-type channels, integral tubesheets on both sides, and
tubesheets extended as shell flanges. They can be designed as counterflow one-to-one exchangers
(i.e., single pass on the tubeside and on the shellside) or with multipasses on the tubeside. Where
three or five passes have been specified for the tubeside, the inlet and outlet connections will be on
opposite sides. For fixed tubesheet exchangers, a temperature analysis must be made considering
all phases of operation (i.e., start-up, normal, upset, abnormal) to determine if thermal stress is a
problem and how to relieve it [28].
Figure 5.41 shows important dimensions of a fixed tubesheet heat exchanger.
5.11.2 U-Tube Exchangers
In this type of construction, tube bundle and individual tubes are free to expand and the tube bundle
is removable. A U-tube exchanger, CFU type, is shown in Figure 5.40b. U-tube exchangers can be
used for the following services [28]:
1. Clean fluid on the tubeside
2. Extreme HP on one side
3. Temperature conditions requiring thermal relief by expansion
4. For H2 service in extreme pressures, utilizing an all-welded construction with a nonremov-
able bundle
5. To allow the shell inlet nozzle to be located beyond the bundle
6. High degree of protection against contamination of streams
7. Double tubesheet is possible
5.11.2.1 Shortcomings of U-Tube Exchangers
Some of the drawbacks associated with U-tube exchangers are the following:
1. Mechanical cleaning from inside tubes is difficult; the chemical cleaning is possible.
2. Flow-induced vibration can also be a problem in the U-bend region for the tubes in the
outermost row because of long unsupported span.
3. Due to the bend radius, U-tube bundles have less heat transfer area compared to straight
tube bundles.
FIGURE 5.41 Important dimensions of a fixed tubesheet heat exchanger.

4. Interior tubes are difficult to replace, many times requiring the removal of outer layers or
plugging the leaking tube.
5. Erosion damage of U-bends is seen with high tubeside velocity.
6. Tubeside pressure drop will be on the higher side due to flow reversals in the U-end.
U-tube exchangers may be used with A-, B-, C-, N-, or D-type front head.
5.11.3 Floating Head Exchangers
The floating head exchanger consists of a stationary tubesheet and one floating tubesheet that is free
to accommodate the thermal expansion of the tube bundle. A floating head exchanger with TEMA
designations AES, AJW, and AEP are shown in Figure 5.40c through e. They may be used with A-, B-,
or C-type front head. There are four basic types of floating head exchangers. They are discussed next.
Floating head, outside packed floating head: The floating head (P head), outside packed stuff-
ing box heat exchanger uses the outer skirt of the floating tubesheet as part of the floating head. The
packed stuffing box seals the shellside fluid while allowing the floating head to move. The tube bundle
is removable. Maintenance is also very easy since all bolting is from outside only. With this floating
head, any leak (from either the shellside or the tubeside) at the gaskets is to the outside, and there is no
possibility of contamination of fluids. Since the bundle-to-shell clearance is large (about 1.5 in. or 38
mm), sealing strips are usually required. The earlier types are recommended for LP, low-temperature,
nonhazardous fluids.
Floating head, externally sealed floating tubesheet: In the floating head (W head), externally
sealed floating tubesheet, or outside packed lantern ring heat exchanger uses a lantern ring
around the floating tubesheet to seal the two fluids as the floating tubesheet moves back and
forth. The lantern ring is packed on both sides and is provided with vent or weep holes so that
leakage through either should be to the outside. Number of tube passes is limited to one or two.
The tube bundle is removable. This is the lowest cost of the floating head design and can be
used with type A, B, or C front head. This type is recommended for LP, low-temperature, and
nonhazardous fluids.
Floating head, pull-through head: In the floating head (T head), pull-through head exchanger,
a separate head or cover is bolted to the floating tubesheet within the shell. In this design, the tube
bundle can be removed without dismantling the joints at the floating end. Due to the floating head bon-
net flange and bolt circle, many tubes are omitted from the tube bundle at the tube bundle periphery,
and hence it accommodates the smallest number of tubes for a given shell diameter. This results in
the largest bundle-to-shell clearance or a significant bundle-to-shell bypass stream C. To overcome
the reduction in thermal performance, sealing devices are normally required, and the shell diameter
is somewhat increased to accommodate a required amount of surface area. An ideal application for
the T head design is as the kettle reboiler, in which there is ample space on the shellside and the flow
bypass stream C is of no concern.
Floating head with backing device: In the floating head (S head) with backing device, the floating
head cover (instead of being bolted directly to the floating tubesheet as in the pull-through type) is
bolted to a split backing ring. The shell cover over the floating head has a diameter larger than the
shell. As a result, the bundle to shell clearance is reasonable, and sealing strips are generally not
required. The tube bundle is not removable. Both ends of the heat exchanger must be disassembled
for cleaning and maintenance. This type is recommended for HP, nonhazardous process fluids.
5.11.3.1 Sliding Bar/Surface
All removable tube bundles whose mass exceeds 5,450 kg (12,000 lb) shall be provided with a con-
tinuous sliding surface to facilitate removal of tube bundle. If sliding bars are provided, they should
be welded to the transverse baffles and the support plate to form a continuous sliding surface. For
more details, refer to TEMA standard.

5.11.3.2 Kettle-Type Reboiler
Kettle-type reboiler is shown Figure 5.40f, and it is described later.
5.12 DIFFERENTIAL THERMAL EXPANSION
Means should be identified to accommodate the thermal expansion or contraction between the
shell and the tube bundle due to high mean metal temperature differentials between the shell
and the tube bundle. This is particularly true for fixed tubesheet exchangers. Differential thermal
expansion is overcome by the following means in the shell and tube heat exchangers:
U-tube design: The U-bend design allows each tube to expand and contract independently.
Fixed tubesheet design: For fixed tubesheet exchangers, when the difference between shell and
tube mean metal temperatures becomes large (greater than approximately 50°C for carbon steel),
the tubesheet thickness and tube end loads become excessive [29]. When a thermal expansion
problem exists, an expansion joint is incorporated in the shell. This permits the shell to expand
and contract.
Floating head designs: The floating head exchangers solve the expansion problem by having one
stationary tubesheet and one floating tubesheet that is free to accommodate the thermal expansion
of the tube bundle.
5.13 TEMA CLASSIFICATION OF HEAT EXCHANGERS
BASED ON SERVICE CONDITION
TEMA has set up mechanical standards for three classes of shell and tube heat exchangers: R, C, and
B. Class R heat exchangers specify design and fabrication of unfired shell and tube heat exchangers
for the generally severe requirements of petroleum and related processing applications, class C for the
generally moderate requirements of commercial and general process applications, and class for chemi-
cal process service. Salient features of TEMA standards are discussed in Chapter 11. Table 5.1 shows
some major differences between TEMA classes R, C, and B. For more details on TEMA classes, consult
Ref. [30].
5.14 SHELL AND TUBE HEAT EXCHANGER SELECTION
The fixed tubesheet exchanger is usually the cheapest. If, however, an expansion joint has to be
used, then a U-tube exchanger may prove cheaper. If the bundle has to be removable, a U-tube will
be the cheapest.
5.14.1 Shell Types
Seven types of shells are standardized by TEMA [2]. They are as follows:
1. E One-pass shell
2. F Two-pass shell with longitudinal baffle
3. G Split flow
4. H Double split flow
5. J Divided flow
6. K Kettle type reboiler
7. X Crossflow
Shellside flow for E, F, G, H, and J shells are shown schematically in Figure 5.42. A brief description
of each type is provided next.

TABLE 5.1
Major Differences between TEMA Classes R, C, and B
Item Description Classes Remarks
RCB 1.5 Corrosion allowances R,C + B 1/8 in. (3.2 mm), 1/16 in. (1.6 mm)
RCB 2.5 Tube pitch R,C,B 1.25; 1.25/1.2, 1.2 times tube OD
Minimum cleaning lanes 1/4 in., 3/16 in./1/4 in.
RCB 4.3 Baffle thickness R,C+B 1/8 in. (3.2 mm), 1/16 in. (1.6 mm)
RCB 4.3 Longitudinal baffle thickness R,C+B Min.1/4 in. (6.4 mm),
1/4 in. (6.4 mm) but not less than 1/8 in. (3.2 mm)
RCB4.71 Tie-rod size R,C+B 3/8 in. (9.5 mm), 1/4 in. (6.4 mm)
RCB 5.11 Floating head covers minimum
depth vs. tube area in one pass
R,C + B 1.3 times flow area through tubes of one pass
one time flow area through tubes of one pass
RCB 5.3 Lantern ring design C,R + B Design pressure limitation
RCB 6.2 Gasket material—metal jacketed
or solid metal
R,C + B 300 psi and above: int. float. head and all types of joints,
int. float. head
RCB 6.3 Minimum width of gaskets R + C,B Full face gasket
RCB 6.32 Gasket surface flatness R,C + B Tolerances
RCB 6.5 Pass partition gasket R,C + B Confined; confined or unconfined
RCB 7.13 Minimum tubesheet thickness R,C,B Function of tube diameter
RCB 7.44 Tube hole grooving C,R + B C only above 300 psi; two grooves 1/8 in. (3.2 mm)
wide and 1/64 in. (0.4 mm) deep
RCB 7.51 Length of tube-to-tubesheet joints C,R + B Length not less than 2 in. or two tube diameter or the
tubesheet thickness minus 1/8 in.; lesser of 2 in. or
tubesheet thickness minus 1/8 in.
RCB 7.6 Pass partition grooves R,C + B Pressure limit for C, B
RCB 7.8 Clad thickness of tubesheet
(expanded tubes)
C,R + B 3/16 in. (4.8 mm), 5/16 in. (7.8 mm)
RCB 7.8 Clad thickness tubesheet (welded
tubes)
C,R + B 1/8 in. (3.2 mm)
RCB 9.11 Channels and bonnets R,C + B Minimum thickness
RCB 11.1 End-flange minimum bolt size R,C,B 3
4
1
2, , in.5
8
M20, M12, M16
Note: Refer to [2] for details.
(a) (b) (c)
(d) (e)
FIGURE 5.42 TEMA shell types and shellside flow distribution pattern. (a) Single-pass shell, (b) two-pass
shell with longitudinal baffle, (c) split flow, (d) double split flow, and (e) crossflow.

5.14.1.1 TEMA E Shell
The E shell is the most common due to its cheapness, simplicity, and ease of manufacture. It has
one shell pass, with the shellside fluid entry and exit nozzles attached at the two opposite ends
of the shell. The tubeside may have a single pass or multiple passes. The tubes are supported by
transverse baffles. This shell is the most common for single-phase shell fluid applications. Multiple
passes on the tubeside reduce the exchanger effectiveness or LMTD correction factor F over a
single-pass arrangement. If F is too low, two E shells in series may be used to increase the effec-
tive temperature difference and thermal effectiveness. Possible flow arrangements are E1-1, E1-2,
E13, and E1-N (Figure 5.43).
5.14.1.2 TEMA F Shell
The F shell with two passes on the shellside is commonly used with two passes on the tubeside as shown
in Figure 5.44 so that the flow arrangement is countercurrent, resulting in F factor 1.0. This is achieved by
the use of an E shell having a longitudinal baffle on the shellside. The entry and exit nozzles are located at
the same end. The amount of heat transferred is more than that in an E shell but at the cost of an increased
pressure drop (compared to E shell, the shellside velocity is two times and pressure drop is eight times).
Counterflow
t2
t1
T1
(a) T2
t1
t2
Parallelflow
Parallel flow
Counter flow
E1–2 flow arrangement
E1–2 temperature distribution
Second pass
First pass
Mean metal temp
Mean metal temp
T1
T1
T1
1
L
T1
T2
t2
T2
T2
T2
t2
t2
t1
t1
t1
t2
(b) (c)
t1
FIGURE 5.43 TEMA E shell flow arrangement and temperature distribution. (a) E1-1—parallelflow and
counterflow arrangement; (b) E1-1—temperature distribution and (c) E1-2—flow arrangement and temperature
distribution.

Although ideally this is a desirable flow arrangement, it is rarely used because of many problems associ-
ated with the shellside longitudinal baffle. They include the following:
1. There will be a conduction heat transfer through the longitudinal baffle because of the
temperature gradient between the shellside passes.
2. If the longitudinal baffle is not continuously welded to the shell, or if seals are not provided
effectively between the longitudinal baffle and the shell, there will be fluid leakage from
the HP to LP side.
Both the factors will reduce the mean temperature difference and the exchanger effectiveness more
than the gain by achieving the pure counterflow arrangement. The welded baffle construction has a
drawback: It does not permit the withdrawal of the tube bundle for inspection or cleaning. Hence, if
one needs to increase the mean temperature difference, multiple shells in series are preferred over
the F shell.
5.14.1.3 TEMA G, H Shell
TEMA G and H shell designs are most suitable for phase change applications where the bypass
around the longitudinal plate and counterflow is less important than even flow distribution. In this
type of shell, the longitudinal plate offers better flow distribution for vapor streams and helps to flush
out noncondensables. They are frequently specified for use in horizontal thermosiphon reboilers and
total condensers.
5.14.1.4 TEMA G Shell or Split Flow Exchanger
In this exchanger, there is one central inlet and one central outlet nozzle with a longitudinal baffle.
The shell fluid enters at the center of the exchanger and divides into two streams. Hence, it is also
known as a split flow unit. Possible flow arrangements (G1-1, G1-2, and G1-4) are shown in Figure 5.45.
G shells are quite popular with heat exchanger designers for several reasons. One important reason
is their ability to produce “temperature correction factors” comparable to those in an F shell with
only a fraction of the shellside pressure loss (same as E shell) in the latter type [31].
5.14.1.5 TEMA H Shell or Double Split Flow Exchanger
This is similar to the G shell, but with two inlet nozzles and two outlet nozzles and two horizon-
tal baffles resulting in a double split flow unit. It is used when the available pressure drop is very
limited. Possible pass arrangements are H1-1 and H1-2 (Figure 5.46). The H shell approaches the
crossflow arrangement of the X shell, and it usually has low shellside pressure drop compared to E,
F, and G shells [4], i.e., compared to E shell, the shellside velocity is 1/2 times and pressure drop
is 1/8 times.
Section–AA
A
A
FIGURE 5.44 TEMA F shell.

5.14.1.6 TEMA J Shell or Divided Flow Exchanger
The divided flow J shell has two inlets and one outlet or one inlet and two outlet nozzles (i.e., a
single nozzle at the midpoint of shell and two nozzles near the tube ends). With a single inlet nozzle
at the middle, the shell fluid enters at the center of the exchanger and divides into two streams.
These streams flow in longitudinal directions along the exchanger length and exit from two nozzles,
one at each end of the exchanger. The possible pass arrangements are one shell pass, and one, two,
four, N (even) or infinite tube passes. J shell pass arrangements with temperature distribution are
shown in Figure 5.47 [32]. With a TEMA J shell, the shellside velocity will be one-half that of the
TEMA E shell and hence the pressure drop will be approximately one-eighth that of a comparable
E shell. Due to this reason, it is used for LP-drop applications like condensing in vacuum [4]. For a
condensing shell fluid, the J shell is used with two inlets for the gas phase and one central outlet for
the condensates and leftover gases.
5.14.1.7 TEMA K Shell or Kettle Type Reboiler
The K shell is used for partially vaporizing the shell fluid. It is used as a kettle reboiler in the
process industry and as a flooded chiller in the refrigeration industry. Usually, it consists of a hori-
zontal bundle of heated U tubes or floating head placed in an oversized shell. The tube bundle is
T1
t1 t2
T2
T1
t2
t1
T1
T2
(a) (b)
T1
T2
FIGURE 5.46 H shell flow arrangement. (a) H1-1 and (b) H1-2.
Shell
fluid
T1
T1 T1
t1
t2
t2
t1
LL (b)(a)
T2
T2 T2
T2
Longitudinal
baffle
Shell
fluid T1
Longitudinal
baffle
Tube
fluid
Tube pass 2
Tube pass 1
Tubes on
shell outlet side
Tubes on
shell inlet side
Tube
fluid
FIGURE 5.45 G shell flow arrangement and temperature distribution. (a) G1-1 and (b) G1-2.

free to move and it is removable. Its diameter is about 50%–70% of the shell diameter. The large
empty space above the tube bundle acts as a vapor-disengaging space. Kettle boiler heat exchanger
of TEMA-type AKT is shown in Figure 5.41f. The liquid to be vaporized enters at the bottom,
near the tubesheet, and covers the tube bundle; the vapor occupies the upper space in the shell,
and the dry vapor exits from the top nozzle(s), while a weir (the vertical unperforated baffle shown
in Figure 5.41f) helps to maintain the liquid level over the tube bundle. The bottom nozzle in this
space is used to drain the excess liquid. Kettle boiler heat exchanger is shown in Figure 5.48.
5.14.1.8 TEM X Shell
The X shell (Figure 5.49) is characterized by pure shellside crossflow. No transverse baffles are used
in the X shell; however, support plates are used to suppress the flow-induced vibrations. It has nozzles in
the middle as in the G shell. The shellside fluid is divided into many substreams, and each substream
flows over the tube bundle and leaves through the bottom nozzle. Flow maldistributions on the shell-
side can be a problem unless a proper provision has been made to feed the fluid uniformly at the inlet.
Uniform flow distribution can be achieved by a bathtub nozzle, multiple nozzles, or keeping a clear
lane along the length of the shell near the nozzle inlet [4]. The tubeside can be single pass, or two
passes, either parallel crossflow or counter-crossflow. For a given set of conditions, the X shell has the
lowest shellside pressure drop compared to all other shell types (except the K shell). Hence, it is used
for gas heating and cooling applications and for condensing under vacuum.
Shell
fluid
Tube
fluid T2 T2
T2
L L(a) (b) (c) L
T1
T1
T1
T1
T2
T2
T2
T2
T1
T1
t1
t1
t2 t2
t2
t2
t1
t1
t1
t1
t1
t2
t2
FIGURE 5.47 TEMA J shell flow arrangement and temperature distribution. (a) J1-1, (b) J1-2, and (c) J1-4.
(From Jaw, L., Trans. ASME, J. Heat Transfer, 56C, 408, 1964.)
Shellside
Temp: 124°C
Temp: 316°C
Thk: 20 mm
Thk: 26 mm
Tubeside
Mat. SA 516 70
Pressure: 28 bar
Pressure: 75 bar
Mat. SA 516 70
FIGURE 5.48 Kettle-type reboilers. (Courtesy of Brembana Costruzioni Industriali S.p.A., Milan, Italy.)

5.14.1.9 Comparison of Various TEMA Shells
In general, E- and F-type shells are suited to single-phase fluids because of the many different baffle
arrangements possible and the relatively long flow path [9]. When the shellside pressure drop is a limiting
factor, G and H shells can be used. The G and H shells are not used for shellside single-phase applications,
since there is no edge over the E or X shells. They are used as horizontal thermosiphon reboilers, condens-
ers, and in other phase-change applications. The longitudinal baffle serves to prevent flashing out of the
lighter components of the shell fluid, helps flushing out noncondensables, provides increased mixing, and
helps flow distribution [4]. Velocity head and pressure drop for various TEMA shells are given in Ref. [33].
5.14.2 Front and Rear Head Designs
Head designs can vary from plain standard castings to fabricated assemblies with many special
features. Two of the major considerations in the choice of heads are [6] (1) accessibility to the tubes
and (2) piping convenience. Where fouling conditions are encountered or where frequent access for
inspection is desired, a head or cover plate that can be easily removed is an obvious choice. In this
head, connections are located on the sides, not on the ends of removable heads. Typical open-end
heads used for this purpose are called channels. They are fabricated from cylindrical shells and
fitted with easily removable cover plates so that the tubes can be cleaned without disturbing piping.
5.14.2.1 Designations for Head Types
Front head: For the variable front head, the constants and their meanings are thus:
A Channel with removable cover
B Bonnet with integral cover
C Channel integral with the tubesheet and removable cover when the tube bundle is removable
N Channel integral with the tubesheet and having a removable cover but the tube bundle is
not removable
D Special HP closure
Rear head:
L Fixed tubesheet like “A” stationary head
M Fixed tubesheet like “B” stationary head
N Fixed tubesheet like “N” stationary head
P Outside packed floating head
S Floating head with backing device
T Pull-through floating head
U U-tube bundle
W Externally sealed floating tubesheet
(a) (b)
FIGURE 5.49 (a) Cross section of TEMA X shell—schematic and (b) tube heat exchanger.

Salient features of these heads are discussed and tabulated by Larowski et al. [9]. Few of the pos-
sible combinations of front and rear heads result in the following removable bundle exchanger:
1. BEU/AEU, 2. CEU, 3. BEW/AEW, 4. AEP/BEP, 5. AES/AET, 6. NEU, 7. NEN, 8. AEM/BEM/
AEL, etc.
5.14.3 TEMA Specification Sheet
TEMA specification sheet (both in metric and in FPS-English units) for shell and tube heat
exchanger is shown in Figure 5.50. It is used as a basic engineering document in the thermal design,
purchasing, and construction of shell and tube heat exchangers.
5.15 SHELLSIDE CLEARANCES
Even though one of the major functions of the plate baffle is to induce crossflow over the tube bun-
dle, this objective is achieved partially. Various clearances on the shellside partially bypass the fluid.
Bypassing is defined as a leakage flow where fluid from the crossflow stream, intended to flow through
the tube bundle, avoids flowing through it by passing through an alternative, low-resistance flow path
[34]. A major source of bypassing is the shellside clearances. Clearances are required for heat exchanger
fabrication. Fabrication clearances and tolerances have been established by the TEMA, and these have
become widely accepted around the world and are enforced through inspection during fabrication.
Three clearances are normally associated with a plate baffle exchanger. They are (1) tube-to-baffle hole,
(2) baffle to shell, and (3) bundle to shell. Additionally, in a multipass unit, the tube layout partitions
may create open passages for the bypass of the crossflow stream. Since bypassing reduces heat transfer
on the shellside, to achieve good shellside heat transfer, bypassing of the fluid must be reduced. These
clearances and their effect on the shellside performance are discussed in detail next.
5.15.1 Tube-to-Baffle-Hole Clearance
The holes in the baffles must be slightly larger than the tube outer diameter to ensure easy tube
insertion. The resultant clearance is referred to as the tube-to-baffle-hole clearance (Figure 5.51).
It should be kept at a minimum (1) to reduce the flow-induced vibration and (2) to minimize the
A leakage stream (various shellside bypass streams are discussed next). As per TEMA RCB-4.2,
where the maximum unsupported tube length is 36 in. (914.4 mm) or less, or for tubes larger than
1.25 in. (31.8 mm) outer diameter, the clearance is 1/32 in. (0.80 mm); where the unsupported
tube length exceeds 36 in. for tube outer diameter 1.25 in. or smaller, the clearance is 1/62 in.
(0.40 mm).
5.15.2 Shell-to-Baffle Clearance
The clearance between the shell inner diameter and baffle outer diameter is referred to as the baffle-
to-shell clearance. It should be kept to a minimum to minimize the E leakage stream. TEMA rec-
ommends that maximum clearance as per RCB-4.3 [2] varies from 0.125 in. (3.175 mm) for 6 in.
(152.4 mm) shell inner diameter to 0.315 in. (7.94 mm) for 60 in. (1524 mm) shell inner diameter.
5.15.3 Shell-to-Bundle Clearance
Since the tube bundle does not fill the shell, there is a shell-to-bundle clearance. This allows the so-
called bypass stream C flowing around the bundle. Sealing strips are used to block this space and
force the bypass stream to flow across the tubes. The use of sealing strips is recommended every five
to seven rows of tubes in the bypass stream direction.

FIGURE 5.50 (a) TEMA specification sheet for shell and tube heat exchanger—metric units.

FIGURE 5.50 (continued) (b) TEMA specification sheet for shell and tube heat exchanger—FPS system
units. (© Standards of Tubular Exchanger Manufacturers Association, Inc., 9th edn., 2007.)

5.15.4 Bypass Lanes
The lanes provided for the tubeside partition ribs are a source of bypass on the shellside. The pass
partition lanes are, however, placed perpendicular to the crossflow whenever possible, or the bypass
lanes are usually blocked by tie-rods, which act similar to the sealing strips. Hence, the effect of the
bypass lanes on thermal performance usually can be neglected.
5.16 DESIGN METHODOLOGY
5.16.1 Shellside Flow Pattern
5.16.1.1 Shell Fluid Bypassing and Leakage
In shell and tube exchangers with segmental plate baffles, the shellside flow is very complex due to
a substantial portion of the fluid bypassing the tube bundle through various shellside constructional
clearances defined earlier. Another contributing factor for bypassing is due to notches made in the
bottom portion of the baffles for draining purposes. Notches are usually not required for draining
because the necessary fabrication tolerances provide ample draining [4]. To achieve good shellside
heat transfer, bypassing of the fluid must be reduced.
5.16.1.2 Bypass Prevention and Sealing Devices
Sealing devices can be employed to minimize the bypassing of fluid around the bundle or through
pass partition lanes [34]. If tube bundle-to-shell bypass clearance becomes large, such as for pull-
through bundles, resulting in decreased heat transfer efficiency, the effectiveness can be restored by
fitting “sealing strips.” As a rule of thumb, sealing strips should be considered if the tube bundle-
to-shell diameter clearance exceeds approximately 2.25 in. (30 mm). Fixed tubesheet and U-tube
heat exchangers usually do not require sealing strips, but split ring and pull-through floating head
designs usually require sealing strips.
Types of sealing devices: Sealing devices are strips that prevent bypass around a bundle by “seal-
ing” or blocking the clearance area between the outermost tubes and the inside of the shell. Some
common types include [7] tie-rods, sealing devices, and tie-rods.
1. Tie-rods and spacers hold the baffles in place but can be located at the periphery of the
baffle to prevent bypassing.
2. Sealing strips. These are typically longitudinal strips of metal between the outside of the
bundle and the shell and fastened to the baffles (Figure 5.52); they force the bypass flow
back into the tube field. A typical flow pattern with sealing strips in an effective penetra-
tion area is shown in Figure 5.52.
Tube
Section: A–A
A
A
Orifice
FIGURE 5.51 Tube-to-baffle leakage stream.

Number of sealing strips pair in between two baffles: Bypassing of the shellside fluid
can be adequately controlled by providing one sealing device for every four tube rows
on the bundle periphery and by providing one sealing device for every two tube rows at
bypass lanes internal to the bundle such as pass partition lanes [1]. The use of sealing strips
to divert flow within heat exchangers was studied by Taylor et al. [35]. They examined
the variation of sealing strip shape (Figure 5.53), location, and gap size, i.e., the distance
between the sealing device and the nearest tube. According to their study, (1) rectangular-
shaped sealing strips are preferred, (2) sealing strips placed close together (3.6 rows apart)
will provide optimum heat transfer characteristics, and (3) most significant results were
obtained when the gap size = p − d.
3. Tie-rods with “winged” spacers. The wings are extended longitudinal strips attached to the
spacers.
Dummy tubes: Usually closed at one end, dummy tubes are used to prevent bypassing through lanes
parallel to the direction of fluid flow on the shellside (Figure 5.25a). They do not pass through the
tubesheet. In moderate to large exchangers, one dummy tube is as effective in promoting heat trans-
fer as 50 process tubes [7].
By pass stream
Shell ID
Penetration
area
Sealing
strip
(a)
Crossflowstream
Few tubes removed
for clarity
Clearance between
shell ID–OTL
(b)
Tie rod
and spacer
Baffle drain notch
Slide
Sealing
ﬂat
FIGURE 5.52 Sealing strips. (a) Typical flow pattern with sealing strips. (Adapted from Palen, J.W. and
Taborek, J., Chem. Eng., Symp. Ser., No. 92, Heat Transfer—Philadelphia, 65, 53, 1969.) (b) Shows attach-
ment of sealing strip, baffle drain notch, tie-rod, and slide plate attached to the tube bundle.
Tube
(a) (b) (c)
FIGURE 5.53 Forms of sealing strips. (a) Rectangular, (b) semicircular, and (c) triangular. (From Taylor,
C.E. and Currie, I.G., Trans. ASME J. Heat Transfer, 109, 569, 1987.)

5.16.1.3 Shellside Flow Pattern
An ideal tube bundle (the term introduced by Heat Transfer Research, Incorporated (HTRI), CA
refers to segmentally baffled circular bundles with no clearance between tubes and baffles, baffles
and shell, or outer tubes and the shell, so that all fluid must flow across the tube bundle [13]. In
a practical tube bundle, the total shellside flow distributes itself into a number of distinct partial
streams due to varying flow resistances through the shellside clearances. This stream distribution
pattern is now well established and is shown schematically in Figure 5.54. Figure 5.54a shows three
regions of flow over the tube bundle, Figure 5.54b shows regions of parallelflow, and Figure 5.54c
shows different streams flow through the tube bundle. This flow model was originally proposed
by Tinker [36] and later modified by Palen et al. [13] for a segmentally baffled exchanger. Various
streams in order of decreasing thermal effectiveness are discussed next.
A stream: This is a tube-to-baffle-hole leakage stream through the clearance between the tubes
and the tube holes in the baffles (Figure 5.54c). This stream is created by the pressure difference on
the sides of the baffle. As heat transfer coefficients are very high in the annular spaces, this stream
is considered fully effective.
B stream: This is a crossflow stream through tube bundle. This stream is considered fully effec-
tive for both heat transfer and pressure drop.
C stream: This is a bundle-to-shell bypass stream through the annular spaces between the tube
bundle and the shell. It flows between successive baffle windows. This stream is only partially effec-
tive for heat transfer as it contacts the tubes near the tube bundle periphery.
E stream: This is a shell-to-baffle leakage stream through the clearance between the edge of a
baffle and the shell. This stream is the least effective for heat transfer, particularly in laminar flow,
because it may not come in contact with any tubes.
F stream: This is a tube pass partition bypass stream through open passages created by tube lay-
out partition lanes (when placed in the direction of the main crossflow stream) in a multipass unit.
Crossflow(a) Window flow Endzone flow
Area of parallelflow
Baffle
(b)
(c)
E E
E
A
A
B
B
C C
B B
C
A
FIGURE 5.54 Shellside flow distribution. (a) Three regions of flow over the tube bundle, (b) regions of paral-
lel flow, and (c) shows different streams flow through the tube bundle.

This stream is less effective than the A stream because it comes into contact with less heat transfer
area per unit volume; however, it is slightly more effective than the C stream.
From the earlier discussion, the fluid in streams C, E, and F bypasses the tubes, which reduces
the effective heat transfer area. Stream C is the main bypass stream and will be particularly signifi-
cant in pull-through bundle exchangers, where the clearance between the shell and the bundle is of
necessity large. Stream C can be considerably reduced by using sealing strips.
5.16.1.4 Flow Fractions for Each Stream
Each of the streams has a certain flow fraction of the total flow such that the total pressure drop for each
stream is the same. Each stream undergoes different frictional processes and has different heat transfer
effectiveness as discussed earlier. The design of the plate baffle shell and tube exchanger should be
such that most of the flow (ideally about 80%) represents the crossflow B stream. However, this is rarely
achieved in practice. Narrow baffle spacing will result in higher pressure drop for the B stream and forces
more flow into the A, C, and E streams.
Based on extensive test data, Palen et al. [13] arrived at the flow fractions for various streams
both for laminar flow and for turbulent flow. Even for a good design, the crossflow stream represents
only 65% of the total flow in turbulent flow and 50% in laminar flow. Hence, the predicted perfor-
mance based on the conventional LMTD method will not be accurate in general. As a result, there
is no need to compute very accurate F factors for the various exchanger configurations [13]. If the
computed values of the B stream are lower than those indicated, the baffle geometry and various
clearances should be checked.
5.16.1.5 Shellside Performance
Many investigators have studied the shellside thermal performance. One of the earliest was
Tinker [36,37]. Perhaps the most widely accepted and recognized study is known as the Bell–
Delaware method [38]. The original method has been further refined by Bell [39] and presented
also in Ref. [40], and other modifications and improvements have been made by Taborek [15]. For
generic details on shell and tube heat exchangers, their classification, stream analysis and guidance
for thermal design refer to Mukurjee [41] and Hewitt et al. [42].
5.16.2 Sizing of Shell and Tube Heat Exchangers
The design of shell and tube heat exchanger involves the determination of the heat transfer coef-
ficient and pressure drop on both the tubeside and the shellside. A large number of methods [37,43–
45] are available for determining the shellside performance. Since the Bell–Delaware method
is considered the most suitable open-literature method for evaluating shellside performance, the
method is described here. Before discussing the design procedure, tips for thermal design, and heat
transfer coefficient and pressure drop are discussed, some guidelines for shellside design and points
to be raised while specifying a heat exchanger are listed, followed by preliminary sizing of a shell
and tube heat exchanger.
5.16.3 Guidelines for STHE Design
Tips for thermal design
1. Always specify counterflow operation for maximum performance.
2. The heat exchanger can be mounted vertically if required; however, this may require spe-
cial mounting brackets.

3. If the sizing procedure suggests a nonstandard shell length, use the next larger size or con-
sider using two shorter heat exchangers.
4. Consider using two or more heat exchangers when the heat duty is on the higher side or
space for locating the heat exchanger is limited, or temperature and flow parameters are
outside the recommended range for a single heat exchanger.
5.16.3.1 Heat Transfer Coefficient and Pressure Drop
5.16.3.1.1 Heat Transfer Coefficient
The tubeside heat transfer coefficient is a function of the Reynolds number, the Prandtl number, and
the tube diameter. The earlier-mentioned nondimensional numbers are based on the fundamental
parameters such as fluid physical properties (i.e., viscosity, thermal conductivity, and specific heat),
tube diameter, and mass velocity. For turbulent flow, the tubeside heat transfer coefficient varies to
the 0.8 power of tubeside mass velocity. Also the variation in liquid viscosity has a dramatic effect
on heat transfer coefficient.
The shellside heat transfer coefficient is dependent on shellside parameters like fluid velocity,
shell inside diameter, baffle cut, baffle spacing, tube hole clearance in the baffle plate, various
shellside clearances other than the desired fluid flow path, number of passes on shellside, shell
type, etc.
5.16.3.1.2 Pressure Drop
Fluid pressure drop is controlled by a wide variety of design variables and the process fluid
flow parameters. For the tubeside stream, the controlling variables are tube diameter, tube
length, tube geometry (straight or U-tubes), number of tube passes and number of shells in
series or parallel, and nozzle size. For turbulent flow, tubeside pressure drop is proportional to
the square of velocity. Consequently, there will be an optimum mass velocity above which it
will be wasteful to increase the velocity further. In addition to higher pumping costs, very high
velocities lead to erosion. However, the pressure-drop limitation usually becomes the control-
ling factor long before the erosive velocity limits are attained. The minimum recommended
liquid velocity inside tubes is 1.0 m/s, while the maximum is 2.5–3.0 m/s. Since pressure drop
depends on the total length of travel, as the number of tube passes increases, for a given num-
ber of tubes and a given tubeside flow rate, the pressure drop rises dramatically. Shellside fluid
pressure drop is influenced by equipment design variables such as tube diameter, tube pitch,
tube layout, shell diameter, baffle type, baffle cut, baffle spacing, number and size of shellside
nozzles, and the exchanger shell type.
5.16.4 Guidelines for Shellside Design
Recommended guidelines for shellside design include the following [1]:
1. Accept TEMA fabrication clearances and tolerances and enforce these standards during
fabrication.
2. For segmental baffles employ 20% battle cuts.
3. Employ NTIW design to eliminate the damage from flow-induced vibration.
4. Evaluate heat transfer in the clean condition and pressure drop in the maximum fouled
condition.
5. Employ sealing devices to minimize bypassing between the bundle and shell for pull-
through floating heat exchanger and through pass partition lanes.
6. Ratio of baffle spacing to shell diameter may be restricted to values between 0.2 and 1.0.
Baffle spacing much greater than the shell diameter must be carefully evaluated.
7. Avoid shell longitudinal baffles that are not welded to the shell; all other sealing methods
are inadequate.

5.16.4.1 Specify the Right Heat Exchanger
When specifying an exchanger for design, various factors to be considered or questions that should
be raised are listed by Gutterman [28]. A partial list includes the following:
1. Type of heat transfer, i.e., boiling, condensing, or single-phase heat transfer.
2. Since the heat exchanger has two pressure chambers, which chamber should receive the
cold fluid?
3. More viscous fluid shall be routed on the shellside to obtain better heat transfer.
4. It is customary to assign the higher pressure to the tubeside to minimize shell thickness.
5. Consider various potential and possible upset conditions in assigning the design pressure
and/or design temperature.
6. Pass arrangements on the shellside and tubeside to obtain maximum heat transfer?
7. Have you considered the tube size and the thickness?
8. What is the acceptable pressure drop on the tubeside and the shellside? Is the sum of the
pumping cost and the initial equipment cost minimized?
9. Have you considered the maximum allowable pressure drop to obtain the maximum heat
transfer?
10. Are the tubeside and shellside velocities high enough for good heat transfer and to mini-
mize fouling but well below the limits that can cause erosion–corrosion on the tubeside,
and impingement attack and flow-induced vibration on the shellside?
11. Have you considered the nozzle sizes and adequate shell escape area? Are the nozzle
orientations consistent with tube layout pattern?
12. Is the baffle arrangement designed to promote good flow distribution on the shellside and
hence good heat transfer, and to minimize fouling and flow-induced vibration?
13. Does the design provide for efficient expulsion of noncondensables that may degrade the
performance? (A prime example in this category is surface condensers.)
14. Is the service corrosive or dirty? If so, have you specified corrosion-resistant materials and
reasonable fouling factors?
15. Does the design minimize fouling?
16. Do you want to remove the bundle? If so, are adequate space and handling facilities available
for tube bundle removal?
17. Is leakage a factor to be considered? If so, did you specify (a) seal-welded tube joint, (b) rolled
joint, (c) strength welded joint? Is the tube wall thickness adequate for welding? Are you
specifying tube holes with grooves or without grooves?
18. What kind of tests do you specify to prove the tube-to-tubesheet joint integrity?
All of these and numerous other factors determine the type of exchanger to be specified.
5.16.5 Design Considerations for a Shell and Tube Heat Exchanger
The basic criterion that a given or designed heat exchanger should satisfy is that it should perform the given
heat duty within the allowable pressure drop. The design is also to satisfy additional criteria such as [46]
1. Withstand operating conditions, start-up, shutdown, and upset conditions that influence the
thermal and mechanical design
2. Maintenance and servicing
3. Multiple shell arrangement
4. Cost
5. Size limitations
In terms of the five factors just mentioned, multishell arrangement needs some comments on it.
Consider the advantages of a multishell arrangement to allow one unit to be taken out of service

for maintenance without severely upsetting the rest of the plant. For part load operations, multiple
shells will result into an economical operation. Shipping and handling may dictate restrictions on
the overall size or weight of the unit, resulting in multiple shells for an application.
5.16.5.1 Thermal Design Procedure
The overall design procedure of a shell and tube heat exchanger is quite lengthy, and hence it is
necessary to break down this procedure into distinct steps:
1. Approximate sizing of shell and tub heat exchanger
2. Evaluation of geometric parameters also known as auxiliary calculations
3. Correction factors for heat transfer and pressure drop
4. Shellside heat transfer coefficient and pressure drop
5. Tubeside heat transfer coefficient and pressure drop
6. Evaluation of the design, i.e., comparison of the results with the design specification
In this section, approximate sizing of the shell and tube exchanger by Bell’s method is discussed
first; then this is extended to size estimation, and subsequently the rating is carried out as per the
Bell–Delaware method. Finally, the rated unit is evaluated.
Bell’s method [46] for approximate sizing of a shell and tube heat exchanger: The approximate
design involves arriving at a tentative set of heat exchanger parameters, and if the design is accepted after
rating, then this becomes the final design. Various stages of approximate design include the following:
1. Compute overall heat transfer coefficient
2. Compute heat transfer rate required
3. Compute the heat transfer area required
4. Design the geometry
A flowchart for approximate sizing is given in Figure 5.55.
Start
Compute LMTD
correction factor
F
Compute
heat transfer
rate, q
Terminal temperatures
of shellside fluid and
tubeside fluid
Aspect ratio
L/Ds
assume eight initially
Shell
length
Shell
diameter
Approximate
area required
Compute overall
heat transfer
coefficient
Film
coefficients
Fouling
resistances
Thermal resistance
due to conduction
effect
Mass flow
rate
Specific
heat
Compute
LMTD
FIGURE 5.55 Flowchart for approximate sizing of STHE.

Estimation of heat load: The heat load is calculated in the general case from

q M c T T M c T T= − = −h p,h h,i h,o c p,c c,o c,i )( ) (

(5.5)
where
cp,h and cp,c are the specific heats of the hot and cold fluids
Th,i and Th,o are the inlet and outlet temperatures of the hot stream
Tc,i and Tc,o are the inlet and outlet temperatures of the cold stream
Estimation of log mean temperature difference: Determine the logarithmic mean temperature
difference for countercurrent flow using the temperatures as defined earlier:

LMTD h,i c,o h,o c,i
h,i c,o h,o c,i
=
− − −
− −[ ]
( ) ( )
ln ( ) / ( )
T T T T
T T T T

(5.6)
LMTD correction factor: Values of F can be found from the thermal relation charts given in
Chapter 2 for a variety of heat exchanger flow configurations. However, for estimation purposes, a rea-
sonable estimate may often be obtained without restoring to the charts.
1. For a single tube pass, purely countercurrent heat exchanger, F = 1.0.
2. For a single shell with any even number of tubeside passes, F should be between
0.8 and 1.0. (For other shell types refer to Chapter 2, Section 2.2.3.3).
Method to determine number of shells: Quickly check the limits:
2
2
T T T
T T T
h,o c,i c,o
c,o h,i h,o
≥ +
≤ +
hot fluid on the shell side
coold fluid on the shell side
If these limits are approached, it is necessary to use multiple 1 − 2N shells in series. There is a rapid
graphical technique for estimating a sufficient number of 1 − 2N shells in series. The procedure is
discussed here. The terminal temperatures of the two streams are plotted on the ordinates of an
arithmetic graph paper sheet as shown in Figure 5.56. The distance between the ordinates is arbi-
trary. Starting with the cold fluid outlet temperature, a horizontal line is laid off until it intercepts
the hot fluid line. From that point, a vertical line is drawn to the cold fluid temperature. The process
is repeated until a vertical line intercepts the cold fluid operating line at or below the cold fluid
inlet temperature. The number of horizontal lines (including the one that intersects the right-hand
tm2
3
2
Q
tm1
t1
1
Tm1
T2
Tm2
T
T1
t2
FIGURE 5.56 Procedure to determine the number of shells. Note: T1 and T2 are shellside terminal tempera-
tures and t1 and t2 are tubeside terminal temperatures.

ordinate) is equal to the number of shells in series that is clearly sufficient to perform the duty.
Following this procedure will usually result in a number of shells having an overall F close to 0.8.
Estimation of U: The greatest uncertainty in preliminary calculations is estimating the overall
heat transfer coefficient. Approximate film coefficients for different types of fluids are given by
Bell [43]. Thus, U can be calculated from the individual values of heat transfer coefficient on the
shellside (hs) and the tubeside (ht), wall resistance (kw), and fouling resistance (Rfo and Rfi), using the
following equation:

U
h R t k A A R h A A
=
+ + + +( ) 
1
( ) ( )( ) ( / )1 1s fo w w o m fi t o i

(5.7)
where tw is the wall thickness and Am is the effective mean wall heat transfer area, which is approxi-
mated by the arithmetic mean, using the outside and inside radii, ro and ri:
A L r rm o i= +π ( ) (5.8a)

For a bare tube
A
A
r
r
o
i
o
i
→

(5.8b)

A
A
r
r r
o
m
o
o i
→
+
(5.8c)
Heat transfer coefficient for finned tubes: Bell [46] suggests that the values given for plain tubes
can be usually used with caution for low-finned tubes if the controlling resistance is placed on the
shellside; the values should be reduced by 10%–30% if the shellside fluid is of medium or high vis-
cosity, and by 50% if the shellside fluid is of high viscosity and is being cooled. Whitley et al. [11]
suggest reducing the value for finned tubes to 90% of those of plain tubes.
Fouling resistance: Fouling resistance values may be chosen from TEMA Table RGP-T-2.4. Also
refer to Chapter 9 for more details on fouling resistances.
Calculation of Ao: Once q, U, LMTD, and F are known, the total outside heat transfer area
(including fin area) Ao is readily found from the following equation:

A
q
UF
o =
(LMTD)
(5.9)
Determination of shell size and tube length from heat transfer area, Ao (after Taborek [26]): The
problem now arises of how to interpret the value of A in terms of tube length and shell diameter,
when both values are not known. If the problem specification specifies the limitation on shell length
and diameter, the problem can be simplified. In the absence of these values, Ao is given by
A dL No ta t= π (5.10)
and for estimation purposes, the tube count Nt is given in terms of tube pitch, Ltp, by

N
D
C L
t
ctl
tp
=
0 78 2
1
2
.

(5.11)
where C1 is the tube layout constant given by

C
C
1
1
30
45
= = °
= = °
0.86 for
1.0 for
θ
θ
tp
tp and 90∞

(5.12)

Substituting Equation 5.11 into Equation 5.10, the resulting equation is given by

A
d
C L
L Do
tp
ta ctl= 


( . )0 78
1
2
2
π

(5.13)
In Equation 5.13, the first term is a constant; the second term reflects the tube size and the tube
layout geometry; and the third term includes the values of tube length and shell diameter (known
as aspect ratio), which are the items to be determined. Heat transfer surface Ao can be obtained by
various combinations of the parameter Lta and Dctl for any given tube layout pattern. An initially
assumed aspect ratio of 8 is suggested. Some tube count tables are available in Refs. [10,12,21], and
there is a tube count chart in Ref. [46] for various tube layout patterns, tube diameters, and shell
diameters. This helps to calculate Ao easily. If such a source is not available, the designer must
assume a rational tube length and calculate the corresponding diameter Dctl and finally the shell
inside diameter Ds.
5.16.5.2 Detailed Design Method: Bell–Delaware Method
Designing a shell and tube heat exchanger with the Bell–Delaware method is explained here. A
flowchart for designing with the Bell–Delaware method is shown in Figure 5.57.
5.16.5.2.1 Evaluation of Geometric Parameters
After the determination of shell inside diameter and tube length, the next step is the evaluation of
geometric parameters, such as
1. Baffle and bundle geometry
2. Flow areas
3. Various flow areas for calculating various correction factors
The calculation of various geometric parameters is known as auxiliary calculations in the Bell–
Delaware method [41]. These calculations are required for the determination of shellside heat
transfer coefficient and pressure drop. The auxiliary calculations are defined in the following
steps.
5.16.5.2.2 Input Data
The Bell–Delaware method assumes that the flow rate and the inlet and the outlet temperatures
(also pressures for a gas or vapor) of the shellside fluid are specified and that the density, viscosity,
thermal conductivity, and specific heat of the shellside fluid are known. The method also assumes
that the following minimum set of shellside geometry data is known or specified:
Tube outside diameter, d
Tube layout pattern, θtp
Shell inside diameter, Ds
Tube bank OTL diameter, Dotl
Effective tube length (between tubesheets), Lti
Baffle cut, Bc, as a percent of Ds
Central baffle spacing, Lbc (also the inlet and outlet baffle spacing, Lbi and Lbo, if different from Lbc)
Number of sealing strips per side, Nss
From this geometrical information, all remaining geometrical parameters pertaining to the shell-
side can be calculated or estimated by methods given here, assuming that the standards of TEMA
are met with respect to various shellside constructional details.

5.16.5.2.3 Shellside Parameters
Bundle-to-shell clearance, Lbb: A suitable tube bundle is selected based on the user’s requirement,
and the bundle-to-shell clearance is calculated based upon these equations:
For a fixed tubesheet heat exchanger,
L Dbb s12 5 mm= +. . ( )0 0 00
For a U-tube exchanger,
L Dbb s5= +12.0 . (mm)0 00
Problem
specification
Properly
data
Approximate
design
Bundle and
baffle geometry
Shell and
tube geometry
Compute various
flow areas
Determine
tubeside
pressure drop
Determine
tubeside
pressure drop
Design
complete
(a) (b) (c)
OK OK
Not
acceptable
Not
acceptable
Not
acceptable
Modify the
design
Determine
shellside
heat transfer
coefficients
Determine
tubeside
heat transfer
coefficient
Determine
overall
heat transfer
coefficient
Determine
heat transfer
correction factors
and pressure drop
FIGURE 5.57 Flowchart for detailed design of STHE. (a) ΔPt ≤ allowed pressure drop, (b) compare area
required with area available for heat transfer, and (c) ΔPs ≤ allowable pressure drop.

Bundle diameter (Dctl): This is computed from the equation
D D L
D d
otl s bb
ctl
= −
= +
Shell length: This is taken as the overall nominal tube length, Lto, given by
L L Lto ta ts= + 2
where Lts is tubesheet thickness. Its value may be assumed initially as 1 in. (25.4 mm) for calcula-
tion purposes.
Central baffle spacing, Lbc. The number of baffles Nb is required for calculation of the total num-
ber of cross passes and window turnarounds. It is expressed as

N
L
L
b
ti
bc
= −1

(5.14)
where Lti and Lbc are the tube length and central baffle spacing, respectively. Tube length Lti is
defined in Figure 5.58. A uniform baffle spacing (Lbc) is assumed initially, equal to the shell diam-
eter, Ds. To determine Lti, we must know the tubesheet thickness. If drawings are not available, the
tubesheet thickness, Lts, can be roughly estimated as Lts = 0.1Ds with limit Lts = 25 mm. Otherwise
assume the minimum tubesheet thickness as specified in TEMA [2]. For all bundle types except
U-tubes, Lti = Lto − Lts, whereas for U-tube bundles, Lto is nominal tube length.
The number of baffles is rounded off to the lower integer value, and the exact central spacing is
then calculated by

L
L
N
bc
ta
b
=
+1
(5.15)
5.16.5.3 Auxiliary Calculations, Step-by-Step Procedure
Step 1: Segmental baffle window calculations. Refer to Figure 5.59, which reveals the basic segmen-
tal baffle geometry in relation to the tube field. Calculate the centriangle of baffle cut, θds, and upper
centriangle of baffle cut, θctl.
The centriangle of baffle cut, θds, is the angle subtended at the center by the intersection of the
baffle cut and the inner shell wall as shown in Figure 5.59. It is given by

θds
c
= −




−
2 1
2
100
1
cos
B

(5.16)
Tubesheet
Lts Lti=Lta
Lto
Lts Lts Lti
Lta
Lto
Baffle tangent to
outer tube row
Outer tube
bend radius
0.3 Dotl
FIGURE 5.58 Shell and tube heat exchanger tube length definition.

The upper centriangle of baffle cut, θctl, is the angle subtended at the center by the intersection of the
baffle cut and the tube bundle diameter, as shown in Figure 5.59. It is given by

θctl
s
ctl
c
= −










−
2 1
2
100
1
cos
D
D
B

(5.17)
Step 2: Shellside crossflow area. The shellside crossflow area, Sm, is given by

S L L
D
L
L dm bc bb
ctl
tp,eff
tp= + −





( )

(5.18)
where
L D D
D D d
L L
bb s otl
ctl otl
tp,eff tp
o o
for and
= −
= −
=
=
30 90
0
layouts
.. layouts
tube pitch
707 45L
L
tp
o
tp
for
=
Basic tube layout parameters are given in Table 5.2.
Step 3: Baffle window flow areas. The gross window flow area, i.e., without tubes in the window,
Swg, is given by

S Dwg s
2 ds ds
4 2
sin
2
= −




π θ
π
θ
π
(5.19)
From the calculations of centriangle and gross window flow area, calculate the fraction of tubes in
baffle window, Fw, and in pure crossflow, Fc, i.e., between the baffle cut tips as indicated in Figure 5.59
by distance Ds[1 − 2(Bc/100)]:
F Fc w= −1 2 (5.20)
Shell internal dia
Dotl
D
ctl
Outer tube limit dia
Centerline tube limit dia
Ds
Ds
Lbb/2
Lp(By pass lane)
Baffle cut
1–2
Bc
100
θctl
θds
FIGURE 5.59 Basic segmental baffle geometry.

where Fw is the fraction of number of tubes in the baffle window, given by

Fw
ctl ctl
2
= −
θ
π
θsin
2π
(5.21)
The segmental baffle window area occupied by the tubes, Swt, can be expressed as

S N dwt tw=
π
4
2

(5.22a)

t w= N F d
π
4
2

(5.22b)
TABLE 5.2
Tube Layout Basic Parameters
Crossflow → 𝝷tp Lpn Lpp
θtp
Ltp
Ltp
Lpp
Lpn
30° 0.5Ltp 0.866Ltp
θtp
Ltp=Lpp
Lpn=Ltp
90° Ltp Ltp
θtp
Ltp
Ltp
Ltp–d1.44Ltp
Lpp
Lpn
d
45° 0.707Ltp 0.707Ltp

The number of tubes in the window, Ntw, is expressed as
N N Ftw t w= (5.23)
The net crossflow area through one baffle window, Sw, is the difference between the gross flow area, Swg,
and the area occupied by the tubes, Swt. Net crossflow area through one baffle window, Sw, is given by

S S Sw wg wt= −

(5.24)
Step 4: Equivalent hydraulic diameter of a segmental baffle window, Dw. The equivalent hydrau-
lic diameter of a segmental baffle window, Dw, is required only for pressure-drop calculations in
laminar flow, i.e., if Res 100. It is calculated by classical definition of hydraulic diameter, i.e., four
times the window crossflow area Sw divided by the periphery length in contact with the flow. This
is expressed in the following equation:

D
S
dN D
w
w
tw s ds
=
+
4
2π π θ π/
(5.25)
Step 5: Number of effective tube rows in crossflow, Ntcc and baffle window, Ntew. The number of
effective tube rows crossed in one crossflow section, i.e., between the baffle tips, is expressed as Ntcc:

N
D
L
B
tcc
s
pp
c
= − −



1
2
100

(5.26)
where Lpp is the effective tube row distance in the flow direction, which is given in Table 5.2. The
effective number of tube rows crossed in the baffle window, Ntcw, is given by

N
L
D B D D
tcw
pp
s c s ctl
= −
−





0 8
100 2
.

(5.27)
Step 6: Bundle-to-shell bypass area parameters, Sb and Fsbp. The bypass area between the shell and
the tube bundle within one baffle, Sb, is given by

S L D D Lb bc s otl pl= − +( )

(5.28)
where Lpl expresses the effect of the tube lane partition bypass width (between tube walls) as fol-
lows: Lpl is 0 for all standard calculations; Lpl is half the dimension of the tube lane partition Lp.
For estimation purposes, assume that Lp = d.
For calculations of the correction factors J1 and R1, the ratio of the bypass area, Sb, to the overall
crossflow area, Sm, designated as Fsbp, is calculated from the expression

F
S
S
sbp
b
m
=

(5.29)
Step 7: Shell-to-baffle leakage area for one baffle, Ssb. The shell-to-baffle leakage area, Ssb, is a fac-
tor for calculating baffle leakage effect parameters J1 and R1. The diametral clearance between the
shell diameter Ds and the baffle diameter Db is designated as Lsb and given by
L Dssb = +3 1 0 004. . (5.30)
The shell-to-baffle leakage area within the circle segment occupied by the baffle is calculated as

S D
L
sb s
sb ds
=
−


π
π θ
π2
2
2
(5.31)

Step 8: Tube-to-baffle-hole leakage area for one baffle, Sth. The tube-to-baffle-hole leakage area
for one baffle, Sth, is required for the calculation of the correction factors J1 and R1. The total tube-
to-baffle leakage area is given by

S d L d N Ftb tb t w= + −


 −
π
4
12 2
( ) ( )

(5.32)
where Ltb is diametral clearance between tube outside diameter and baffle hole. TEMA standards specify
recommended clearances as a function of tube diameter and baffle spacing. Its value is either 0.8 or 0.4.
Step 9: Calculate shellside crossflow velocity, Us. The shellside crossflow velocity Us from shell-
side mass flow rate Ms is given by

U
M
S
s
s
s m
=
ρ

(5.33)
where ρs is the mass density of the shellside fluid. Equation 5.33 gives shellside crossflow veloc-
ity as per the Bell–Delaware method. Since flow-induced vibration guidelines given in the TEMA
Standards are based on crossflow velocity as per Tinker [37], the procedure to calculate crossflow
velocity is given in Appendix 5.A.
5.16.6 Shellside Heat Transfer and Pressure-Drop Correction Factors
Heat transfer correction factors: In the Bell–Delaware method, the flow fraction for each stream is
found by knowing the corresponding flow areas and flow resistances. The heat transfer coefficient
for ideal crossflow is then modified for the presence of each stream through correction factors. The
shellside heat transfer coefficient, hs, is given by
h h J J J J Js i c l b s r= (5.34)
where hi is the heat transfer coefficient for pure crossflow of an ideal tube bank. The correction fac-
tors in Equation 5.34 are thus:
Jc is the correction factor for baffle cut and spacing. This correction factor is used to express
the effects of the baffle window flow on the shellside ideal heat transfer coefficient hi,
which is based on crossflow.
J1 is the correction factor for baffle leakage effects, including both shell-to-baffle and tube-
to-baffle leakage.
Jb is the correction factor for the bundle bypass flow (C and F streams).
Js is the correction factor for variable baffle spacing in the inlet and outlet sections.
Jr is the correction factor for adverse temperature gradient buildup in laminar flow.
The combined effect of all of these correction factors for a reasonably well-designed shell and
tube heat exchanger is typically of the order of 0.6; i.e., the effective mean shellside heat transfer
coefficient for the exchanger is of the order of 60% of that calculated if the flow took place across
an ideal tube bank corresponding in geometry to one crossflow section. It is interesting to note
that this value was suggested by McAdams [47] in 1933 and has been used as a rule of thumb [1].
Pressure-drop correction factors: The following three correction factors are applied for pressure drop:
1. Correction factor for bundle bypass effects, Rb
2. Correction factor for baffle leakage effects, R1
3. Correction factor for unequal baffle spacing at inlet and/or outlet, Rs

5.16.6.1 Step-by-Step Procedure to Determine Heat Transfer
and Pressure-Drop Correction Factors
Step 10: Segmental baffle window correction factor, Jc. For the baffle cut range 15%–45%, Jc is
expressed by
J Fc c= 0.55 + 0.72 (5.35)
This value is equal to 1.0 for NTIW design, increases to a value as high as 1.15 for small baffle cut,
and decreases to a value of about 0.52 for very large baffle cuts. A typical value for a well-designed
heat exchanger with liquid on the shellside is about 1.0.
Step 11: Correction factors for baffle leakage effects for heat transfer, J1, and pressure drop, R1. The
correction factor J1 penalizes the design if the baffles are put too close together, leading to an excessive
fraction of the flow being in the leakage streams compared to the crossflow stream. R1 is the correction fac-
tor for baffle leakage effects. For computer applications, the correction factors are curve-fitted as follows:

J r r el s s
rlm
= − + − −[ ] −
0 44 1 1 0 44 1 2 2
. ( ) . ( ) .

(5.36)

R r r1 1 33 1= − +[ ]exp . ( )s lm
x

(5.37)
where

x r= − + +[ ]0 15 1 0 8. ( ) .s

(5.38)
The correlational parameters used are

s
sb
sb tb
r
S
S S
=
+
(5.39)

r
S S
S
lm
sb tb
m
=
+

(5.40)
where
Ssb is the shell-to-baffle leakage area
Stb the tube-to-baffle leakage area
Sm the crossflow area at bundle centerline
A well-designed exchanger should have a valve of Jl, not less than 0.6, preferably in the range
0.7–0.9. If a low Jl value is obtained, modify the design with wider baffle spacing, increase tube
pitch, or change the tube layout to 90° or 45°. More drastic measures include change to double or tri-
ple segmental baffles, TEMA J shell type, or both. A typical value for Rl is in the range of 0.4–0.5,
though lower values may be found in exchangers with closely spaced baffles.
Step 12: Correction factors for bundle bypass effects for heat transfer, Jb, and pressure drop, Rb.
To determine Jb and Rb, the following parameters must be known:
1. Nss, the number of sealing strips (pairs) in one baffle spacing
2. Ntcc, the number of tube rows crossed between baffle tips in one baffle section
The expression for Jb is correlated as

J C F rb bh sbp ss= − −


{ }exp ( ) /
1 2 1 3

(5.41)

where
C Jbh b= ≤ =1.25 for laminar flow, Re 100,with the limit of ,s 1 at ssr ≥
=
0 5
10
.
1.35 for turbulent and trasition flow, Res 00
The expression for Rb is given by
R eb
C F rbp sbp ss
=
− −[ { ( ) }]/
1 1 3
(5.42)
where

rss
ss
tcc
=
N
N
(5.43)
with the limits of
R r
C
b ss
bp s
at= ≥
= ≤
=
1 0 5
100
.
4.5 for laminar flow, Re
3.7 for turbuulent and transition flow, Re 100s
For the relatively small clearance between the shell and the tube bundle, Jb is about 0.9; for the
much larger clearance required by pull-through floating head construction, it is about 0.7. Jb can be
improved using sealing strips.
A typical value for Rb ranges from 0.5 to 0.8, depending upon the construction type and
number of sealing strips. The lower value would be typical of a pull-through floating head
with only one or two pairs of sealing strips, and the higher value typical of a fully tubed fixed
tubesheet exchanger.
Step 13: Heat transfer correction factor for adverse temperature gradient in laminar flow, Jr. Jr
applies only if the shellside Reynolds number is less than 100 and is fully effective only in deep
laminar flow characterized by Res less than 20. For Res 20, Jr can be expressed as

J
N
r
c
=
1 51
0 18
.
.

(5.44)
where Nc is the total number of tube rows crossed in the entire exchanger. Nc is given by
N N N Nc tcc tcw b= + +( )( )1 (5.45)
For Res between 20 and 100, a linear proportion is applied resulting in

J
N N
r
c
s
c
Re
= +
−


 −




1 51 20
80
1 51
10 18 0 18
. .
. .

(5.46)
with the limit
J
J
r
r
0.400 for Re 100
1 for Re 100
= ≤
=
s
s

Step 14: Heat transfer correction for unequal baffle spacing at inlet and/or outlet, Js. Figure 5.60
shows a schematic sketch of an exchanger where the inlet and outlet baffle spacing Lbi and Lbo are
shown in comparison to the central baffle spacing, Lbc:

J
N L L
N L L
n n
s
b i o
b i o
=
− + ( ) + ( )
− + −( )+ −( )
− −
( ) * *
( ) * *
1
1 1 1
1 1

(5.47)
where

L
L
L
L
L
L
i
bi
bc
o
bo
bc
* *= =

(5.48)
Js will usually be between 0.85 and 1.0. If L L L L L L Jbi bo bc i sor *= = = = = =* * . , 1.00 1 0 . For
turbulent flow, n = 0.6, and values of L* larger than 2 would be considered poor design, especially
if combined with a few baffles only, i.e., low Nb. In such a case, an annular distributor or other
measures should be used. Typical arrangements for increasing effectiveness of end zones are
presented by Tinker [36]. For laminar flow, the correction factor is about halfway between 1 and Js
computed for turbulent conditions.
Step 15: Pressure-drop correction for unequal baffle spacing at inlet and/or outlet, Rs. Rs is
given by

R
L L
s
i
n
o
n
=





 +






− −
1 1
2 2
* *

(5.49)
with n = 1 for laminar flow, Res ≤ 100, and n = 0.2 for turbulent flow.
1. For Lbc = Lbo = Lbi, Rs = 2.
2. For the reasonable extreme case Lbo = Lbi = 2Lbc, Rs = 1.0 for laminar flow, and Rs = 0.57
for turbulent flow.
3. For a typical U-tube, Lbi = Lbc and Lbo = 2Lbc, Rs = 1.5 for laminar flow, and Rs = 3.0 for
turbulent flow.
Lbi Lbc
Lbo
FIGURE 5.60 Typical layout of baffle spacing.

5.16.6.2 Shellside Heat Transfer Coefficient and Pressure Drop
5.16.6.2.1 Shellside Heat Transfer Coefficient
1. Calculate the shellside mass velocity Gs, Reynolds number Res, and Prandtl number Prs:

G
M
S
s
s
m
mkg/ m s) or lb / h ft= ( ( )2 2
i i

(5.50)

Re Prs
s
s
s
s ps
s
= =
dG C
kµ
µ

(5.51)
2. Calculate the ideal heat transfer coefficient hi given by

h
j C G
i
i ps s s
n
s
=
( )
Pr /
φ
2 3

(5.52)
where ji and (ϕs)n are defined next.
The term ji is the ideal Colburn j factor for the shellside and can be determined from the
appropriate Bell–Delaware curve for the tube layout and pitch and a typical curve. For example,
d = 0.75 in. (19.05 mm), pitch = 1.0 in. (25.4 mm), and θtp = 30°; curve fits for ji are given by
Bell [40]:

ji s s= ≤ −
1 73 1 1000 694
. Re Re( . )

(5.53a)
s s= ≤ −
0 717 100 10000 574
. Re Re( . )
(5.53b)
s s= ≤−
0 236 10000 346
. Re Re( . )

(5.53c)
The term (ϕs)n is the viscosity correction factor, which accounts for the viscosity gradient at the tube
wall (μw) versus the viscosity at the bulk mean temperature (μs) of the fluid and is given by [48]:

( )
.
φ
µ
µ
s
n s
w
=




0 14

(5.54)
For liquids, ϕs is greater than 1 if the shellside fluid is heated and less than 1 if shellside fluid is
cooled. In order to determine μw, it is essential to determine Tw, which is estimated as follows using
the approximate values of ht and hs [48]:

T T
T T
h h
w t,av
s,av t,av
t s/
= +
−
+1
(5.55)
where Ts,av and Tt,av denote the average mean metal temperatures of shell and tube, both of them
being the arithmetic means of inlet and outlet fluid temperatures on the shellside and tubeside,
respectively. The mean temperature calculation method for shellside and tubeside fluids and mean

metal temperature for conduction wall is shown graphically in Figure 5.61. An accurate equation to
calculate tube mean metal temperature is given by TEMA. For gases, the viscosity is a weak func-
tion of temperature. The correction factor ϕs is formulated as follows:

For gases being cooled: s( ) .φ n
= 1 0

(5.56)

For gases being heated s
s,av
w
( )
( . )
( . )
φ n T
T
=
+
+





273 15
273 15 
0 25.

(5.57)
For a gas being heated, Tw is always higher than Ts,av and hence the correction factor is less than 1.0.
Calculate the shellside heat transfer coefficient given by
h h J J J J Js i c l s b r= (5.58)
5.16.6.2.2 Shellside Pressure Drop
The shellside pressure drop is calculated in the Delaware method by summing the pressure drop for
the inlet and exit sections, and the internal sections after applying various correction factors. The
total shellside pressure drop Δps consists of the pressure drop due to (1) crossflow Δpc, (2) window
regions Δpw, and (3) entrance and exit sections Δpe as given by Refs. [39,40]:

∆ ∆ ∆ ∆p p p ps c w e= + +

(5.59)
The elements of shellside pressure drop are shown schematically in Figure 5.62. The crossflow pres-
sure drop and the entrance and exit region pressure drop depend on the ideal tube bank pressure
drop, given by

∆ = −
p f N
G
g
b,i s tcc
s
c s
s
n
2
2
ρ
φ( )

(5.60)
T2
t1
t2
t= (t1+t2)/2
t
Tw=(T+t)/2
T=(T1+T2)/2T1
FIGURE 5.61 Mean temperature calculation method for shellside and tubeside fluids and mean metal
temperature for conduction wall.
Entrance and exit section
Window sections
Internal crossﬂow section
FIGURE 5.62 Elements of shellside pressure drop of a TEMA E shell.

The friction factor fs can be determined from the appropriate Bell–Delaware curve for the tube layout
and pitch under consideration. For example, for d = 0.75 in. (19.05 mm), pitch = 1.0 in. (25.4 mm), and
θtp = 30°, curve fits for fs are given by Bell [40]:

fs
s
s= + ≤
52
0 17 1 500
Re
. Re

(5.61a)
s s= ≤
−
0 56 500
0 14
. Re Re
( . )

(5.61b)
Calculate the various terms of shellside pressure drop as given next and finally calculate the overall
heat transfer coefficient.
1. The pressure drop in the interior crossflow sections is affected by both bypass and leakage.
Therefore, the combined pressure drop of all the interior crossflow sections is given by

∆ ∆p N p R Rc b b,i b= −( )( )1 1

(5.62)
2. The pressure drop in the entrance and exit sections is affected by bypass but not by leak-
age, and by variable baffle spacing. Therefore, the combined pressure drop for the entrance
and exit sections is

∆ = ∆ +



p p
N
N
R Re b,i
tcw
tcc
b s2 1( )

(5.63)
3. The pressure drop in the windows is affected by leakage but not by bypass. Therefore, the
combined pressure drop of all the window sections is given by

∆ p N Rw b l

(5.64)
where Δ pw is given as follows:
For Res ≥ 100,

∆ =
+
p
N G
g
w
tcw w
c s
( . )2 0 6
2
2
ρ

(5.65)
For Res 100,

∆
µ
ρ ρ
p
G
g
N
L d
L
D
G
g
w
w s
c s
tcw
tp
bc
w
w
c s
=
−
+





 +26 22
2

(5.66)
in which the window mass velocity Gw is given by

G
M
S S
w
s
m w
=

(5.67)

Summing these individual effects, we obtain the equation for the total nozzle-to-nozzle shellside
pressure drop:

∆ ∆ ∆ ∆p N p R N p R p
N
N
Rs b b,i b b w b,i
tcw
tcc
b= − +[ ] + +



( )( ) ( ) ( )1 2 11 RRs

(5.68)
The total shellside pressure drop of a typical shell and tube exchanger is of the order of 20%–30%
of the pressure drop that would be calculated for flow through the corresponding heat exchanger
without baffle leakage and without tube bundle bypass effects [39].
5.16.6.3 Tubeside Heat Transfer Coefficient and Pressure Drop
5.16.6.3.1 Tubeside Heat Transfer Coefficient
1. Calculate the tubeside mass velocity Gt, Reynolds number Ret, and Prandtl number, Prt:

G
M
A
t
t
t
for single pass=

(5.69a)

=
M
A N
Nt
p
/
for passes
t p

(5.69b)
where

A d Nt i
2
t=
π
4
and where Al is the tubeside flow area, Np the number of tubeside passes, Nt the number of
tubes, and

Rel
t i
i
t
t pt
t
Pr= =
G d C
kµ
µ

(5.70)
2. Calculate the tubeside heat transfer coefficient, ht: For laminar flow with Ret of 2100 and
less, the heat transfer coefficient is determined from the Sider–Tate (1936) empirical equa-
tion for both heating and cooling of viscous liquids:

h d
k
d
L
t i
i
t t
i
t
t
w
Pr Pr=








1 86
0 5
1 3
0 14
. Re
.
/
.
µ
µ

(5.71)
For those cases where the Grashof number Nar exceeds 25,000, the value of ht obtained from
Equation 5.71 must be corrected for the increase in heat transfer due to natural convection effects
by multiplying by the term

0 8 1 0 015 1 3
. . /
+( )Nar

(5.71a)


Na
td g
r
i i c
t
2
=
∆β ρ
µ
2 2

(5.71b)
where
β is the thermal coefficient of cubical expansion, 1/°F
Δt is the temperature difference, °F
Nar is the Grashof number
ρi is the tubeside fluid density, lb/ft3
gc is the acceleration of gravity, 4.17 × 108 ft/h2
μt is the viscosity at bulk mean temperature, lb/h ft
At values above 10,000, turbulent flow occurs and the heat transfer coefficient is determined
from the following correlation:
Sider–Tate equation modified by McAdams:

h d
k
t i
t
t t
t
w
=



0 027 0 8 1 3
0 14
. Re Pr. /
.
µ
µ

(5.72)
In the intermediate region where Reynolds number varies from 2,100 to 10,000, the relation does
not follow a straight line.
Colburn equation

h d
k
t i
l
t t
t
w
=



0 023 0 8 0 4
0 14
. Re Pr. .
.
µ
µ

(5.73a)
Dittus–Boelter equation

h d
k
t i
t
t t
n
= 0 023 0 8
. Re Pr.

(5.73b)
where
n = 0.4 for heating
= 0.3 for cooling
In the intermediate region where Ret varies between 2,100 and 10,000, the relation does not
follow a straight line. In this region, Kern [40] recommends the following formula:

h d
k
d
L
t i
i
t
i
t
t
w
= −


 +












0 116 125 12 3
2 3
1 3
. Re Pr/
/
/ µ
µ




0 14.

(5.74)
5.16.6.3.2 Tubeside Pressure Drop
Pressure drop in tubes and pipes—general: For tubes and pipes, the pressure drop in steady flow
between any two points may be expressed by the following Weisbach–Darcy equation:

∆p f
L
d
G
g
t t
i
t
c t t
r
=




2
2
1
ρ ϕ( )

(5.75)

where

(φ
µ
µ
t
r t
w
tfor) Re
.
=




0 14
2100

(5.76a)

fort
w
t=




µ
µ
0 25
2100
.
Re

(5.76b)
and where L is the length of pipe between two points, di the inside diameter of the pipe, ρt the mass
density of the tubeside fluid, Gt the mass velocity of the fluid inside the pipe, ki or kt is thermal
conductivity of the tubeside fluid, and ft the friction factor. To determine the pressure drop through
the tube bundle, multiply the pressure drop by the number of tubes. For multipass arrangements,
multiply by the number of tubeside passes.
The total pressure drop for a single pass consists of the following items:
1. Pressure drop in the nozzles, Δ pn, which is the sum of pressure drop in the inlet (∆pn,i) and
outlet nozzle (∆pn,o):

∆ p
G
g
n
n
c t
=
1 5
2
2
.
ρ
(5.77)
2. Sudden contraction and expansion losses at the tube entry and exit, ∆pc,e, is given by

∆ = +p
G
g
K K Nc,e
t
c t
c e p
2
2 ρ
( )

(5.78)
where Kc and Ke are the contraction and expansion loss coefficients.
3. Pressure drop through the tube bundle, ∆pt:

∆ =p
fL G N
g d
t
lp t p
c t i t
r
2
2
1
ρ φ

(5.79)
4. Pressure drop associated with the turning losses, ∆pr, given by

∆ =
= ×
p
N G
g
N
r
p t
c t
p Velocity head per pass
4
2
4
2
ρ

(5.80)
Total tubeside pressure drop, ∆pt, is given by

∆ = + + + +





p
G
g N
fL
d
K K Nt
t
e t p
lp
i t
r c e p
2
2
1 5 1
4
ρ (φ
.
)

(5.81)

Determination of friction factor f on the tubeside: The friction factor f has been found to depend
upon Reynolds numbers only. For laminar flow in smooth pipes, the value of f can be derived from
the well-known Hagen–Poiseuille equation.
Accordingly, f for laminar flow is given by

f =
64
Ret
(5.82)
For turbulent flow in smooth pipes, f can be determined from the Blasius empirical formula given by

f =
0 3164
0 25
.
Re .
t
(5.83)
This equation is valid for Reynolds numbers up to 1,000,000. Another formula to determine f for
smooth-walled conduits in the Reynolds number range 10,000–120,000 is given by [49]

f =
0 184
0 2
.
Re .
t
(5.84)
Calculate the overall heat transfer coefficient, U, as per Equation 5.7 using the values of hs and ht
from Equations 5.53 and 5.71, respectively.
Calculate heat transfer area, Ao, required using Equation 5.9 using the U value calculated earlier.
5.16.6.3.3 Evaluation and Comparison of the Results with the Specified Values
In the evaluation stage, the calculated values of the film coefficients and the pressure drop, for both
the streams, are compared with the specified values. If the values match, the design is complete. If
the calculated values and the specified values do not match, repeat the design with new design vari-
ables. Sometimes, even after many iterations, the design may not meet the specified performance
limits in the following parameters [26]:
1. Heat transfer coefficient
2. Pressure drop
3. Temperature driving force
4. Fouling factors
Taborek [26] describes various measures to overcome limitations in these parameters. For the heat trans-
fer-limited cases, utilize the permissible pressure drop effectively. The film coefficients can be increased
by increasing the flow velocities, changing the baffle spacing, changing the number of the tubeside passes,
etc. Attempts to increase the heat transfer coefficient also results in pressure-drop increase. Designs with
inherently low heat transfer coefficients, such as laminar flow or LP gases, may deserve special attention.
For pressure-drop-limited cases, try alternate designs such as [26] the following:
• Double or multiple segmental baffles
• Use TEMA J or X shell
• Reduce tube length
• Increase tube pitch
• Change tube layout pattern
For the temperature–driving-force-limited cases, methods to improve the LMTD correction factor
have been discussed while describing various shell types and pass arrangements. Fouling-limited

cases are dealt with during the design stage by making sure that the factors promoting fouling are
suppressed and/or designed for periodic cleaning.
5.16.6.4 Accuracy of the Bell–Delaware Method
It should be remembered that this method, though apparently generally the best in the open
literature, is not extremely accurate [13]. Palen et al. [13] compare the thermohydraulic perfor-
mance prediction error of Bell–Delaware methods [38,39], stream analysis methods [13], and
Tinker [37].
5.16.6.5 Extension of the Delaware Method to Other Geometries
The Delaware method, as originally developed and as it exists in the open literature, is more
or less explicitly confined to the design of fully tubed E shell configurations using plain tubes.
Extension of this method to other geometries is discussed in Refs. [15,27], and these are discussed
in this subsection.
Applications to low-finned tubes: It is possible to apply the Delaware method to the design of
such heat exchangers in a fairly straightforward way by making use of the results of Brigs and
Young [50] and Briggs, Katz, and Young [51]. As shown by Briggs et al. [51], the Colburn j factor
for low-finned tubes is slightly less than that for a plain tube in the Reynolds number range about
2–1000; the difference is larger in the lower Reynolds number range. The fin-tube j factor jf can be
represented in terms of plain-tube-bank j factor as ji as [15]

j K jf f i=

(5.85)
where Kf is the correction factor whose values, taken from Ref. [50], are presented in Ref. [15]. Its
approximate values at discrete points are as follows:
Re 20 70 100 200 400 600 800–1000
Kf 0.575 0.65 0.675 0.75 0.885 0.975 1.0
For the fin tube friction factor, Bell [39,40] suggests a conservative value that is 1.5 times those for
the corresponding plain tube bank, whereas Taborek [15] recommends 1.4 times the friction factor
of the plain tube bank. The adaptation of the Bell–Delaware method to finned tubes is explained in
Refs. [15,27].
Application to the no-tubes-in-window configuration: In calculations, use Ncw = 0 and the baffle
configuration correction factor Jc = 1. Otherwise, the calculation is essentially identical to a fully
tubed bundle. It is suggested that one choose a smaller baffle cut so that the free flow area through
the window corresponds reasonably closely to the free crossflow area through the tube bank itself.
Application to F shells: Since the shellside is essentially split into two, it is possible to adopt the
Delaware method by reducing all of the areas for flow by half compared to the case for a single shellside
pass. It is assumed that the flow leakage and conduction across the longitudinal baffle are minimized.
Application to J shells: The adaptation of the method to a J shell is straightforward. Take one-half
the length of the exchanger as a “unit” equivalent to an E shell and take one-half the mass flow rate.
Application to double segmental and disk and doughnut exchangers: According to Taborek [15],
the Bell–Delaware method cannot be easily adapted to these baffle types, as the driving forces for
bypass and leakage flow are much smaller than for segmental baffles.
Software for thermal design of shell and tube heat exchanger: Nowadays most of the exchang-
ers are designed using commercially available software such as Xchanger Suite6® of HTRI [52] and
Aspen Shell Tube Mechanical of HTFS, Oxon, UK [53], among others. Typical features of thermal
design program structure of shell and tube heat exchanger are shown in Table 5.3, and output pro-
gram in Table 5.4. These methods are generally restricted for use by members of the organizations.

TABLE 5.4
Typical Features of Output of Thermal Design Program of Shell and Tube Heat Exchanger
Design summary An overview of the most important variables: shell and tubeside temperatures, flow rates,
heat transfer coefficients, velocities, and pressure drops. Description of key heat exchanger
dimensions and geometry
TEMA specification sheet Filling up of TEMA specification sheet (English/Metric units)
Performance evaluation Required area and distribution of resistances in clean, specified fouling, and maximum
fouling conditions
Heat transfer coefficients Film coefficients and their components
MTD and heat flux LMTD, F-correction factors, heat fluxes, and heat flux limitations. Heating curves
Pressure drop Clean and dirty conditions, velocity and pressure-drop distribution from inlet to outlet zone
Shellside flow data Stream analysis—flow fractions and ρV 2 analysis (per TEMA)
Construction of tube
bundle
Baffle and tube layout details, tube count, bundle diameter, shell-to-tube-bundle
clearances, etc.
Flow-induced vibration
analysis details
Critical velocity and natural frequency, fluid elastic instability and turbulent buffeting
analysis, frequency matching for acoustic and vortex shedding at inlet, bundle, outlet, and
user specified spans
Recap of design cases Concise summary of alternative solutions that have been explored and their costs
TABLE 5.3
Typical Features of Thermal Design Program Structure of Shell and Tube Heat Exchanger
Specification Description
Process parameters Heat duty, inlet parameters, pressure drop, fouling resistances
TEMA class TEMA R, B, C
TEMA exchanger types Front head: A, B, C, D, N
Shell: E, F, G, H, J, K, X
Rear head: L, M, N, P, S, T, U, W
Tubesheet Single tubesheet (also OTL, untubed area), double tubesheet
Tube details Plain tube, integral low finned tube, tube material, tube diameters,
and tube length. For U-tubes, U-bend details
Baffle types Single segmental, double segmental, triple segmental, no tubes in
window, disk and doughnut, RODbaffles, EMbaffle®, etc.
Plate baffle details Inlet, central, and outlet baffle spacings
Impingement protection Plate or rod type on shellside
Baffle cuts Horizontal, vertical, rotated, % baffle cut, baffle spacing
Tube patterns Triangular, rotated triangular, square, rotated square, and pitch
Tube passes Possible: 1–16 (odd or even). Specify the number of tube passes
Pass layout types Quadrant, mixed, ribbon
Shell details Diameter, length, number of shells in series/parallel
Nozzles Number, inside diameter, orientation, etc.
Tubeside heat transfer calculation (sensible heat) Laminar flow, turbulent flow—colburn
Single-phase frictional pressure drop Method, Dittus–Boelter equation
Blasius equation or others
Method to calculate shellside pressure drop and
film coefficients for single-phase sensible flow
Stream-analysis method, Bell–Delaware method
Special operating conditions Start-up, transient, and shutdown

5.17 SHELL AND TUBE HEAT EXCHANGERS WITH NON-SEGMENTAL BAFFLES
5.17.1 Phillips RODbaffle Heat Exchanger
The RODbaffle exchanger is a shell and tube heat exchanger that uses an improved support sys-
tem for the tubes. It consists of rods located in a predisposed manner such that they confine tube
movement. RODbaffle heat exchangers are used in process industries to enhance thermohydraulic
performance, eliminate flow-induced tube vibration occurrence, minimize shellside pressure losses,
increase shellside flow-field uniformity, and reduce shellside fouling [54]. The RODbaffle concept
and design came about as a result of tube vibration failures in three shell and tube exchanger bun-
dles resulting in frequent plant shutdowns in a Phillips Petroleum plant in 1970. The emergency
repairs made included the substitution of rod tube supports for the plate baffles, resulting in signifi-
cantly improved operating characteristics. This was the starting point of the RODbaffle concept.
References [54–59] provide general and specific information on RODbaffle heat exchanger design.
5.17.1.1 RODbaffle Exchanger Concepts
The RODbaffle exchangers (Figure 5.63) use rods, with a diameter equal to the clearance between
tube rows, inserted between alternate tube rows in the bundle in both the horizontal and vertical
directions. The support rods are laid out on a square pitch with no nominal clearance between tubes
and support rods. Support rods are welded at each end to a fabricated circumferential baffle ring.
Major components of each individual RODbaffle are support rods, baffle ring, cross-support strips,
partition blockage plate, and longitudinal slide bars. Concept of RODbaffle heat exchanger is shown
in Figure 5.63a. Four different RODbaffle configurations, W–X–Y–Z are welded to longitudinal
Baffle rod
(a)
Heat exchanger tube
W
(b)
Rod baffles
Longitudinal tie bar
X
Y
Z
(c)
Shell
Baffle-shell
ClearanceTube pitch
Baffle ring
Support
rodspacing
FIGURE 5.63 RODbaffle heat exchanger and support. (a) Concept—schematic, (b) RODbaffle cage assembly,
and (c) tube and rod layout.

slide bars to form the RODbaffle cage assembly as shown in Figure 5.63b. Tube and rod layout is
shown in Figure 5.63c.
5.17.1.2 Important Benefit: Elimination of Shellside Flow-Induced Vibration
Although RODbaffle heat exchangers are being increasingly used because of thermohydraulic advan-
tages, flow-induced vibration protection of tubes remains one of the major design considerations. The
RODbaffle bundle eliminates harmful flow-induced vibration by using these major design innovations:
1. Each tube is supported in all four directions
2. Positive four-point confinement of the tubes
3. Minimum convex point contact between rods and tubes
Since these exchangers have longitudinal flow fields, vortex shedding and fluid elastic instability
mechanisms (which lead to flow-induced tube vibration in crossflow exchangers) are not present.
Similarly, because zero nominal clearance exists between tubes and support rods, fretting wear
and collision damage that may occur in plate baffle units are not evident in RODbaffle exchangers.
Under design conditions where plate baffles are required and positive tube support is critical, com-
bination RODbaffle–plate–baffle exchangers may be used [55].
5.17.1.3 Proven RODbaffle Applications
Typical applications for RODbaffle exchangers include gas–gas exchangers, compressor after-
coolers, gas–oil coolers, reactor feed–effluent exchangers, condensers, kettle reboilers, waste heat
boilers, HF acid coolers, and carbon black air preheaters.
5.17.1.4 Operational Characteristics
The unobstructed flow path created by the support rod matrix makes the flow field in a RODbaffle
heat exchanger predominantly longitudinal. Longitudinal flow fields produce the highest thermo-
hydraulic effectiveness of any commercial heat exchanger geometry. The main characteristics of
longitudinal flow on the outside of tube bundles include the following [60]:
1. Extremely LP drop and a very high effectiveness of pressure drop to heat transfer conversion,
compared to baffled crossflow pattern. In longitudinal flow, the friction occurs directly at the
heat transfer surface, and there are no parasitic pressure losses due to window turnarounds.
2. Uniformity of flow distribution, without any stagnant areas characteristic of segmental
baffle exchangers, results in uniform local heat transfer rates and less fouling.
3. The grid baffles not only increase pressure drop through the flow contraction process, but
also enhance heat transfer.
As reported in Refs. [55,56], RODbaffle exchanger heat transfer rates compare favorably with dou-
ble segmental plate baffle exchangers and are generally higher than that in comparable triple seg-
mental plate baffle and “NTIW” designs. Shellside pressure losses in RODbaffle exchangers are
lower because neither bundle crossflow form drag nor repeated flow reversal effects are present.
5.17.1.5 Thermal Performance
For shellside, the expressions for Nusselt number, Nu, for laminar flow and turbulent flow are given by [59]

Nu for laminar flowL h s
n
= C Re Pr ( ). .0 6 0 4
φ
(5.86a)

Nu for turbulent flowT h s
n
= C Re Pr ( ). .0 8 0 4
φ

(5.86b)
where CL and CT are RODbaffle exchanger geometric coefficient functions for laminar flow and
turbulent flow, respectively.

Pressure drop: Shellside pressure loss for flow through a RODbaffle heat exchanger bundle,
excluding inlet and exit nozzles, is defined as the sum of an unbaffled frictional component, ΔpL,
and a baffle flow contribution Δpb as [54]:

∆ ∆ ∆p p pL b= +

(5.87)
According to Gentry [54], shellside pressure losses in RODbaffle exchangers are generally less than
25% of shellside losses produced in comparable double segmental plate baffle exchangers.
5.17.1.6 Design and Rating Program Available
Phillips Petroleum engineers have an ongoing development and testing program on RODbaffle
exchangers from which they have developed basic correlations to predict heat transfer and pressure
drop. The correlations are based on experimental data obtained from different bare and low-finned
tube test bundles using water, light oil, and air as test fluids. The program is available for use on an
IBM mainframe or IBM PC or equivalent.
5.17.2 EMbaffle® Heat Exchanger*
The patented EMbaffle design uses expanded metal baffles made of plate material that has been
slit and expanded. Figure 5.64a shows a section of EMbaffle. The open structure results in a low
hydraulic resistance and enhanced heat transfer. With this new EMbaffle technology, the shell-
side fluid flows axially along the tubes, but in the vicinity of the baffles, the flow area is reduced.
This creates local turbulence in the flow while breaking up the boundary layer over the tubes.
The shape of the grid induces a local crossflow component on top of the longitudinal flow pattern,
which together improve the heat transfer characteristics at the surface of the tubes. The breakup
of the boundary layer occurs repeatedly at each expanded metal baffle along the length of the
heat exchanger, resulting in lower hydraulic resistance while maintaining higher heat transfer [61].
Pressure loss is effectively converted into improved heat transfer, and compared with the segmental
baffle, heat transfer at the same fluid velocity is significantly higher. Figure 5.64 shows the concept
of EMbaffle, heat exchanger tube bundle assembly and completed tube bundle assembly.
As a direct consequence of the longitudinal flow on the shellside, tube vibration in an EMbaffle
heat exchanger is effectively eliminated, significantly reducing the risk of mechanical damage. The
longitudinal direction of the shellside liquid in EMbaffle heat exchangers approaches pure coun-
tercurrent flow; as a result, they can deliver higher heat duty at the same approach temperature.
5.17.2.1 Application of EMbaffle Technology
Initially developed as a potential solution for fouling services, EMbaffle technology has been proven
in a wide range of applications from liquid/liquid and gas/gas to condensing and boiling. In foul-
ing services, for instance, in crude preheat trains, the dead zones typically found with conventional
segmental designs reduce the performance of the heat exchanger with an increasing pressure drop
during operation. However, with EMbaffle, due to the longitudinal flow, no dead zones are created
behind the EMbaffle, and in-service thermal performance has been shown to improve by more
than 50% [61]. It eliminates vibration by virtue of all tubes being fully supported on every baffle.
5.17.2.2 Design
The thermal design parameters for EMbaffle technology have been embedded in the industry stan-
dard HTRIX Changer™ software suite, enabling licensees and users to carry out their own thermal
engineering designs. A complete range of standard and customized grid designs is available for
* EMbaffle® is a registered trademark of EMbaffle B.V., Alphen a/d Rijn, the Netherlands.

all conventional tube sizes and most applications. Baffles are available in most sizes and materials
from carbon steel, stainless, duplex and superduplex steels, high-nickel alloys and copper alloys,
including bronze, brass, and cupronickels. EMbaffle heat exchanger utilizes TEMA tolerances
and the same pressure parts as conventional segmental designs. It is compliant with all relevant
international standards [61].
(i) (ii)
(b)
(a)
(i)
(ii) (iii)
FIGURE 5.64 EMbaffle heat exchanger. (a) (i) Sectional view of tube bundle cage assembly, (ii) Tube bundle
under assembly, and (iii) Assembled tube bundle (2 passes on the tubeside). (b) (i–ii) EMbaffle heat exchanger
tube bundle under assembly. (Courtesy of EMbaffle B.V., LionsParc, A. van Leeuwenhoekweg 38A10, 2408
Amsterdam, the Netherlands.)

5.17.2.3 Benefits of EMbaffle Technology
The benefits of EMbaffle technology compared with conventional designs include the following [61]
a. Improved heat transfer capabilities
b. Elimination of flow-induced tube vibration
c. Uniform flow pattern on the shellside
d. Lower shellside pressure drop
e. Reduced fouling rates
f. Lower energy consumption
5.17.3 Helixchanger® Heat Exchanger*
The Helixchanger heat exchanger is a high-efficiency heat exchanger and a proprietary product
of Lummus Technology Heat Transfer, a division of Lummus Technology. In a Helixchanger heat
exchanger, the conventional segmental baffle plates are replaced by quadrant-shaped baffle plates
positioned at an angle to the tube axis in a sequential arrangement to create a helical flow pattern
creating a uniform velocity through the tube bundle. Figures 5.65 through 5.67 show helical flow pat-
tern on the shellside and orientation of helical baffles of a tube bundle. Shellside helical flow offers
higher thermal efficiency as well as lower fouling rates as compared to the conventional segmental
baffled heat exchangers [62]. Effective protection against flow-induced vibrations is achieved by both
* HELIXCHANGER and HELIFIN are registered trademarks of Lummus Technology Inc.
(a) (b)
FIGURE 5.65 Helixchanger heat exchanger. (a) Shellside flow pattern (schematic) and (b) helical baffle
orientation. (Courtesy of Lummus Technology Heat Transfer, A Division of Lummus Technology Inc.,
Bloomfield, NJ.)
(a) (b)
FIGURE 5.66 Helical baffles. (a) Single helical baffle and (b) double helical baffles (schematic). (Courtesy of
Lummus Technology Heat Transfer, A Division of Lummus Technology Inc., Bloomfield, NJ.)

the single- and the double-helix baffle arrangement. In a double-helix arrangement, two strings of
helical baffles are intertwined to reduce the unsupported tube spans offering greater integrity against
vibrations without compromising the thermohydraulic performance.
5.17.3.1 Merits of Helixchanger Heat Exchanger
In a conventional shell and tube heat exchanger with segmental baffles, uneven velocity profiles,
back flows and eddies results in higher fouling and hence shorter run lengths. In a Helixchanger heat
exchanger, the helical flow offers improved thermal effectiveness, enhanced heat transfer, reduced
pressure drop, lower fouling, and significantly reduced flow-induced vibration hazards [62].
More than 2300 Helixchanger heat exchangers are in operation worldwide, for varied applications in
the oil and gas, refining, petrochemical, and chemical industries. The applications range from crude
preheat exchangers, feed preheat exchangers in delayed cokers, feed/effluent exchangers in refinery
and petrochemical processes, bitumen exchangers in oil sands, major equipment in ethylene plants,
to polymer solution coolers in the chemical industry.
5.17.3.3 Helixchanger Heat Exchanger: Configurations
5.17.3.3.1 Helixchanger Heat Exchanger
In a Helixchanger heat exchanger, quadrant-shaped plate baffles are used on the shellside, placed
at an angle to the tube axis in a successive arrangement to create a helical flow pattern. Figure 5.68
shows the Helixchanger heat exchanger tube bundle assembly.
Baffle
inclination
ø
Baﬄe distance, Hp
(=lead of helix, Hs)
HpHs
HpHs
FIGURE 5.67 Orientation of single helical and double helical baffles.

5.17.3.3.2 Helifin® Heat Exchanger
When a Helixchanger heat exchanger is built with low-fin tubes for the tube bundle, it is
called a Helifin heat exchanger. Low-fin tubes offer extended heat transfer surface on the
outside of the tubes. For process conditions where low-fin tubes are suitable, the Helifin heat
exchanger offers a more economical solution with increased reliability against flow-induced
vibrations.
5.17.3.3.3 Helitower™ Heat Exchanger*
In certain processes where high-temperature effluent is used to preheat the feed stream, a large
bank of horizontal heat exchangers is required in series arrangement. A more economical option
using one or two heat exchangers with longer tubes in a vertical orientation is often better suited
in achieving the desired performance. When Helixchanger heat exchangers are employed in such a
vertical orientation using long tube bundles, they are called Helitower heat exchangers. Figure 5.69
shows a Helitower heat exchanger.
* Helitower is a trademark of Lummus Technology Inc.
(b)(a)
(d)(c)
FIGURE 5.68 Helixchanger heat exchanger tube bundle assembly. (a) A section of tube bundle under
assembly and (b) completed tube bundle assembly. (a and b: Courtesy of Lummus Technology Heat Transfer,
A Division of Lummus Technology Inc., Bloomfield, NJ.) (c) Helixchanger tube bundle under assembly and
(d) Helixchanger tube bundle assembly is inserted into the shell. (c and d: Courtesy of Vermeer Eemhaven
B.V., Rotterdam, the Netherlands.)

5.17.3.4 Performance
Frequently, the fouling mechanism responsible for the deterioration of heat exchanger perfor-
mance is maldistribution of flow, wakes, and eddies caused by poor heat exchanger geometry on
the shellside. In a shell and tube heat exchanger, the conventional segmental baffle geometry is
largely responsible for higher fouling rates. Uneven velocity profiles, backflows, and eddies gen-
erated on the shellside of a segmental baffled heat exchanger result in higher fouling and shorter
run lengths between periodic cleaning and maintenance of tube bundles. In a Helixchanger heat
exchanger, the quadrant-shaped baffle plates are arranged at an angle to the tube axis creating a
helical flow pattern on the shellside. Near-plug flow conditions are achieved in a Helixchanger
heat exchanger with little backflow and eddies, often responsible for fouling and corrosion.
Figure 5.70 shows the flow patterns of a conventional shell and tube heat exchanger compared
with a Helixchanger heat exchanger. The absence of backflows and eddies on the shellside of
Helixchanger heat exchangers significantly reduces fouling while in operation. Figure 5.71 shows
a comparison of typical run lengths between periodic cleaning and maintenance of the tube
FIGURE 5.69 HelitowerTM heat exchanger. (Courtesy of Lummus Technology Heat Transfer, A Division of
Lummus Technology Inc., Bloomfield, NJ.)
hp
d2
D1
sptp
It
sp
d2
D1
tp= Hs
It
s
(a) (b)
FIGURE 5.70 Shellside flow pattern. (a) Conventional shell and tube heat exchanger and (b) Helixchanger
heat exchanger. (Courtesy of Lummus Technology Heat Transfer, A Division of Lummus Technology Inc.,
Bloomfield, NJ.)

bundle of a conventional shell and tube heat exchanger (shorter run length) and the Helixchanger
heat exchanger (longer run length). (Figure 9.6b shows the comparison of the level of fouling of a
conventional shell and tube heat exchanger with a Helixchanger heat exchanger in a typical feed/
effluent exchanger application. The conventional segmental baffle exchanger is fouled heavily
compared to the Helixchanger bundle.)
5.17.4 Twisted Tube® Heat Exchanger*
Koch Heat Transfer Company’s innovative Twisted Tube tube design avoids the need for baffles.
The unique helix-shaped tubes are arranged in a triangular pattern. Each tube is firmly and
frequently supported by adjacent tubes, yet fluid swirls freely along its length. This support sys-
tem eliminates crossflow-induced tube vibration, which is a common problem in conventional
shell and tube heat exchanger services. The twist arrangement for baffle-free support with gaps
aligned between the tubes also provides for easier cleaning on the shellside. The Twisted Tube
heat exchangers are round at each end, allowing for conventional tube-to-tubesheet joints to be
used [63,64].
Crude preheat, feed/effluent for—reformer (CCR and semi-regeneration), hydrotreater, hydrocracker,
alkylation, etc., overhead condensers, reboilers (kettle and J shell), lean/rich amine, compressor
interstage coolers, etc.
5.17.4.2 Advantages
Twisted Tube tubing offers benefits such as increased heat transfer, smaller exchangers or fewer
shells, elimination of flow-induced vibration, and reduced fouling. When used as retrofit bundles or
exchangers, Twisted Tube tubings also offer increased capacity, lower installed costs, lower pres-
sure drop, and extended run time between cleanings.
* Twisted Tube is a registered trademark of Koch Heat Transfer Company, LP, and is registered in the United States and
other countries worldwide.
Time
Helixchanger vs. conventional heat exchanger
Run length performance
Start of run
Scheduled maintenance
End of run
Conventional
HelixchangerDuty
FIGURE 5.71 Comparison of run lengths between periodic cleaning and maintenance of tube bundle of
conventional shell and tube heat exchanger with that of Helixchanger heat exchanger. (Courtesy of Lummus
Technology Heat Transfer, A Division of Lummus Technology Inc., Bloomfield, NJ.)

5.17.4.3 Merits of Twisted Tube Heat Exchanger
Twisted Tube heat exchangers provide a higher heat transfer coefficient than the conventional tubu-
lar heat exchanger due to the following reasons [63]:
a. Uniform fluid distribution combined with interrupted swirl flow on the shellside induces
the maximum turbulence to improve heat transfer.
b. On the tubeside, swirl flow creates turbulence resulting in higher tubeside heat transfer
coefficient.
c. High localized velocities scrub tube wall to combat fouling and offers 40% higher tube-
side heat transfer coefficient.
d. Lower pressure drop: The longitudinal swirl flow of Twisted Tube tubing reduces the
high pressure drop associated with segmental baffles. Twisted Tube heat exchangers are
usually shorter in length and have fewer number of passes, for a lower pressure drop on
the tubeside.
e. Baffle-free tube support and elimination of flow-induced vibration.
5.17.5 End Closures
5.17.5.1 Breech-Lock™ Closure
Breech-Lock closure is used to seal the tubeside of shell and tube heat exchangers in specific appli-
cations (Figure 5.72). Breech-Lock heat exchangers are fabricated and supplied by heat exchanger
manufacturers under fabrication license from ABB Lummus Heat Transfer and the Breech-Lock is
a registered trademark of ABB LHT.
The tubesheet for the Breech-Lock heat exchanger is designed for a differential pressure. The
internal bolts are used to apply the seating load to the gasket at the tubesheet and shell interface.
The pressure load is absorbed by the threaded closure and the outer row of external bolts applies the
seating load to the channel gasket. The inner row of external bolts is used to increase the seating
load between the tubesheet and shell gasket in the event of relaxation of the inner bolts. Since the
hydrostatic pressure load is taken by the channel body and not by heavy bolting (bolts are only sized
for gasket compression loading), the design results in a relatively thin channel (no edge bending
due to bolting) with consequent reduction in the exchanger’s size and weight. These exchangers are
easy to operate and comparatively easy to dismantle and reassemble, which results in more reliable
FIGURE 5.72 Breech-Lock end closure. (Courtesy of Brembana Costruzioni Industriali S.p.A., Milan, Italy.)

operation and shorter shut down time. Koch Heat Transfer Company, LP, Houston, Texas, is one
of the leading manufacturers of Breech-Lock Closure heat exchangers. The main features of the
Breech-Lock Closure are hereunder:
1. Extremely reliable high-pressure sealing
2. Seating of gaskets by small-diameter bolts
3. Absence of threaded holes in forging or in cladding
4. Easy dismantling/reassembly for inspection
5. No need of welding during reassembly
6. Reduced maintenance times and cranage costs with special dismantling jig
5.17.5.2 Easy Installation and Dismantling Jig
IMB™ has developed a unique proprietary jig assembly designed to facilitate dismantling and reas-
sembling operations. With the IMB jig, it is possible to open the channel, remove the internals, and
then reassemble and reclose of the Breech-Lock exchangers in a very short time without the need
for heavy cranage.
5.17.6 Taper-Lok® Closure
The Taper-Lok closure is typically used for high pressure up to 15,000 psi (1,055 kg/cm2) applica-
tions. The Taper-Lok closure uses separate tubeside and shellside flanges, bolting, and gasketing.
The unique feature of this closure offers a reusable Taper-Lok ring that acts as a self-energizing seal.
More details on Taper-Lok closure are given in Chapter 11.
5.17.7 High-Pressure End Closures
Construction, fabrication, qualification and design of high-pressure vessels, heat exchangers,
separators, and reactors up to 250 bar(g) on the shellside and up to 1000 bar(g) on the tubeside
are treated as high-pressure heat exchangers. A typical high-pressure heat exchanger is shown in
Figure 5.73.
FIGURE 5.73 High pressure heat exchanger for hydrocracking plant. (Courtesy of Brembana Costruzioni
Industriali S.p.A., Milan, Italy.)

5.A APPENDIX A
5.A.1 Reference Crossflow Velocity as per Tinker
Reference crossflow velocity as per Tinker [37] is given by

U
F M
MA
s
h s
x s
=
ρ
(5.88)
where
Ax is the crossflow area within the limits of the tube bundle
Fh is the fraction of total fluid flowing through Ax of clean unit
M is the Ax multiplication factor
Ms is the mass flow rate of shellside fluid
ρs is the mass density of shellside fluid
A a L Dx x bc= 3 (5.89)

F
N S
h
h
=
+
1
1
(5.90)

M
L
D M
=
+ −


















1
1
0 7 1
1
1
0 6
1 67
.
.
.
bc
w

(5.91)
The list of expressions required to evaluate Nh, Mw, is

a
D
D
1
1
3
=

(5.92)
For units with sealing strips, a1 is given by

a
D D D D
D
1
1 3 1 2
1
1
1
4
1 5= +
−




 +
−





/
.

(5.93)

a
d d
d
2 =
−B

(5.94)

a
D D
D
3
1 2
1
=
−

(5.95)

b
a
a
1
1
1 5
1
1
=
−( ) .

(5.96)


b
a
a
2
2
1
1 5
= .

(5.97)

b a a3 3 1=

(5.98)
The terms ax, a4, a5, a6, and m are dependent on the tube layout pattern, and they are given in
Table 5.5.
The expression for a7 is

a a
p
p d
7 4
1 5
=
−




.

(5.99)
Values for a8 are given in Table 5.6.

A a a
D
L
d
p
p
p d
=







 −



5 8
bc
1
2

(5.100)

E a
p
p d
D
L
h
D
=
−







 −



6
1
bc 1
1

(5.101)
N a b Ab b Eh = + +7 1 2 3
(5.102)
M maw = 1
0 5.

(5.103)
TABLE 5.5
Terms to Find Crossflow Velocity
30° 90° 45° 60°
ax 0 97. ( )p d
p
− 0 97. ( )p d
p
− 1 372. ( )p d
p
− 0 97. ( )p d
p
−
a4 1.26 1.26 0.90 1.09
a5 0.82 0.66 0.56 0.61
a6 1.48 1.38 1.17 1.28
M 0.85 0.93 0.80 0.87
Source: Tinker, T., Trans. ASME, vol. 80, 36, 1958.
Note: Values for 60° have been taken from TEMA [2].
TABLE 5.6
Baffle Cut Ratio and the Term a8 for Crossflow Velocity
h/D1 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
a8 0.94 0.90 0.85 0.80 0.74 0.68 0.62 0.54 0.49
Source: Tinker, T., Trans. ASME, vol. 80, 36, 1958.

5.A.2 Design of Disk and Doughnut Heat Exchanger
In shell and tube heat exchangers with baffle disks and rings, known as disk and doughnut heat
exchanger (Figure 5.74), the flow inside the shell is made to alternate between longitudinal and
transverse (or crossflow) directions in relation to the tube bundle. This type of heat exchanger is
used in some European countries. Occasionally, oil coolers at thermal power stations are of this
type. It has been reported that for the same pressure drop in shellside fluid, the heat transfer coef-
ficient obtained with disk and doughnut baffles is approximately 15% more than that obtained with
segmental baffles [65]. Exchangers are fabricated for horizontal or vertical installation.
5.A.2.1 Design Method
The effect of clearance between segmental baffles and the shell on the performance of a heat
exchanger has been reasonably well studied, but there is hardly any corresponding published lit-
erature available for the disk-and-doughnut-type heat exchangers. Very few open literature meth-
ods are available for the thermal design of disk and doughnut heat exchangers. Notable among
them are Donohue [66], Slipcevic [67,68], and Goyal et al. [69]. Donohue’s thermal design method
was recently discussed by Ratnasamy [70]. In this section, the Slipcevic and Donohue’s method
is discussed.
5.A.2.1.1 Slipcevic Method
5.A.2.1.1.1 Design Considerations
Follow these design guidelines on the shellside [67]:
1. The spacing between the baffle disks and rings usually amounts to 20%–45% of the inside
shell diameter. Less than 15% is not advisable.
2. Since the heat transfer coefficient for flow parallel with the tubes is lower than that for flow
normal to the tubes, space the baffle plates so that the velocity in the baffle spacing open-
ing is higher than that of the flow normal to the tubes.
3. It is advisable to make the annular area between the disk and the shell, Sk1, the same as the
area inside the ring, Sk2, such that

S D Dk1 s= −( )π
4
2
1
2

(5.104)

S Dk2 =
π
4
2
2

(5.105)
S S D D Dkl k2 s= → = +2
1
2
2
2
(5.106)
Doughnut
Ds
D1
D2
D2
Dm
Disk
Nt2
Nt3
Nt1
FIGURE 5.74 Disk and doughnut heat exchanger with tubes in various flow areas. Note: Dm = 0.5(D1 + D2),
where D1 is disk diameter.

5.A.2.2 Heat Transfer
Step 1: Calculate the individual flow area for longitudinal flow:
1. Flow area in the annular region between the disk and the shell, S1:

S D D N d1
2
1
2 2
4
= − −( )π
s t1

(5.107)
2. Flow area in the ring opening, S2:

S D N d2 2
2
2
2
4
= −( )π
t

(5.108)
Step 2: Calculate the effective crossflow area, Sq:

S L xq s= ∑

(5.109)
where Σx is the sum of the clear distances between the neighboring tubes closest to the mean diam-
eter, Dm = 0.5(D1 + D2). Determine the sum of clear distances between neighboring tubes closest to
Dm, either from a drawing (as shown in Figure 5.75) or by computational methods.
The number of tubes in the flow areas S1, S2, and crossflow area S3 (to be defined later) is Nt1, Nt2
and Nt3, respectively. They are shown in Figure 5.74.
Step 3: Calculate the hydraulic diameter for the longitudinal flow in the annulus, Dhl, and in the
ring opening, Dh2:

D
S
N d D D
h1
t1 s
=
+ +
4 1
1π( )
(5.110)

D
S
N d D
h2
t2
=
+
4 2
2π( )
(5.111)
Step 4: Calculate the heat transfer coefficients h1 and h2 for the longitudinal flow through the cross
section S1 and S2 from the equation of Hausen [71]:

Nu Re b
w
1 1
0 8 0 33
0 14
0 024=



. Pr. .
.
µ
µ

(5.112)
Dm
FIGURE 5.75 Mean diameter to calculate effective crossflow area of a disk and doughnut heat exchanger.


Nu Re s
w
2 2
0 8 0 33
0 14
0 024=



. Pr. .
.
µ
µ

(5.113)
where

Nu h1
1
1
=
h D
k
(5.114)
Nu h2
2
2
=
h D
k

Re 1 h1
s
1 =
U D
µ
(5.115a)

Re2
2
=
U Dh2
sµ
(5.115b)
and U1 and U2 are based on S1 and S2, respectively.
Step 5: Calculate the heat transfer coefficient h3 for crossflow across the bundle from McAdams
[47] for the turbulent range:

Nu b
w
3 3
0 6 0 33
0 14
=



K
T
T
Re Pr. .
.

(5.116)
where K = 0.33 for the staggered tube arrangement and K = 0.26 for the in-line tube arrangement.
To calculate Re3, use U3 calculated using the crossflow area Sq:

Re3
3
=
U d
µs
(5.117)
Alternately, Slipcevic recommends calculating the heat transfer coefficient of the individual tube
row with the corresponding flow cross section. From these heat transfer coefficients, calculate the
weighted mean average of heat transfer coefficients.
Step 6: Calculate the heat transfer area in the longitudinal flow section A1, A2, crossflow section
A3, and total heat transfer area, A:
A dLN1 = π t1 (5.118a)
A dLN2 = π t2 (5.118b)
A dLN3 = π t3 (5.118c)
where
N N N Nt3 t 2 t1 t 2( )= − +
(5.119)
2 3A A A A= + +1 (5.120a)
t= πdN L
(5.120b)

Step 7: Calculate the heat transfer coefficient h referred to the entire heat transfer surface A:

h
h A h A h A
A
=
+ +1 1 2 2 3 3

(5.121)
5.A.2.3 Shellside Pressure Drop
Refer to Slipcevic [68] for pressure-drop calculation.
5.A.2.4 Shortcomings of Disk and Doughnut Heat Exchanger
The disadvantages of this design include the following [4]: (1) All the tie-rods to hold baffles are
within the tube bundle, and (2) the central tubes are supported by the disk baffles, which in turn
are supported only by tubes in the overlap of the larger diameter disk over the doughnut hole.
5.A.3 NORAM RF™ Radial Flow Gas Heat Exchanger
The NORAM RF radial flow gas heat exchanger (by NORAM Engineering and Constructors
Limited, Vancouver, British Columbia, Canada) offers a fundamental improvement in gas heat
exchanger performance over designs traditionally used in the sulfuric acid industry. The RF design
far surpasses existing single and double segmental heat exchanger design in heat transfer rates, at a
significantly lower pressure loss.
In the RF gas exchanger, tubes are arranged in an annular pattern using disk and doughnut
baffles (Figure 5.76). Flow is directed from an inner core outward across the tube bundle and from
FIGURE 5.76 NORAM RF radial flow gas heat exchanger. (Courtesy of NORAM Engineering and
Constructors Limited, Vancouver, British Columbia, Canada.)

an outer annulus inward across the tube bundle. The gas turns in the inner core and outer annulus
are not restricted by tubes so that pressure losses are minimized. The flow resistance across the tube
bundle is uniform, resulting in uniform flow and LP losses due to minimal gas acceleration and
deceleration. Also the radial design minimizes the number of tube rows that have to be crossed by
the gas, resulting in a low shellside pressure drop. Steps are taken in the design to maintain uniform
velocity through the core, the bundle, and the annulus to minimize overall flow resistance. Heat
transfer rates in the RF gas exchanger are maximized because all the heat transfer surface is fully
utilized. Shell gas flow is always perpendicular to the tubes providing the maximum heat transfer
coefficients.
5.A.3.1 Tube Layout
The RF design makes effective use of the heat transfer surface by placing tubes only in areas of
crossflow. The gas flows radially across the tube bundle between an open core and an open outer
annulus, directed by disk and doughnut baffles. All tubes are located in an annular domain between
the core and the outer annulus.
5.A.4 Closed Feedwater Heaters
A feedwater heater is an unfired heat exchanger designed to preheat feedwater by means of con-
densing steam extracted or bleed from a steam turbine. Feedwater heaters are used in regenerative
water-system cycle to improve the thermodynamics efficiency, resulting in a reduction of fuel con-
sumption and thermal pollution. The boiler feedwater is heated up by steam extracted from suitable
turbine stages. The heater is classified as closed, since the tubeside fluid remains in a closed circuit
and does not mix with the shellside condensate, as is the case with open feedwater heaters. They
are unfired since the heat transfer within the vessel does not occur by means of combustion, but by
convection and by condensation.
Leading feedwater heaters manufacturers include Alstrom, Holtec International, Balcke-Durr,
an SPX Company, and Westinghouse among others. Most feedwater heaters are of a standard
shell and tube configuration, although some are of header type. The majority uses U-tubes, which
are relatively tolerant to the thermal expansion during operation. They are designed as per HEI
Standard for closed feedwater heaters [72] or other national standards. For design of power plant
heat exchangers, refer to Ref. [73].
Based on operating pressure, it is as classified as
i. LP heater
ii. HP heater
iii. Intermediate pressure heater (if present).
iv. Orientation shall be either horizontal or vertical channel down or vertical channel up
Figure 5.77 shows LP feedwater heater and HP feedwater heater.
There are three separate zones within the shell in a feedwater heater and their details are given
hereunder:
1. Condensing zone: All of the steam is condensed in this area, and any remaining noncon-
densable gases must be removed. A large percentage of the energy added by the heater
occurs here. All feedwaters have this zone.
2. The condensed steam subcooling zone (optional).
3. Desuperheating zone (optional): The incoming steam enters this zone, giving up most of its
superheat to the feedwater.

5.A.4.1 Low-Pressure Feedwater Heaters
The feedwater heaters placed between the main condensate pumps and the boiler feedwater pumps
are named LP feedwater heaters. They are U-tube bundle heat exchangers. The recommended tube
material is stainless steel. The advantage is the resistance to corrosion and erosion. The tubes are
longitudinally welded, which allows small tube wall thickness to be realized. The LP feedwater
heaters are arranged horizontally.
5.A.4.2 High-Pressure Feedwater Heaters
The feedwater heaters placed between boiler feedwater pump and boiler are named high-pressure
feedwater heaters. The tube material is mostly specified by the consumer. The standard is using
seamless low-alloy carbon steel tubes. The advantages are the good thermal conductivity and its
(a)
(b)
FIGURE 5.77 Feedwater heater. (a) LP feedwater heater and (b) HP feedwater heater. (Courtesy of Holtec
International, Marlton, NJ.)

good mechanical properties at high temperatures. In special cases, austenitic or ferritic stainless
steel are also utilized since these materials offer high resistance to erosion–corrosion. HP heaters
are either installed vertically (channel/waterbox down as a rule) or horizontally.
5.A.5 Steam Surface Condenser
The condenser is simply a large heat exchanger with tubes usually horizontally mounted. The
condenser has thousands of small tubes that are made out of admiralty brass, copper, ferritic/super
austenitic stainless steel, titanium, etc. The function of a surface condenser is to create the low-
est possible turbine or process operating back pressure while condensing steam. The condensate
generated is usually recirculated back into the boiler and reused. Steam enters the condenser shell
through the steam inlet connection usually located at the top of the condenser. It is distributed
longitudinally over the tubes through the space designated as dome area. When the steam contacts
the relatively cold tubes, it condenses. This condensing effect is a rapid change in state from a gas
to a liquid. This change in state results in a great reduction in specific volume, and it is this reduc-
tion in volume that creates the vacuum in the condenser. The vacuum produced by condensation
will be maintained as long as the condenser is kept free of air. A vacuum venting system is utilized
to support the condenser vacuum by continually removing any air entering the system. The con-
densate is continually removed from the hotwell by condensate pump(s) and is discharged into the
condensate system. The air in the system, generally due to leakage in piping, around shaft seals,
valves, etc., enters the condenser and mixes with the steam. The saturated air is removed from the
condenser by the vacuum venting equipment such as steam jet air ejectors, liquid ring vacuum
pumps, or a combination of both. It is necessary to continuously remove air from the system in
order to maintain the desired vacuum. An increasing amount of air in the condenser would reduce
its capacity and cause the pressure to rise. For standards on steam surface condensers refer to Ref.
[74]. A typical steam surface condenser is shown in Figure 5.78. Figure 5.79 shows air-removing
section of a surface condenser.
FIGURE 5.78 Steam surface condenser. (Courtesy of GEA Iberica S.A., Barrio de San Juan, Vizcaya, Spain.)

5.A.5.1 Mechanical Description
The tubes in the condenser are normally expanded into the tubesheets at both ends. The tubes are sup-
ported by properly located baffle plates to help prevent deflection and flow-induced vibration of the tubes.
The tube holes in the supports are de-burred on each side to prevent damage to the tubes. The waterbox/
tubesheet/shell joints are fastened together in three ways, depending upon the tubesheet design.
1. Tubesheet is flanged to the shell—The waterboxes on either end of the shell are bolted to
the tubesheets and shell flanges utilizing staked studs and stud bolts. Stake studs can be
identified by the double nuts included on the shellside. The stake studs are threaded into
the tubesheet. The stud bolts are through bolts with no threads in the tubesheet. The staked
studs permit the operator to remove the waterboxes without disturbing the seal between the
tubesheets and shell flanges.
2. Tubesheet is welded to the shell—The tubesheet outside diameter is larger than the shell,
and it extends to form a flange. In this case, the waterbox is simply bolted to the tubesheet
with through bolts. All of the through bolts must be removed in this type of design in order
to remove the waterboxes.
3. Tubesheet is welded to the shell and to the waterbox—The waterboxes are not remov-
able. The waterbox covers can be removed by simply removing all of the through
bolts.
Figure 5.80 shows a circular shell surface condenser under fabrication.
5.A.5.2 Parts of Condenser
(1) Steam inlet; (2) exhaust connection for turbine; (3) impingement protection—a plate (perforated
or solid), dummy tubes, or solid rods used to protect the tubes against high entrance impingement
velocity; (4) condenser shell—cylindrical or rectangular body; (5) baffle plate; (6) shell expansion
joint; (7) tubes; (8) dome area—an open area above the tubes that permits the steam to easily dis-
tribute throughout the length of the bundle without stagnant or overloaded zones; (9) shell flange;
(10) air removal section; (11) air ejector; (12) hotwell-storage area with volume sufficient to contain
all the condensate produced in the condenser in a given time period. Normally 1 min retention time
is specified under design operating conditions. Bath tub or cylindrical types may be used, depending
upon the volume and deaeration requirements; (13) condensate outlet(s); (14) support saddles; (15)
tubesheets; (16) waterbox—commonly referred to as inlet waterbox, outlet waterbox, return water-
box, return bonnet: provides a directional pathway for circulating water through the tube bundle;
(17) waterbox cover flat plate bolted to the ends of channel type waterboxes; (18) waterbox flanges;
(19) pass partitions ribs.
FIGURE 5.79 Steam surface condenser showing dome for steam entry at the top, air removal section in the
middle of the core, and condensate collection well at the bottom. (Courtesy of GEA Iberica S.A., Barrio de
San Juan, Vizcaya, Spain.)

5.A.5.3 Condenser Tube Material
Condenser tube material selection is one of the most important decisions faced by designers. Typical
criteria for evaluating condenser tube materials include waterside erosion–corrosion resistance,
steam side corrosion resistance and resistance against impingement attack, resistance to pitting due
to chlorides and sulfate-reducing bacteria, resistance to ammonia attack and SCC, compatibility
with other system materials to avoid galvanic corrosion, heat transfer capability, economics, etc. A
partial list of condenser tube material is given as follows:
Tube Material ASTM Spec.
Titanium Gr1, 2, 3 B-338
304L A249
304N A249
316L A249
2205 A789
904L B674
254SMO™ B676
AL-6XN™ B676
Sea-Cure™ A268
AL29-4C™ A268
Copper (iron bearing) B111/B543
Admiralty brass (inhibited) B111/B543
Al brass B111/B543
Al bronze B111/B543
Arsenical copper B111/B543
CuNi 70/30 B111/B543
CuNi 90/10 B111/B543
Carbon steel A179
Carbon steel A214
FIGURE 5.80 Circular shell surface condenser under fabrication. (Courtesy of Caldemon Iberica, S.A.,
a unit of GEA Heat Exchangers, Cantabria, Spain.)

5.A.5.4 Condenser Support Systems
1. Clean the condenser tubes—the tubes are generally kept clean by an automatic tube cleaning
system that injects small abrasive sponge like balls or periodical manual cleaning.
2. Maintain the water level in the condenser so that efficiency is not degraded.
3. Generally, the colder the circulating water, the more efficient the plant. Power plants
become less efficient when the condenser tubes are fouled.
4. The waterboxes are kept full using an air ejector or other system that keeps water level in
the column from the waterbox as high as needed—above the tubes.
5. Maintain condenser vacuum—vacuum in the condenser is maintained by either a mechan-
ical vacuum pump or steam-driven air ejectors that suck gases (not steam) from the
condenser.
NOMENCLATURE
A total heat transfer area on the shellside
An crossflow area within the limits of tube bundle
Aw area of one baffle window
A1 heat transfer area for longitudinal flow in the annulus between the shell and the disk
A2 heat transfer area for longitudinal flow through the ring opening
A3 heat transfer area for crossflow
a1 bypass clearance constant
a2 baffle hole clearance constant
a3 baffle edge clearance constant
a1–a8 factors required to determine Fh
b1,b2,b3 factors required to determine Fh
CL laminar heat transfer bundle geometry function
CT turbulent heat transfer bundle geometry function
D1 disk diameter
D1 shell inside diameter (Ds)
D2 diameter of ring opening
D2 baffle diameter
D3 diameter of OTL (Dotl)
dB baffle hole diameter
Dm mean diameter for calculating the crossflow area = 0.5 (D1 + D2)
Ds shell inside diameter
d tube outer diameter (for finned tubes, equal to fin root diameter)
Fh fraction of total fluid flowing within the limits of tube bundle
gc acceleration due to gravity
h baffle cut
h1 heat transfer coefficient for the longitudinal flow corresponding to Nu1
h2 heat transfer coefficient for the longitudinal flow corresponding to Nu2
h3 heat transfer coefficient for the crossflow corresponding to Nu3
K heat transfer correlation coefficient
L tube length
Lbc baffle spacing
M multiplication factor in Equation 5.86
Ms mass flow rate of shellside fluid
MwAx multiplier to obtain geometric mean of Ax and Aw
N1 total number of tubes

Nt1 number of tubes in annulus between the shell and the disk
Nt2 number of tubes in the ring opening
Nt3 number of tubes in crossflow
Nu Nusselt number
Nu1 Nusselt number to calculate h1
p tube pitch
Pr Prandtl number
Reh Reynolds number
Re1 Reynolds number in the longitudinal flow area S1
S exchanger size ratio = D1/p
S1 cross-sectional area for longitudinal flow through the annulus between the shell and the
disk
S2 cross-sectional area for longitudinal flow through the ring opening
Sk1 annular area between the disk and the shell
Sk2 area inside the ring
Sq crossflow area through tube bundle
Ss mean longitudinal flow area = 0.5(S1 + S2)
Tb bulk mean temperature of the shellside fluid
Tw tube wall temperature
U1 shellside velocity through the cross-sectional area S1
Δ pL pressure drop due to unbaffled frictional component
Δ pb pressure drop due to baffle flow contribution
μs viscosity at bulk mean temperature of the shellside fluid (kg/m s)
μw viscosity at tube wall temperature of the shellside fluid (kg/m s)
(ϕs)n bulk-to-wall viscosity correction (μs/μw)0.14
ρs density of shellside fluid
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DC, 1981, pp. 581–618.
40. Bell, K. J., Delaware method for shellside design, in Heat Transfer Equipment Design (R. K. Shah,
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Refining, 40, 221–233 (1961).
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56. Gentry, C. C., Young, R. K., and Small, W. M., RODbaffle heat exchanger thermal and hydraulic predic-
tive methods, Proceedings of the 7th International Heat Transfer Conference, Munich, Germany, Vol. 6,
57. Gentry, C. C., Young, R. K., and Small, W. M., RODbaffle heat exchanger thermal and hydraulic predic-
tive methods for bare and low finned tubes, Proceedings of the 22nd National Heat Transfer Conference,
Heat Transfer, Niagara Falls, NY, 1984, AIChE Symp. Ser., 80, 104–109 (1984).
58. Gentry, C. C., Young, R. K., and Small, W. M., A conceptual RODbaffle nuclear steam generator design,
1982 ASME Joint Power Generation Conference, Nuclear Heat Exchanger Sessions, Denver, CO,
October 17–21, 1982.
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Vol. 1, Institution of Mechanical Engineers, London, U.K., 1988, pp. 787–800.
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pp. 72–78.
61. (a) EMbaffle® Technology, a major advance in heat exchanger technology, (www.shellglobalsolutions.
com/EMbaffle); (b) EMbaffle® Technology, Shell Global Solutions, (www.shellglobalsolutions.com/
EMbaffle).
62. (a) Chunangad, K. S., Master, B. I., Thome, J. R., and Tolba, M. B., Helixchanger heat exchanger:
Single-phase and two-phase enhancement, Proceedings of the International Conference on Compact
Heat Exchangers and Enhancement Technology for the Process Industries, Begell House, New York,
1999, pp. 471–477; (b) Zhang, Z. and Fang, X., Comparison of heat transfer and pressure drop for the
helically baffled heat exchanger combined with three-dimensional and two-dimensional finned tubes,
Heat Transfer Eng., Taylor Francis Group, LLC, 27(7), 17–22 (2006).
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Houston, TX. (www.kochheattransfer.com); (b) Heat Transfer Innovators, Byron Black, Brown fintube
innovators, pp. 1–9.
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advances in industrial heat transfer, IChemE, 87–95 (1996).

65. Short, B. E., Heat Transfer and Pressure Drop in Heat Exchangers, Publication No. 4324, University of
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(1969).
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68. Slipcevic, B., Shellside pressure drop in shell and tube heat exchangers with disk and ring baffles, Sulzer
Tech. Rev., 60, 28–30 (1978).
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exchanger, Trans. ASME J. Heat Transfer, 106, 759–765 (1984).
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SUGGESTED READINGS
Bell, K. J., Overall design methodology for shell and tube exchangers, in Heat Transfer Equipment Design
(R. K. Shah, E. C. Subbarao, and R.A. Mashelkar, eds.), Hemisphere, Washington, DC, 1988, pp. 131–144.
Escoe, K. A., Mechanical Design of Process Systems, Vol. 2, Shell and Tube Heat Exchangers, Rotating
Equipment, Bins, Silos, Stacks, Gulf Publishing Company, Houston, TX, 1995.
Gentry, G. C., Gentry, M. C., and Scanlon, G. E., Heating the Process and Fluid Flow, Shell and Tube Heat
Exchanger Applications, PTQ Autumn, 1999, pp. 95–101.
Gulley, D., Troubleshooting shell and tube heat exchangrs, Hydrocarbon Process., September, 91–98, 1996.
McNaughton, K. J. (ed.), The Chemical Engineering Guide to Heat Transfer, Vol. I. Plant Principles,
Hemisphere/McGraw-Hill, New York, 1986.
Mehra, D. K., Shell and tube exchangers, in The Chemical Engineering Guide to Heat Transfer, Vol. I, Plant
Principles (K. J. McNaughton and the staff of Chemical Engineering, eds.), Hemisphere/McGraw-Hill,
New York, 1986, pp. 43–52.
Saunders, E.A. D., Heat Exchangers: Selection, Design and Construction,Addison Wesley Longman, Reading,
MA, 1989.
Soler, A. I., Expert system for design integration—Application to the total design of shell and tube heat
exchangers, Proceedings of the ASME, Thermal/Mechanical Heat Exchanger Design, Karl Gardner
Memorial Session, Vol. 118 (K. P. Singh and S. M. Shenkman, eds.), ASME PVP, Washington, DC,
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Vol. I, Plant Principles (K. J. McNaughton, ed.), Hemisphere, New York, 1986, pp. 76–92.

337
6 Regenerators
6.1 INTRODUCTION
Waste heat recovery is an old technology dating back to the first open hearths and blast furnace
stoves. The drastic escalation of energy prices has made waste heat recovery more attractive over
the past two decades. Manufacturing and process industries such as glass, cement, primary and
secondary metals, etc., account for a significant fraction of all energy consumed. Much of this
energy is discarded in the form of high-temperature flue gas exhaust streams. Recovery of waste
heat from flue gas by means of heat exchangers known as regenerator can improve the overall plant
efficiency and serves to reduce the national energy needs and conserve fossil fuels. Figure 6.1 shows
the cross section of a regenerative furnace [1]. Currently, interest in storage-type regenerators has
been renewed due to their applications of heat recovery, heat storage, and general energy-related
problems [2]. The objective of this chapter is to acquaint the readers with various types of regenera-
tors, construction details, and thermal and mechanical design. Additionally, some industrial heat
recovery devices for waste heat recovery are discussed.
6.1.1 Regeneration Principle
For many years, the regeneration principle has been applied to waste heat recovery by preheating the air
for blast furnaces and steam generation. In the former, the regeneration is achieved with periodic and
alternate blowing of the hot and the cold stream through a fixed matrix of checkered brick. During the
hot flow period, the matrix receives thermal energy from the hot gas and transfers it to the cold stream
during the cold stream flow. In the latter, the metal matrix revolves slowly with respect to two fluid
streams. The two gas streams may flow either in parallel directions or in opposite directions. However,
counterflow is mostly preferred because of high thermal effectiveness. The inclusion of an air preheater
in a steam power plant improves the boiler efficiency and overall performance of the power plant.
6.1.2 Regenerators in Thermodynamic Systems and Others
The addition of regeneration as a thermodynamic principle improves the overall performance of the
gas turbine power plants, steam power plants, and the heat exchangers embodying the thermody-
namic cycle of Stirling, Ericssion, Gifford, McMohan, and Vuilleumier [3]. Regenerators are also
used as a dehumidifier for air-conditioning applications, cryogenic separation processes, and in non-
catalytic chemical reactors such as the Wisconsin process for the fixation of nitrogen and the Wulff
process for pyrolysis of hydrocarbon feedstocks to produce acetylene and ethylene. The principle of
regeneration applied to a gas turbine plant is described next.
6.1.3 Gas Turbine Cycle with Regeneration
The simple gas turbine plant consisting only of compressor, combustion chamber, and turbine has
the advantages of light weight and compactness. However, it is known for high specific fuel con-
sumption compared to the modern steam power plant and reciprocating internal combustion engines.
The single improvement that gives the greatest increase in thermal efficiency is the addition of a
regenerator for transferring thermal energy from the hot turbine exhaust gas to the air leaving the
compressor, especially when it is employed in conjunction with intercooling during compression.

The addition of a regenerator results in a flat fuel economy versus load characteristic, which is
highly desirable for the transportation-type prime movers like the gas turbine locomotives, marine
gas turbine plant, and the aircraft turboprop.
6.1.4 Waste Heat Recovery Application
Substantial gains in fuel efficiency can be achieved by recovering the heat contained in the flue gas
by the following four means [4]:
1. Reheating process feedstock.
2. Waste heat boiler and feed water heating for generating steam (low-temperature recovery
system).
3. Preheating the combustion air (high-temperature recovery system).
4. Space heating—Rotary heat exchanger (wheel) is mainly used in building ventilation or in
the air supply/discharge system of conditioning equipment. The wheel transfers the energy
(cold or heat) contained in exhaust air to the fresh air supply to indoor. It is one important
equipment and key technology in the field of construction energy saving.
Each of these methods of heat recovery has its own merits. According to Liang et al. [4], feedstock
preheating is often best suited for continuous counterflow furnaces. Applications of this method,
however, are often limited by high capital costs and large space requirements. Steam generation
is an effective means for heat recovery when the demand for steam corresponds well to the avail-
ability of flue gas. Typical methods of steam generation include simple forced recirculation cycle,
exhaust heat recovery with economizer, and exhaust heat recovery with superheater and econo-
mizer. Combustion air preheating is the most adaptable of heat recovery systems because it requires
minimum modification to the existing system. This improves the system efficiency, and preheating
the cold combustion air reduces the fuel requirement.
6.1.5 Benefits of Waste Heat Recovery
Benefits of waste heat recovery can be broadly classified into two categories as follows.
6.1.5.1 Direct Benefits
Recovery of waste heat has a direct effect on the efficiency of the process. This is reflected in fuel
savings.
Exh. gas
Regenerator bed
Air
Exh. gas
Furnace
Air Exh. gas
Air Air Exh. gas
Regenerator bed
Air
Exh. gas
FIGURE 6.1 Regenerative furnace.

339Regenerators
6.1.5.2 Indirect Benefits
1. Reduction in pollution: A number of toxic combustible wastes such as carbon monoxide
gas, sour gas, oil sludge, plastic chemicals, etc., released to atmosphere if burnt in the
incinerators are avoided.
2. Reduction in sizes of flue gas handling equipment such as fans, stacks, ducts, and burners
since waste heat recovery reduces the fuel consumption, which leads to reduction in the
flue gas produced.
3. Reduction in energy consumption by auxiliary equipment due to reduction in equipment sizes.
6.1.5.3 Fuel Savings due to Preheating Combustion Air
Recuperators of high-temperature furnaces can provide and increase the process efficiency. Fuel
savings depends on parameters such as [5]
1. Exhaust gas temperature
2. Preheat combustion air temperature
3. Effectiveness of the recuperator
The higher the percentage of exhaust gas temperature, the higher the percentage of fuel that can
be saved. For a flue gas temperature of 1350°C and an air preheated temperature of 1100°C, the
theoretical fuel savings achievable is approximately 65% of fuel consumption of an unrecuperated
furnace operating at the same temperature levels.
6.2 HEAT EXCHANGERS USED FOR REGENERATION
The heat exchanger used to preheat combustion air is called either a recuperator or a regenerator.
Thermodynamically, the exhaust gas thermal energy is in part recuperated or regenerated, and this
same thermodynamic function is served regardless of the type of heat exchanger employed. The
thermodynamic principle of regeneration is discussed in the following.
6.2.1 Recuperator
A recuperator is a convective heat transfer-type heat exchanger where the two fluids are separated
by a conduction wall through which heat transfer takes place due to convection or a combination
of radiation and convective design. The fluids flow simultaneously and remain unmixed. There
are no moving parts in the recuperator. Some examples of recuperators are tubular, plate-fin,
and extended surface heat exchangers. Recuperators are used when the flue gas is clean and
uncontaminated. An integral bypass solution can be applied to the waste heat recovery units. The
system consists of louvre-type dampers, which can be either pneumatic actuated or hydraulic
operated depending on individual customer requirements. The gas flow over the heat convection
bank is modulated depending on the outlet fluid temperature. A convective recuperator is shown
in Figure 6.2.
6.2.1.1 Merits of Recuperators
The recuperators have the advantages of (1) ease of manufacture, (2) stationary nature, (3) uni-
form temperature distribution and hence less thermal shock, and (4) absence of sealing problem.
However, their use is limited due to the requirement of temperature-resistant material to withstand
the high-temperature flue gas and to retain its shape under operating temperature and pressure.
Also, recuperators are subject to degradation in heat recovery performance by fouling from exhaust-
gas-borne volatiles and dust.

6.2.2 Regenerator
A regenerator consists of a matrix through which the hot stream and cold stream flow periodically
and alternatively. First the hot fluid gives up its heat to the regenerator. Then the cold fluid flows
through the same passage, picking up the stored heat. The passing of hot fluid stream through a
matrix is called the hot blow and the cold flow is called the cold blow. Thus, by regular reversals,
the matrix is alternatively exposed to the hot and cold gas streams, and the temperature of the
packing, and the gas, at each position fluctuates with time. Under steady-state operating condi-
tions, a number of cycles after the start-up of the regenerator, a condition of cyclic equilibrium is
reached where the variations of temperature with time are the same during successive cycles and
the period of hot blow and the cold blow should ensure sufficient time to absorb and release heat.
From this, the regenerators can be distinguished from recuperators. In the case of recuperators,
heat is transferred between two fluid streams across some fixed boundary, and conditions at any
point depend, during steady-state operation, only on the position of that point, whereas in the case
of regenerators, the heat transport is transient and conditions depend on both position and time.
Figure 6.3 shows the temperature field in a regenerator, for both the fluid and matrix at the instant
of flow reversal. The upper curve represents the temperature of the fluid and matrix at the end of
the hot blow and the start of the cold blow. The lower curves represent temperature conditions at
the end of the cold blow and the start of hot blow. At any particular station along the length of the
matrix, the temperatures may fluctuate between the upper and lower curves in a time-dependent
relationship.
6.2.3 Types of Regenerators
Since the matrix is alternatively heated by the hot fluid and cooled by the cold fluid, either the
matrix must remain stationary and the gas streams must be passed alternatively or the matrix must
be rotated between the passages of the hot and cold gases. Hence, the regenerator may be classi-
fied according to its position with respect to time as (1) fixed-matrix or fixed-bed and (2) rotary
regenerators.
FIGURE 6.2 Waste heat recovery recuperative heat exchanger. (Courtesy of GEA Iberica S.A., Vizcaya, Spain.)

341Regenerators
6.2.4 Fixed-Matrix or Fixed-Bed-Type Regenerator
The fixed-matrix or fixed-bed or storage-type regenerator is a periodic-flow heat transfer device
with high thermal capacity matrix through which the hot fluid stream and cold fluid stream pass
alternatively. To achieve continuous flow, at least two matrices are necessary as shown in Figure 6.1.
The flow through the matrix is controlled by valves. According to the number of beds employed,
the fixed matrix regenerators are classified into two categories: (1) single-bed and (2) dual-bed
valved. In a dual-bed valved type, shown in Figure 6.4, initially matrix A is heated by the hot fluid
.1
.1
.2
.3
.4
.5
.6
.7
.8
1.0
0
0
.2 .3 .4 .5 .6 .7 .8
Flow length (X*)
(Th*, out) ave
Flow length
T*=Temperature
Th*
δc*
δh*
η
=
Phη=
Pc
(Tc*, out) ave
Tc*
Tm*
II* = 1/Cr/Cmin
(c)
(d)
(b)
(a) Ntu0 =10 hA*=1
Cr/Cmin=5 Cmin/Cmax=1
λ tot=0
rl r0
Temperature(T*)
.9 1.0
x*=
x
L
T– Tc, I
Th,I – Tc, I
FIGURE 6.3 Balanced regenerator temperature distribution at switching instants. (a) Hot fluid tempera-
ture at end of the hot blow; (b) matrix temperature at end of the hot blow and start of the cold blow, (c) hood
arrangements and (d) matrix temperature at the end of the cold blow; and (d) cold fluid temperature at the end
of cold blow. (From Mondt, J.R., Trans. ASME J. Eng. Power, 86, 121, 1964.)
Hot fluid Cold fluid
Cold fluid
Th2 Tc1
Tc2
BA
Hot fluid
Matrix
Th1
FIGURE 6.4 Dual-bed valved-type regenerator. (Adapted from Mondt, J.R., Regenerative heat exchangers:
The elements of their design, selection and use, Research Publication GMR-3396, General Motors Research
Laboratories, Warren, MI, 1980.)

and matrix B is cooled by the cold fluid. After a certain interval of time, the valves are operated
so that the hot fluid flows through B and transfers heat to it. Cold fluid, however, flows through
A and the fluid is being heated. The switching process continues periodically. Some examples of
storage-type heat exchangers are fixed-bed air preheaters for blast furnace stoves, glass furnaces,
and open hearth furnaces.
Shape: The shape of matrix used for the construction of a fixed-matrix regenerator is depen-
dent upon the application. For example, in the glass-making industry, the matrix is often con-
structed from ceramic bricks arranged in patterns such as pigeonhole setting, closed basket
weave setting, and open basket weave setting. In the steel-making industry, the gases are much
cleaner and a variety of proprietary configurations such as Andco checkers, McKee checkers,
Kopper checkers, and Mohr checkers are used in place of the brick arrangements. Most of these
types of checkers employ tongue-and-grove shapes, which provide a bonded structure of higher
stability, because regenerators in the steel-making industry are normally much taller than in the
glass industry.
Construction features: A fixed regenerator is generally constructed of either a porous matrix or
checkers. The porous matrix forms a long, tortuous path for the flowing fluid in order to provide the
largest possible contact surface between the regenerator matrix and the fluid. Checkers are blocks
with holes pierced through them. Additional details on checkers and settings are given next.
Checkers: Checkers are the tools of heat recovery; they consist of a large quantity of bricks prop-
erly arranged in an orderly setting creating many small flues and offering a large surface area for
heat absorption and release. The design of the brick, their proper setting, and flow of turbulent gases
in the flues are the keys to efficient heat recovery.
Settings: The development of special strapped bricks and their setting in checkers potentially
yield higher efficiencies through improved heat transfer features. The open basket weave setting has
been popular in the glass industry. The brick checkers geometry commonly used in the valved-type
glass furnace regenerator are essentially an offset strip fin having a large fin thickness.
6.2.4.1 Fixed-Matrix Surface Geometries
Noncompact surface geometry: The commonly used checker shapes have a surface area density
range of 25–42 m2/m3 (8–13 ft2/ft3). The checker flow passage (referred to as flue) size is relatively
large primarily due to the fouling problem. A typical heat transfer coefficient in such a passage is
about 5 W/m2 K (1 Btu/h ft2°F) [3].
Compact surface geometry: The surface geometries used for the compact fixed-matrix regenerator
are similar to those used for rotary regenerators, but in addition quartz pebbles, steel, copper, or lead
shots, copper wool, packed fibers, powders, randomly packed woven screens, and crossed rods are used.
6.2.4.2 Size
The fixed-bed regenerators are usually very large heat exchangers, some having spatial dimensions
up to 50 m height and having unidirectional flow periods of many hours.
6.2.4.3 Merits of Fixed-Bed Regenerators
Fixed-bed regenerators consisting of a packed bed of refractory offer the following inherent
advantages:
1. If loosely packed, the bed material is free to expand thermally; hence, thermal stresses
are low.
2. Regenerators of this type are easily equipped so that the bed materials can be removed,
cleaned, and replaced.
3. Unlike a recuperator, accumulated fouling does not reduce the heat exchanger capability of
a regenerator; it merely increases the resistance to flow [6].

343Regenerators
The major disadvantages of fixed-bed regenerators are the additional complexity and cost associ-
ated with the flow-switching mechanisms.
6.2.5 Rotary Regenerators
A rotary regenerator (Figure 6.5), also known as heat wheel, consists of a rotating matrix through which
the hot and cold fluid streams flow continuously. The rotary regenerator is also called a periodic-flow
heat exchanger since each part of the matrix, because of its continuous rotation, is exposed to a regular
periodic flow of hot and cold gas streams. The rotary regeneration principle is achieved by two means:
(1) the flow through the matrix is periodically reversed by rotating the matrix, and (2) the matrix is
held stationary whereas the headers are rotated continuously. Both the approaches are rotary because
for either design approach, heat transfer performance, pressure drop, and leakage considerations are
the same, and rotary components must be designed for either system. The examples for rotary regen-
erators are (1) the Rothemuhle type and (2) the Ljungstrom type. In the Rothemuhle type, the connect-
ing hood rotates while the heat transfer matrix is stationary (Figure 6.5c(ii)), whereas in Ljungstrom
type the matrix rotates and connecting hood is stationary (Figure 6.5c(i)). The rotary regenerators are
also used in vehicular gas turbine engines and as a dehumidifier in HVAC applications.
6.2.5.1 Salient Features of Rotary Regenerators
The periodic flow rotary regenerator is characterized by the features such as those given in the
following:
1. A more compact size (β = 8800 m2/m3 for rotating type and 1600 m2/m3 for fixed matrix
type), shape, desired density, porosity, and low hydraulic diameter can be achieved by
pressing the metal strips, wire mesh, or sintered ceramic and hence less expensive surface
per unit transfer area.
2. The porous matrix provides a long, tortuous path and hence large area of contact for the
flowing fluids.
3. The absence of a separate flow path like tubes or plate walls but the presence of seals to
separate the gas stream in order to avoid mixing due to pressure differential.
4. The presence of moving parts like the rotary core in rotary regenerators and alternate clos-
ing and opening of valves in a fixed regenerator.
5. With rotary regenerators, high effectiveness can be obtained since the matrix can be heated
up to nearly the full exhaust gas temperature.
6. To achieve very high thermal effectiveness approaching unity, the thermal capacity of the
matrix should be very large compared to the working fluids. This requirement restricts the
use of regenerators exclusively to gaseous applications.
7. Bypass leakage from the high-pressure cold stream to the low-pressure hot stream and car-
ryover loss from one stream to the other with flow reversal or rotary nature of the matrix.
However, the bypass leakage problem is less in a dehumidifier for an air-conditioning
application.
8. Application to both high temperatures (800°C–1100°C) for metal matrix, and 2000°C for
ceramic regenerators for services like gas turbine applications, melting furnaces or steam
power plant heat recovery, and cryogenic applications (–20°)
9. Operating pressure of 5–7 bar for gas turbine applications and low pressure of 1–1.5 bar for
air dehumidifier and waste heat recovery applications.
10. Regenerators have self-cleaning characteristics because the hot and cold gases flow in the
opposite directions periodically through the same passage. As a result, compact regenera-
tors have minimal fouling. If heavy fouling is anticipated, regenerators are not used.
11. Normally a laminar flow condition prevails, due to the small hydraulic diameter.

(c) (i) (ii)
Fixed
inlet hood
Movable
hood
Movable
hood
Stationery
matrix
Rotary
matrix
Cold fluid
Cold fluid
Axial flow
Radial flow
Hot fluid
(a)
Hot fluid
(b)
Cmax
Cmax
Cmin
Cmin
Typical
element
Typical
element
K =0
K =∞ K=∞
K=0
K =∞
FIGURE 6.5 Rotary regenerator. (a) Disk and drum type (From Coppage, J.E. and London, A.L., Trans.
ASME, 75, 779, 1953), (b) illustrative arrangement of matrix (From Bahnke, G.D. and Howard, C.P.,
Trans. ASME J. Eng. Power, 86, 105, 1964), and (c) two alternative forms of disk-type rotary regenerator:
(i) Ljungstrom type and (ii) Rothemuhle type.

345Regenerators
6.2.5.2 Rotary Regenerators for Gas Turbine Applications
One of the important areas of rotary regenerator applications is in vehicular gas turbine engines.
Starting in the 1950s, the vehicle industry intensively researched gas turbine power plants, which
included rotary regenerators. Both disk and drum regenerators were developed by General Motors
and other vehicle builders for gas turbine engines. Their engine programs significantly advanced all
facets of regenerator technology such as improved modeling, heat transfer surfaces for the matrix,
sealing designs, and materials, both metals and ceramics [2].
6.2.5.3 Types of Rotary Regenerators
Though two types of rotary regenerators—(1) disk and (2) drum types (shown in Figure 6.5a)—the
most commonly used configuration is of disk type. The disk-type matrix consists of alternate lay-
ers of corrugated, flat, thin metal strips wrapped around a central hub or ceramic pressing in a
disk shape. Gases flow normal to the disk. In an ideal circumstance without maldistribution, the
single-disk design is favored due to less seal length and lower seal leakage. Depending upon the
applications, disk-type regenerators are variously referred to as heat wheel, thermal wheel, Munter
wheel, or Ljungstrom wheel. The schematic of disk-type rotary regenerator with ducts is shown in
Figure 6.5c. The drum-type matrix consists of heat exchanger material in a hollow drum shape.
Gases flow radially through the drum. The cost of fabricating a drum-type regenerator is much
higher than that for a disk-type regenerator, and hence the drum is not used in any applications.
6.2.5.4 Drive to Rotary Regenerators
The matrix in the regenerator is rotated by a hub shaft or a peripheral ring gear drive. Most ceramic
regenerators have been driven at the periphery, probably because of their brittleness.
6.2.5.5 Operating Temperature and Pressure
The regenerators are designed to cover an operating temperature range from cryogenic to very high
temperatures. Metal regenerators are used for operating temperatures up to about 870°C (1600°F).
Ceramic regenerators are used for higher temperature, up to about 2000°C (3600°F). Regenerators
are usually designed for a low-pressure application. Rotary regenerators are limited to operating
pressures about 615 kPa or 90 psi and even lower pressures for fixed-matrix regenerators.
6.2.5.6 Surface Geometries for Rotary Regenerators
The rotary regenerator surfaces consist of many uninterrupted passages in parallel. The most com-
mon are triangular, rectangular, circular, or hexagonal smooth continuous passages. Details on the
foregoing surface geometries are provided in Ref. [2]. Interrupted passage surfaces (such as strip
fins, louver fins) are not used because a transverse flow leakage will be present if the two fluids are
at different pressures. Hence, the matrix generally has continuous, uninterrupted flow passages and
the fluid is unmixed at any cross section for these surfaces. Some surface geometries for rotary
regenerator are shown in Figure 6.6.
6.2.5.7 Influence of Hydraulic Diameter on Performance
Packings having small hydraulic diameter will provide the highest heat transfer coefficients; for
laminar flow, h ∝ 1/Dh. However, the associated fouling by the hot gas may limit the size of the
flow passages. Very small passage size may be used in air ventilation heat recovery regenerators
compared to in those used for exhaust gas heat recovery, particularly from coal-fired exhaust
gases or glass furnace exhausts. As passage size is reduced, the number of passages required
increases, while the passage length must decrease if the pressure drop is to be maintained con-
stant. The conventional shell and tube heat exchanger cannot exploit this characteristic very far
as a large number of small tubes introduce fabrication difficulties and short tube lengths prevent
the use of counterflow.

6.2.5.8 Size
Typical power-plant regenerators have the rotor diameter up to 10 m (33 ft) and rotational speeds in
the range of 0.5–3 rpm. The air ventilating regenerators have the rotors with 0.25–3 m (0.8–9.8 ft)
diameters and rotational speeds up to 10 rpm. The vehicular regenerators have diameters up to
0.6 m (24 in.) and rotational speeds up to 18 rpm [3].
6.2.5.9 Desirable Characteristics for a Regenerative Matrix
Desirable characteristics of a regenerator matrix include the following [7]:
1. A large and solid matrix, for maximum heat capacity.
2. A porous matrix without obstruction, to minimize the possible blocking and contamination.
3. A large, finely divided matrix, to achieve maximum heat transfer rate.
4. A small, highly porous matrix, for minimum flow losses.
5. A small, dense matrix, for minimum dead space.
Other desirable matrix properties include negligible thermal conduction in the direction of fluid
flow, to minimize longitudinal conduction, and maximum specific heat, for high thermal capacity.
6.2.5.10 Total Heat Regenerators
Up to this point, consideration has only been given to the transfer of sensible heat between two fluid
streams and the intermittent storage of thermal energy, as sensible heat, in a solid matrix. A num-
ber of variations on these conditions are possible; for example, rotary regenerators are designed to
(a) (b)
10 nm
(c)
FIGURE6.6 Surfacegeometriesforrotaryregeneratormatrix.(a)Nonuniformcomplexprofile,(b) rectangular,
and (c) triangular. (From Mondt, J.R., Regenerative heat exchangers: The elements of their design, selection and
use, Research Publication GMR-3396, General Motors Research Laboratories, Warren, MI, 1980.)

347Regenerators
transfer both sensible heat and latent heat of vapors mixed with the gas stream, known as total regen-
erators. They are intended mainly for air-conditioning applications and can employ both absorbent
fibrous materials and nonabsorbent materials like plastics.
6.2.5.11 Merits of Regenerators
Among their advantages, regenerators
1. Can use compact heat transfer materials
2. Can use less expensive heat transfer surfaces
3. Are self-cleaning because of periodic flow reversals
4. Can use simpler header designs
In contrast, there are several major disadvantages of the periodic flow regenerators. They are
as follows:
1. Seals suitable for pressure differentials of 4–7 bar represent a major problem; the neces-
sity of provision of seals between the hot fluids due to high-pressure differential, and
the leakage problem enhanced due to the thermal expansion and contraction of the
matrix.
2. Many more changes of flow direction are required as compared to the recuperators, result-
ing in flow losses and requiring expensive ducting.
3. Restrictions in pressure drop make necessary a large flow area with the usual matrix sur-
face. As a consequence, the advantage of small matrix volume is somewhat nullified by the
requirement of bulky approach ducting.
4. Carryover and leakage losses, especially for the high-pressure compressed air that has
absorbed the compressor work.
5. Always some amount of mixing of the two fluids due to carryover and bypass leakages.
Where this leakage and subsequent fluid contamination is not permissible (e.g., cryogenic
systems), the regenerator is not used.
6. The high thermal effectiveness, approaching unity, provided by the regenerator demands a
heat capacity of the matrix considerably larger than that of the working fluid. This require-
ment restricts the use of regenerators to gases only.
7. The rotary designs require a drive and support system.
6.3 ROTARY REGENERATIVE AIR PREHEATER
An air preheater is a general term used to describe any heat transfer device designed to heat air
before it is used in another process, for example, combustion in a boiler. Air preheaters may also be
used as process gas heat exchangers, which recover waste heat from one gas stream and use it to heat
or preheat another. Available in a broad range of sizes, arrangements, and materials, Ljungström®
rotary regenerative air preheater finds applications in electrical power generating plants, fluidized
bed boilers, large industrial boilers, hydrocarbon and chemical processes, waste incinerators and
drying systems, flue gas and other reheating systems, etc., due to its high thermal effectiveness,
proven performance and reliability, effective leakage control, compactness of its design, and its
adaptability to various fuel burning process. Construction types of regenerative air preheaters
include traditional two sector type, three sector, four sector, and concentric types. A picture of
Howden air preheater is shown in Figure 6.7. Air preheaters and gas-to-gas heat exchangers func-
tion similarly. Regenerative gas–gas heater is a special type of regenerative heater by design and
material, and it is adapted to hard conditions of power plant desulphurization. Leading air preheater
manufacturers include Howden, UK, ALSTOM Power Air Preheater Company and Balcke-Dürr
GmbH, Germany. Salient features of air preheater are discussed later.

6.3.1 Design Features
Metallic heat transfer surfaces are contained in the rotor that turns at 1–3 rpm, depending on the
size of the unit. A typical rotor under refurbishment is shown in Figure 6.8. The rotor housing and
rotor have sealing members to form separate gas and air passages through the heat exchanger. The
rotor drive unit, cleaning device mechanism, rotor bearing assemblies, and sealing surface adjuster
FIGURE 6.7 Picture of air preheater. (© Howden Group Limited.)
FIGURE 6.8 Refurbishment of air preheater rotor matrix. (© Howden Group Limited.)

349Regenerators
are all located externally and are readily accessible while the unit is in operation. The overall design
of the rotary regenerative heat exchanger lends itself to modularization. This helps reduce the time
and effort required for on-site erection and maintenance.
6.3.2 Heating Element Profiles
The selection of the optimum heat transfer surface configuration for each application results in the
highest level of thermal efficiency for the available pressure drop, which is cleanable and otherwise
compatible with the fuel that is being fired. With a range of individual profiles, simple “open” pro-
files that have a lower tendency for fouling but correspondingly lower heat transfer properties to
more complex profiles which are more compact and induce turbulence in the gas flow to improve
heat transfer. The choice of heating element is vital to ensure that the optimum combination of heat
transfer and pressure drop is achieved. Few profiles of heating elements are shown in Figure 6.9.
6.3.3 Enameled Elements
In applications where heat transfer surfaces are exposed to highly corrosive atmospheres and low
exit gas temperatures, alloy steels or porcelain enamel coatings can be utilized. Selective enameled
heat exchanger elements of Howden make are shown in Figure 6.10. It was found that porcelain
enamel coatings are the most cost-effective means of providing an extremely high level of acid
resistance for this application. Additionally, this enamel coating has been found to provide a highly
smooth glass-like surface, more readily facilitating the cleaning of ash deposits.
6.3.4 Corrosion and Fouling
All air preheaters on coal- and oil-fired plants are subject to some degree of corrosion and foul-
ing caused by the approach to either the sulfuric acid or water dew point. Cold end fouling can be
caused by the high sulfur content in the fuel oil in combination with very low combined cold end
temperatures or due to insufficient ash in the flue gas to absorb the condensing acid formed from
the sulfur in the fuel. Cold end corrosion can be minimized by the use of a cold end layer of higher
grade steel or enamel coating. Hot end elements are prone to fouling as a result of large particles of
fused ash becoming lodged in the element passages and smaller particles compacting behind them.
These large particles generally arise as a result of less than optimum combustion conditions in the
furnace. This can be overcome by the use of an element profile that is less prone to fouling and
easier to clean and/or by the installation of hot end soot blowers.
6.3.5 Heat Exchanger Baskets
Baskets are designed and manufactured to ensure that the elements remain tightly packed to avoid
damage caused by vibration while the air preheater or gas–gas heater is operating. A typical heat
exchanger basket of Howden air preheater is shown in Figure 6.11.
FIGURE 6.9 Regenerator heating elements profile.

6.3.6 Seals and Sealing System Components
6.3.6.1 Radial Seals and Sector Plates
Radial seals and sector plates are located at the hot and cold ends of the air preheater. The radial
seals that separate the individual rotor compartments, and as the rotor turns the seals pass in close
proximity to the sector plates located between the air and gas sides of the air preheater. The purpose
of these seals is to reduce the area available for leakage from the air to the gas side between the rotor
and the air preheater housing.
FIGURE 6.10 Enameled elements of rotary regenerative heat exchanger. (© Howden Group Limited.)
FIGURE 6.11 Rotary regenerator heat exchanger elements basket. (© Howden Group Limited.)

351Regenerators
6.3.6.2 Axial Seals and Sealing Plates
Axial seals, used in conjunction with bypass seals, minimize leakage passing radially around the
rotor shell. The axial seals are mounted on the outside of the rotor shell and seal against the axial
seal plates mounted on the air preheater housing.
6.3.6.3 Circumferential Seals and Circumferential Sealing Ring
Circumferential seals are mounted on the rotor and the sealing ring connected to the housing.
The circumferential seals and sealing ring prevent air and gas from bypassing the heating surface
through the space between the rotor and the housing shell. They also prevent air and gas from flow-
ing axially around the rotor.
6.3.7 Leakage
Air preheaters suffer from leakage drift, i.e., the significant increase in leakage over a period of
time. This can affect boiler operation in a number of ways, such as increasing fan power, increas-
ing velocities in the precipitators, reducing the flow of hot air to the mills, or shrinking the draught
fan margins. Hence, reducing and maintaining low air preheater leakage is vital for the overall
performance of the thermal system. Seals can wear due to soot blowing, corrosion, erosion, and
contact with the static sealing surfaces on start-up and/or shutdown. Seal wear and seal settings
should be checked as per schedule so that seals can be reset to proper clearances or replaced should
they exhibit excessive wear. Sealing plate surfaces may also wear due to contact with the seals and
erosion, and they may also become out of level and out of plane. Seal plate wear should also be
repaired, plate alignments should be verified as soon as the need is detected. By fitting the sealing
as that of Howden VN sealing system, these problems can be reduced or eliminated. Figure 6.12
shows computer model of Howden VN air preheater. The system improves the seal design on both
the rotor and the casing, and dispenses with the need for actuated sector plates. In addition to better
heat recovery and improved thermal performance, a peripheral benefit of using the Howden VN
sealing system is a reduction in maintenance requirements on the air preheater.
6.3.8 Alstom Power Trisector Ljungström® Air Preheater
Designed for coal-fired applications, the Alstom Power trisector Ljungström® air preheater permits
a single heat exchanger matrix to perform two functions: coal drying and combustion air heating.
Because only one gas duct is required, the need for ductwork, expansion joints, and insulation
FIGURE 6.12 Computer model of Howden VN air preheater-ducting removed. (© Howden Group Limited.)

is greatly reduced when compared with a separate air heating system. Equipment layout is simpli-
fied, less structural steel is needed to install the system, and less cleaning equipment is required.
The design has three sectors: one for flue gas, the second sector for primary air that dries the coal
in the pulverizer, and the third sector is for preheating the secondary air that goes to the boiler
for combustion.
6.4 COMPARISON OF RECUPERATORS AND REGENERATORS
1. A recuperator is easier to build and rugged in design. For a given size, the recuperator
is less effective than the regenerator due to lower overall mean temperature difference.
The regenerator, on the other hand, is smaller and, for its size, a much more efficient heat
exchanger. Much higher surface area, higher heat transfer coefficients because of random
nature of flow through the packing, and a higher overall temperature difference as the top
of the packing is heated to the exhaust gas temperature [7] are found.
2. Because a recuperator is not rotating and is at a constant temperature, there is less thermal
shock and many normal materials can be used. Because of periodic flow, regenerators are
subjected to thermal shock.
3. A recuperator does not have the problem of sealing between the hot and cold gas
streams.
6.5 CONSIDERATIONS IN ESTABLISHING A HEAT RECOVERY SYSTEM
Although the addition of a regenerator is highly attractive from a thermodynamic point of view,
its bulk, shape, mass, or cost may be such as to nullify the thermodynamic advantages. Optimum
design therefore will call for a careful consideration of the following factors [4]:
1. Heat recovery—Quality and quantity
Quality: Depending upon the type of process, waste heat can be recovered at virtually
from that of chilled cooling water to high temperature waste gases from an industrial fur-
nace or kiln. Usually higher the temperature, higher the quality and more cost effective is
the heat recovery.
Quantity: In any heat recovery situation, it is essential to know the amount of heat recover-
able and also how it can be used.
2. Compatibility with the existing process [8].
3. Initial capital cost.
4. Economic benefits.
5. Life of the equipment.
6. Maintenance and cleaning requirement.
7. Controllability and production scheduling.
Other limitations include manufacturing limitations, and weight, space, and shape limitations.
6.5.1 Compatibility with the Existing Process System
In order for a heat exchanger to be integrated into a process, the system design must be compatible
with the process design parameters. One key area of compatibility is pressure drop. Many combus-
tion processes are designed to use the natural draft of a stack to remove the products of combustion
from the process. The heat recovery equipment designed for such a process either must be designed
within the pressure drop limitations imposed by natural draft or must incorporate an educator to
overcome these pressure-drop restrictions [8].

353Regenerators
6.5.2 Economic Benefits
It is necessary to evaluate the selected waste heat recovery system on the basis of financial analysis
such as investment, depreciation, payback period, fuel savings, rate of return, etc.
6.5.2.1 Capital Costs
The capital costs include the heat exchanger costs and the ancillary equipment required for the
functioning of the system. Such ancillary equipment includes the following:
Blowers: Both the flue gas and the preheat air streams would require blowers to overcome pres-
sure losses in the system.
Ducting: Ducting is between the furnace and the heat exchanger to conduit the flue gas and the
preheat air.
Controls: The proposed heat recovery system would be operated in conjunction with the demand
of the furnace. A control mechanism would be established for this purpose.
Energy savings: The benefits of energy savings due to the heat recovery system should offset the
capital costs on heat exchanger, blowers, ducting and control mechanisms, and maintenance cost.
A break-even analysis (capital costs vs. fuel savings) will help in this regard. The desired economic
benefits can be accomplished by designing a heat exchanger to [8]
1. Maximize the equipment life
2. Maximize the energy cost savings
3. Minimize the equipment capital costs
6.5.3 Life of the Exchanger
The success of waste heat recovery depends on the maximum equipment life against the hostile
environment of exhaust gases. The factors that affect the heat exchanger life are [8]
1. Excessive thermal stress
2. Creep
3. Thermal fatigue and thermal shock
4. High-temperature gaseous corrosion
Corrosion and stress cause accelerated failure in both metal and ceramic recuperators, resulting in
leakage, which degrades the performance.
6.5.4 Maintainability
Ideally, a heat exchanger should provide long service life and the equipment installation should
facilitate easy maintenance. Where necessary, the design should incorporate provisions to iso-
late the heat exchanger from the system so that inspection, maintenance, repairs, and replace-
ment can be made without interrupting the process, and the ability to clean the fouling deposits
from the heat transfer surfaces should be provided for those processes in which fouling will take
place [8].
6.6 REGENERATOR CONSTRUCTION MATERIAL
An important requirement of a regenerator for waste heat recovery is life and extended durabil-
ity. Regenerators are to work under hostile environments including (1) elevated temperatures,
(2) fouling particulates, (3) corrosive gases and particulates, and (4) thermal cycling [9]. To achieve

this requirement, proper material selection is vital. Much of the waste heat is in the form of high
temperature (1900°F–3000°F), and the exhaust gases are corrosive in nature. Therefore, the two
important considerations for selecting material for heat exchangers of a heat recovery system are
(1) strength and stability at the operating temperature, and (2) corrosion resistance. Other param-
eters include low cost, formability, and availability.
6.6.1 Strength and Stability at the Operating Temperature
Metals are ideal for recuperator and regenerator construction because of their ductility and ease
of fabrication. But the metallic units lack the ability to withstand high temperatures and are sus-
ceptible to corrosion from exhaust gases. Stainless steels and certain nickel- and iron-based alloys
are the conventionally preferred materials. Generally, carbon steel at temperatures above 425°C
(800°F) and stainless steel at temperatures above 650°C (1200°F) begin to rapidly oxidize, and
if the exhaust stream contains corrosive constituents, there will be a severe corrosion attack [10].
Approximate temperature ranges for various heat exchanger materials are shown in Figure 6.13 [11].
In general, above 1600°F, metal heat exchangers have limitations due to excessive costs from the
expensive alloys required, requirements of temperature control devices or loss of effectiveness due
to air dilution, and maintenance problems due to high thermal stresses [12]. In some cases, the high-
temperature problem is overcome by diluting the flue gas with a portion of cold air to be preheated.
However, dilution lowers the heat transfer from the flue gas stream.
Cryogenic
applications
Automotive
radiator
Aircraft
liquid-to-
liquid and
liquid-to-air
heat
exchangers
Titanium heat
exchangers
used in
chemical
process plant
Heat exchanger regime
Automotive, industrial and aircraft
Gas
turbine
recuperator
Regime
High temperature heat
Recovery regime
utilizing ceramic exchangers
Silicon carbide
and silicon nitride
Carbon-carbon
composites
Gas
turbine
recuperator
Aluminum
aircraft
air-to-air
exchangers
Stainless
steels
Heatexchangermaterialspecificstrength
Titanium
Temperature (°C)
Temperature (°F)
Aluminum
Copper
0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
954°C
1750°F
100 200 300 400 500 600 700 800 900 1000
Super-
alloys
Advanced gas
turbine recuperator
IHX for nuclear
process heat plant
(VHTR)
Reformers in
petrochemical
plants
Upper limit for practical metallic
heat exchanger design
Heat
resistant
cast
alloys
FIGURE 6.13 Approximate temperature range for various heat exchanger materials. (From McDonald, C.F.,
Trans. ASME J. Eng. Power, 102, 303, 1980.)

355Regenerators
6.6.2 Corrosion Resistance
Materials for high-temperature heat exchangers should exhibit high-temperature gaseous and liquid cor-
rosion resistance to the carburizing, sulfidizing, oxidizing, and other effects of combustion products, and
to the coal ash slag and fuel impurities. Regenerators used for heat recovery from the gases generated by
boiler, furnaces, heaters, etc., should be protected against “cold end corrosion” caused by condensation of
sulfuric acid and water on the heat transfer surface and the volatiles and corrosive fluxes in the exhaust gas.
This problem is overcome either by ceramic units or with the use of the porcelain enameled exchanger.
6.6.3 Ceramic Heat Exchangers
Ceramic units can be very cost effective above 1600°F since they have the potential for greater resistance
to creep and oxidation at very high temperatures, and do not require temperature controls or air dilu-
tion because of their high melting points [12]. At present, a ceramic heat exchanger is probably the most
economical solution for high temperature in excess of 800°C (1475°F) applications where the specific
strength of metallic materials decreases very rapidly. The ceramic recuperators are available as plate-fin
and bayonet tube exchangers. Material properties that favor ceramic as regenerator materials are
Moderate strength, generally inexpensive, high thermal shock resistance and lower high tem-
perature creep, good corrosion resistance, and excellent erosion resistance properties.
Low thermal expansion characteristics; this simplifies the sealing problem. About one-fifth the
density of steel, high specific heats, and higher thermal conductivity.
6.6.3.1 Low Gas Permeability
The inability to join ceramic shapes reliably, once the parts have been densified, is a serious impedi-
ment to the design of large assemblies such as heat exchangers. Among the other drawbacks, the
application of ceramic materials in recuperators is limited by the inherent brittleness, the higher
fabrication costs associated with producing ceramic heat exchangers, and the low thermal conduc-
tivity of many oxide ceramics [13]. According to McNallan et al. [13], because of their higher ther-
mal conductivities and corrosion resistance compared with other ceramics, silicon carbide-based
ceramics have received the most attention as heat exchanger materials.
6.6.4 Ceramic–Metallic Hybrid Recuperator
To overcome the high-temperature heat recovery problem, a ceramic-metallic hybrid recuperator is
used. It consists of a ceramic recuperator operating in series with a conventional plate-fin metallic
recuperator. An air dilution system is employed between the two recuperators to overcome the high-
temperature oxidation problem of the metallic recuperator. This system is capable of handling flue
gas temperatures up to 1370°C (2520°F).
6.6.5 Regenerator Materials for Other than Waste Heat Recovery
The regenerator construction materials used for applications other than waste heat recovery are
discussed by Shah [3]. They include the following:
1. In the air-conditioning and industrial process heat recovery applications, rotary regenera-
tors are made from knitted aluminum or stainless steel wire matrix.
2. For cryogenic applications, ordinary carbon steels become brittle, so materials such as
austenitic stainless steels, copper alloys, certain aluminum alloys, nickel, titanium, and a
few other metals that retain ductility at cryogenic temperatures must be used. Cryogenic
materials are covered in the chapter on material selection and fabrication (Chapter 13).
3. Plastics, paper, and wool are used for regenerators operating below 65°C (150°F).

6.7 THERMAL DESIGN: THERMAL-HYDRAULIC FUNDAMENTALS
6.7.1 Surface Geometrical Properties
A consistent set of geometry-related symbols and factors facilitates comparative studies. The fol-
lowing factors can be used for all geometries, either bluff or laminar [2].
1. Porosity, σ = void volume/total volume
2. Area density, β = surface area/total volume
3. Hydraulic radius, rh = flow area/wetted perimeter = σ/β
4. Flow area, Ax = porosity × frontal area = σAfr
5. Cell density, Nc = number of holes or cells per unit frontal area
Reference [2] presents these surface geometrical factors for several surface geometries—square,
hexagonal, circular, rectangular, and triangular and the same is given in Table 6.1. The surface
geometrical properties, Dh (4rh), L (flow length), σ, and β are the same on both fluid sides. They are
related to each other as follows:

D
A L
A
A
A D
h
o o
fr h
= = = =
4 4 4σ
β
σ β
σ
,

(6.1)
TABLE 6.1
Surface Geometrical Properties for Rotary Regenerators Matrix
Cell Density
Nc (Cells/ln2) Porosity por
Area Density
β (1/m)
Hydraulic
Radius rh (m)
b
— 0.37–0.39 6 1( )− p
b
or b p
p
( )
( )
or
or6 1−
bδ
1
2
( )b + δ
b
b
2
( )+ δ 2
4
2
b
b( )+ δ
b
4
δ1
b
2
3 2
( )b + δ
b
b
2
2
( )+ δ
4
2
b
b( )+ δ
b
4
δ
b
2
3 2
( )b + δ
π
δ
b
b
2
2
2 3( )+
2
3 2
π
δ
b
b( )+
b
4
δ
bb/6
1
6
b
b+



 +δ δ( )
b
b
b
2
6
6
/
+



 +δ δ( )
7 3
6
b
b
b
/
+



 +δ δ( )
b
14
δ
b
60°
4 3
2 3 2
( )b + δ
4
2 3
2
2
b
b( )+ δ
24
2 3 2
b
b( )+ δ
b
6

357Regenerators
If the frontal area is not 50% for each fluid, the disk frontal area, minimum free flow area, and
heat transfer area on each side will not be the same. The method to calculate frontal area and
heat transfer surface area on the hot and cold sides, area for longitudinal conduction, and mass is
described by Shah [14], and various parameters are explained as per Shah’s method. If the flow
area ratio split for both fluids is in the ratio x:y, where x + y = 1, and if the face seal and hub cover-
age are specified as a% of the total face area Afr,t, then the frontal areas on each side, namely, Afr,h
and Afr,c, are given by

A D d A A
a
fr t fr fr,t, ( )= − = −




π
4
1
100
2 2

(6.2)

A
x
x y
A A
y
x y
Afr,h fr fr,c fr=
+
=
+
(6.3)
where
Afr = Afr,h + Afr,c
D is the regenerator disk outer diameter at the end of the heat transfer surface
d is the hub diameter
The effective total volume of the regenerator is given by

V A A L= +( )fr,h fr,c

(6.4)
With the known porosity σ, the minimum free flow area on each side is calculated from Ao = σAfr.
The heat transfer surface areas on the hot and cold sides are given by

A
x
x y
V A
y
x y
Vh c=
+
=
+
β β

(6.5)
The matrix mass Mr is calculated from the following equation for known matrix material density, ρr:

M V A Lr r r fr,1= − = −ρ σ ρ σ( ) ( )1 1
(6.6)
6.7.2 Correlation for j and f
For j and f values of commonly used surface geometries, refer to Mondt [2] and Kays and London
[15]. Basic heat transfer and flow friction design data are presented for three straight, triangular-
passage, glass ceramic heat exchanger surfaces in London et al. [16]. These surfaces have heat
transfer area density ratios ranging from 1300 to 2400 fr2/ft3 corresponding to a passage count of
526 to 2215 passages/in.2 Table 6.2 provides a comparison of the surface geometrical characteris-
tics. Figure 6.14 provides a description of the idealized triangular geometry used to calculate Dh
and α. Glass ceramic heat exchangers are of importance to vehicular gas turbine technology as they
give promise of allowing low mass production costs for the high-effectiveness rotary regenerator
required for most of the vehicular turbine engine concepts now under development.
If manufacturing tolerances are controlled as specified, the recommended j factor for Re 1000
is given by

j =
3 0.
Re
(6.7)

This is approximately 10% lower than the theory to allow for some passage nonuniformity (±20%
of flow area).
The recommended j factor for Re 1000 is given by

j =
14 0.
Re
(6.8)
This is 5% higher than the theory to allow a small margin for the walls and the variation of passage
cross section along flow length.
6.8 THERMAL DESIGN THEORY
The thermal design theory of recuperators is simple and quite straightforward. The effectiveness-
number of transfer units (ε-NTU) method is used to analyze heat transfer in recuperators. In con-
trast, the theory of the periodic-flow-type regenerator is much more difficult. Despite the simplicity
of the differential equations under classical assumptions, their solution has proved to be challeng-
ing, and performances of counterflow regenerators have been widely investigated numerically as
well as analytically [17]. Various solution techniques have been tried for solving the thermal design
problem, and they are discussed here.
TABLE 6.2
Surface Geometrical Properties for Triangular
Geometry Glass Ceramic Heat Exchangers
Core Description/Case No. 505A 503A 504A
Passage count, Nc 526 1008 2215
Number/in.2
Porosity, σ 0.794 0.708 0.644
Hyd. diam., Dh, 10−3 ft 2.47 1.675 1.074
Area density, α ft2/ft3 1285 1692 2397
Cell height/width, d* 0.731 0.709 0.708
L/Dh 101 149.5 233
Source: London, A.L. et al., Trans. ASME J. Eng. Power, 92A,
381, 1970.
d
a
c
FIGURE 6.14 Idealized triangular geometry for glass ceramic heat exchanger. (From London, A.L. et al.,
Trans. ASME J. Eng. Power, 92A, 381, 1970.)

359Regenerators
6.8.1 Regenerator Solution Techniques
For the steady-state behavior of a regenerator, Nusselt [18] has given an exact solution, which con-
sists of an infinite series of integrals. However, this solution is complicated for practical purposes,
and hence several solution techniques were developed. They are
1. Approximate solution methods by simplifying the parameters defining the regenerator
behavior; examples include Hausen’s [19] heat pole method, which approximates the inte-
gral equation for the initial temperature distribution of the matrix. Hausen expressed the
performance result in terms of two dimensionless parameters called the reduced length
and the reduced period.
2. Empirical effectiveness relation correlated by treating the regenerator by an equivalent
recuperator, e.g., that of Coppage and London [20].
6.8.1.1 Open Methods: Numerical Finite-Difference Method
Prior to the availability of general-purpose digital computers, regenerator thermal behavior
was analyzed by restricting the range of parameters. With the availability of digital computers,
Lamberston [21], Bahnke and Howard [22], Mondt [23], and Chung-Hsiung Li [24], among others,
used a numerical finite-difference method for the calculation of the regenerator thermal effectiveness.
In this approach, the regenerator and the gas streams are represented by two separate but dependent
heat exchangers with the matrix stream in crossflow with each gas stream as shown in Figure 6.15.
6.8.1.2 Closed Methods
In the closed methods, the reversal condition is implicitly incorporated in the mathematical model
for solving the differential equations both for the hot period and the cold period. The closed meth-
ods used to solve the Nusselt integral equation are
1. Collocation method of Nahavandi and Weinstin [25] and Willmott and Duggan [26]
2. Galerkin method of Baclic [17] and Baclic et al. [27]
3. Successive integral method (SIM) of Romie and Baclic [28]
6.8.2 Basic Thermal Design Methods
For design purposes, a regenerator is usually considered to have attained regular periodic flow
conditions. The solution to the governing differential equations is presented in terms of the regen-
erator effectiveness as a function of the pertinent dimensionless groups. The specific form of these
Hot ﬂuid
th,i Ch
Cold ﬂuid
tc,o
tr,i
tr,o
th,o tc,i
Cr
Cc
FIGURE 6.15 Regenerator matrix as the third stream. (From Lambertson, T.J., Trans. ASME, 80, 586, 1958.)

dimensionless groups is to some extent optional, and the two most common forms are (1) the effec-
tiveness and modified number of transfer units (ε-NTUo) method (generally used for rotary regen-
erators), whereby

ε φ[ ]= NTUo r, *, *,( )*C C hA

(6.9)
and (2) the reduced length-reduced period (Λ–Π) method (generally used for fixed matrix regenera-
tors) in which

ε φ= ∏ ∏[ ]Λ Λh c h c, , ,

(6.10)
These two methods are equivalent as shown in Ref. [20] and Shah [29]; that is, the thermal
effectiveness of a single fixed regenerator is equal to that of the rotary regenerator with the same
values of the four parameters. This one-to-one correspondence between the two dimensionless
methodologies, as shown in Table 6.3, allows the results obtained in the form of either Equation 6.9
or 6.10 to be used for both types of regenerators.
The ε-NTUo method is mainly used for rotary regenerator design and analysis, and was first
developed by Coppage and London [20]. Their model is explained next.
6.8.3 Coppage and Longon Model for a Rotary Regenerator
The ε-NTUo method was used for the rotary regenerator design and analysis by Coppage and
London [20] with the following idealizations.
1. The thermal conductivity of the matrix is zero in the gas and air flow directions, and infi-
nite in the direction normal to the flow.
2. The specific heats of the fluids and the matrix material are constant with temperature.
3. No mixing of the fluids occurs during the switch over from hot to cold flow.
4. The convective conductances between the fluids and the matrix are constant with flow
length.
5. The fluids flow in counterflow directions.
6. Entering fluid temperatures are uniform over the flow cross section and constant with time.
TABLE 6.3
Equivalence between the ε-NTUo and Λ–Π
Design Methods
ε-NTUo Method Λ–Π Method
NTU
/
/
/
o
c c
c h
c c
c h
r
c
c
c
h
=
+
=
=
=
Λ
Λ
Λ
/
/
( )
*
*
*
Π
Π Π
Π
Π Λ
Π
Π
Π
1 1
C
C
hA
Λ
Λ
Π
h o
c o
h
r
NTU
NTU
= +








= +
= +


C
h
h
C hA
*
*
*
* *
( )
[ ( ) ]
( )
1
1
1
1
1
1
A
A






= +
NTU
NTU
o
c
r
oΠ
1
1
C
hA
*
*[ ( ) ]

361Regenerators
7. Regular periodic conditions are established for all matrix elements, and heat losses to the
surroundings are negligible.
8. Fluid carryover during the switching operation and the pressure leakage effects are negligible.
On the basis of these idealizations, the following differential equations and boundary conditions may be
expressed. For the hot gas flow, energy balance on the element dx, as shown in Figure 6.16, is given by

dq
dx
M C
L
th r r r
=
∂
∂τ
(6.11)

dq
dx
M c
t
x
m c
L
th
h p,h
h h p,h h
= −
∂
∂
+
′ ∂
∂



τ

(6.12)
Equation 6.11 represents the energy received by the matrix in terms of its thermal capacitance. The
right-hand side of Equation 6.12 represents the energy given up by the hot gas, and ′mh /L represents
the mass of the hot gas retained in a flow length dx. The convective heat transfer rate equation is

dq
h A
L
t t dxh
h h
h r= −( )

(6.13)
Elimination of dqh yields the equation

M c
t
x
m c
L
t M c
L
t h A
L
t th
h p,h
h p,h h r r r h h
h r
∂
∂
+
∂
∂
=
∂
∂
=
−
−
′
τ τ
( )

(6.14)
For the cold gas flow, a similar equation results as follows:

M c
t
x
m c
L
t M c
L
t h A
L
t tc p,c
c c p,c c r r r c c
c r
∂
∂
+
′ ∂
∂
= −
∂
∂
=
−
−
τ τ
( )

(6.15)
The boundary conditions are as follows:

For interval of hot flow: constant at
For interval of cold fl
h,it x= = 0
oow: constant atc,it x= = L
Ch
x dx
qhdqh dqc qc
th,i th,o tc,i
Cc
LL
tc,o
FIGURE 6.16 Regenerator basic heat transfer model. Regenerator elemental flow passage and associated
matrix during (a) hot flow period and (b) cold gas flow period. (From Coppage, J.E. and London, A.L., Trans.
ASME, 75, 779, 1953.)

6.8.3.1 Thermal Effectiveness
The overall heat transfer performance of the regenerator is most conveniently expressed as the heat
transfer “effectiveness” ε, which compares the actual heat transfer rate to the thermodynamically
limited maximum possible heat transfer rate. With this definition, the regenerator thermal effective-
ness is simply the dimensionless time-average cold fluid outlet temperature. This is true under the
condition that the cold stream is weaker, that is, it has the lower heat capacity rate. This definition
(for Cc ≤ Ch as is the case for the recuperator) results in

ε =
−
−
t t
t t
c,o c,i
h,i c,i

(6.16)
where tc,o is the bulk average temperature of the cold air stream after passage through the regenera-
tor. The effectiveness is expressed as a function of four nondimensional parameters given by

ε φ= 



C C hA*, *,( )*,r oNTU

(6.17)
Definition of NTU )*o r, *, *,(C C hA
NTUo is the modified number of transfer units, defined as

NTU NTUo c=
+






1
1 ( )*hA

(6.18)
The heat capacity rate ratio C* is simply the ratio of the smaller to larger heat capacity rate of the
fluid steams so that C* should be less than or equal to 1.

C
C
C
Mc
Mc
C
C
*
( )
( )
min
max
min
max
= = =p
p
c
h

(6.19)
Cr
* is the matrix heat capacity rate Cr normalized with respect to Cmin

C
C
C
M c N
Mc
r
r r r
p
*
( )min min
= =

(6.20)
where
Mr is the mass of the matrix
cr is the specific heat of the matrix material
N is the speed of the matrix in revolution per unit time
(hA)* is the ratio of the convective conductance on the Cmin side to that on the Cmax side:

( )* ( )
( )
( )
( )
min
max
hA
hA
hA
hA
hA
= =
on the side
on the side
cC
C hh
(6.21)

363Regenerators
Various terms used here are defined as follows:
Ac = matrix transfer area on cold side
Ah = matrix transfer area on hot side
Cc = fluid stream capacity rate (Mcp) for cold gas flow
Ch = fluid stream capacity rate (Mcp) for hot gas flow
Cr = capacity rate of the rotor matrix (MrcrN)
(hA)* = thermal conductance
hc = convective conductance for cold gas
hh = convective conductance for hot gas
Mc = mass flow rate of cold gas
Mh = mass flow rate of hot gas
Mr = matrix mass
(Mcp)c = capacity rate of cold gas
(Mcp)h = capacity rate of hot gas
Mrcr = thermal capacitance of matrix
′mc = mass of cold gas retained in the matrix length L
′mh = mass of hot gas retained in the matrix length L
L = matrix flow length
N = rpm of the matrix
tc = temperature of the cold gas
th = temperature of the hot gas
tr = temperature of the matrix
tc,i,tc,o = cold fluid terminal temperatures
th,i,th,o = hot fluid terminal temperatures
τ = flow period
For the special case of Cr/Cc = ∞, the behavior becomes identical in form to that of a counterflow
direct-type exchanger and its effectiveness is given by

εcf
NTU
NTU
o
o
for=
−
−

− −
− −
1
1
1
1
1
e
e
[ ( )]
[ ( )]
*
* *
*
C
C
C
C

(6.22a)

NTU
1 NTU
for *o
o
=
+( )
=C 1

(6.22b)
The following formula for thermal effectiveness was first empirically correlated by Lambertson [21]
and later modified by Kays and London [15]:

ε ε= −








cf
r
1
1
9 1 93
C* .

(6.23)
Equation 6.23 agrees with accurate numerical results within ±1% for the following ranges [14]:
(1) 3 ≤ NTUo ≤ 9, 0.90 ≤ C* ≤ 1, 1.25 ≤ Cr
* ≤ 5; (2) 2 ≤ NTUo ≤ 14, C* = 1, Cr
* ≥ 1.5; (3) NTUo ≤ 20,
C* = 1, Cr
* 2; and (4) the complete range of NTUo, C* = 1, Cr
* ≥ 5. In all cases, 0.25 ≤ (hA)* ≤ 4.
Note that the value of C* is limited to between 0.9 and 1.0.
The regenerator effectiveness increases with NTUo asymptotically and approaches unity for
specified values of C* and Cr
*. Thus, in this case, the periodic-flow-type regenerator would have
the same performance as a counterflow direct-type unit possessing the same hot-side and cold-side

transfer areas and the same convection heat transfer coefficients, providing only negligible thermal
resistance offered by the wall structure. To provide a sense of magnitude for these parameters, the
following tabulations were presented by these authors to indicate extreme ranges of values to be
expected in gas turbine design work:

ε =
=
=
= =
50 90
0 90 1 00
1
0 2 1
% %
. .
( )
( )
.
–
–
–10
( )* –
NTU
c
h
r
c
c
h
c
C
C
C
C
hA
hA
hA
== ≈
=
2 20
1 10
– ( twice NTU )
NTU –
o
o
6.8.3.2 Heat Transfer
For rotary regenerators, the magnitude of the heat transfer rate between the gas and the matrix dur-
ing a flow period is necessarily the same for both flow periods, and therefore

q Mc t t= −ε( ) ( )p c h,i c,i

(6.24a)
in which th,i and tc,i are constant inlet temperatures of the hot and cold gases. For stationary regen-
erators, the heat transfer rate is

q Mc t t= −ε( ) ( )p c h,i c,iτ

(6.24b)
6.8.4 Parameter Definitions
Various parameters definitions and their equivalents for the stationary and rotary regenerators are
given in Table 6.4.
TABLE 6.4
Parameter Definitions and
Equivalents for Stationary and Rotary Regenerators
Stationary Rotary
NTUo Λc
1+ ( )*hA
NTUc
1
1+





( )*hA
C* ( )
( )
Mc
Mc
p c
p h
τ
τ
( )
( )
Mc
Mc
p c
p h
Cr
* M c
Mc
r r
p c( )τ
M c N
Mc
r r
p c( )
(hA)* ( )
( )
hA
hA
τ
τ
c
h
( )
( )
hA
hA
c
h

365Regenerators
Note: While defining various parameters, throughout this chapter, it is assumed that the cold fluid
is the Cmin fluid and accordingly, subscripts c for cold fluid and h for hot fluid are allotted. However,
parameter definition can be generalized to subscripts a and b such that the term

C
C
a
b
b a
a b
1 or 1≤ ≤
Λ Π
Λ Π
(6.25)
6.8.5 Classification of Regenerator
Based on the values of C* and (hA)*, or Λ–Π, regenerators are classified into eight types [29,30]: (1)
balanced regenerator, (2) unbalanced regenerator, (3) symmetric regenerator, (4) unsymmetric regenera-
tor, (5) symmetric and balanced regenerator, (6) unsymmetric and balanced regenerator, (7) symmetric
and unbalanced regenerator, and (8) unsymmetric and unbalanced regenerator. For a balanced regenera-
tor, the heat capacity of the fluids blown through the regenerator is equal and a regenerator is termed
symmetric if the reduced length of each period is equal. The unsymmetric and unbalanced regenerator
operation is the most general one, and the others are merely subsets [30]. These designations are shown
in Table 6.5. The utilization factor Uh on the hot side and Uc on the cold side are given by

U
C
C
c
c
r
c
=



 =
Λ
Π

(6.26a)

U
C
C
h
h
r
h
=



 =
Λ
Π

(6.26b)
6.8.6 Additional Formulas for Regenerator Effectiveness
Tables of thermal effectiveness are given by many sources: Kays and London [15], Baclic [17],
Lamberston [21], Bhanke and Howard [22], and Romie [31], among others. Methods of computing
the thermal effectiveness are described by, for example, Baclic [17], Willmott and Duggan [26],
Baclic et al. [27], Romie and Baclic [28], Ref. [32], and many others. Additional formulas and closed
form solutions from a few of these references are given next.
TABLE 6.5
Designation of Regenerators
Terminology Λ–Π Method NTUo Method
1. Balanced regenerator (defined in terms
of utilization factor U or heat capacity
rate ratio C*)
Uh = Uc
Uh/Uc = 1
Λh/Πh = Λc/Πc
Ch = Cc
Ch/Cc = 1
C* = 1
2. Unbalanced regenerator Uh ≠ Uc
Uh/Uc ≠ 1
Λh/Πh ≠ Λc/Πc
Ch ≠ Cc
Ch/Cc ≠ 1
C* ≠ 1
3. Symmetric regenerator (defined in terms
of (i) reduced length Λ or reduced period
Π or (ii) thermal conductance ratio (hA)*)
Λh = Λc
Πh = Πc
(hA)h = (hA)c
(hA)* = 1
4. Unsymmetric regenerator Λh ≠Λc
Πh ≠ Πc
(hA)h ≠ (hA)c
(hA)* ≠ 1
5. Symmetric and balanced regenerator Λh = Λc, Πh = Πc
Uh = Uc
i.e., Λh/Πh = Λc/Πc
(hA)* = 1
C* = 1

6.8.6.1 Balanced and Symmetric Counterflow Regenerator
Baclic [17] obtained a highly accurate closed form expression for the counterflow regenerator effec-
tiveness for the balanced and symmetric regenerator; that is, for C* = 1 and (hA)* = 1 by the
Galerkin method:

ε = −















=
∑
Λ
Π
2 1Bj
j o
N

(6.27)
where Bj is determined by solving the set of equations of the form

a Bjk j
j
N
=
∑ =
0
1

(6.28)
where

a
k j
k j
k j
k m
Vjk
m
j m j m
=
+ +
+ +
+ + +
−
−
+ + +
( )!( )!
( )!
( )!
( )
( )!
,
1 1
1
1 1
1
2 Π
Λ
Λ ++
=












∑ l
m
k
0

(6.29)

V x y e
n
m
y
x
I xy mm
x y
n
n
n m
( , ) ( )[ ( )]
/
=
−









 ≥− +
= −
∞
∑ 1
2 1
2
1

(6.30a)

n
m
n
m n m−





 =
− − +1 1 1
!
( )!( )!

(6.30b)
For N = 2, the equation for ε simplifies to the following equation:

ε
β
β
=
+ − − − − +
+ − − − −
C
B R A N E
B R A N
r
* { [ ( )]}
{ [ (
1 7 24 2 90 2
1 9 24 6 20
2 1 1 1
2 −− 3E)]}
(6.31)
where

B = − + −3 13 303 4 5 6β β β β( )

(6.32)
and

R = − −β β β β2 4 5 63 5 3 4[ ( )]

(6.33)

A = − + −β β β β β3 3 4 5 63 5 3 4 12[ ( )]
(6.34)

N = − + +β β β β β4 4 5 62 3 3[ ( )] 5
2

(6.35)

E = − − + −β β β β β β β β β β β2 4 6 2 6 3 4 525
2
5
2
4
3
(6.36)

N1 4 4 5 62 2= − + +β β β β β[ ( )] 5
2

(6.37)

A1 3 3 4 5 615 4 12= − + −β β β β β[ ( )]

(6.38)

R1 2 4 5 615 2= − −β β β β[ ( )]

(6.39)

367Regenerators

βi i
i
i
=






=
∏
=
−
−
V
C
V
i
i
2 2
2
2 3
1
1
NTU
NTU
*
NTU
for
o
o
r
o
,
( )
( , )
, , ,
Λ
Λ
… 66

(6.40)

V x y e
n
i
y
x
I xy ii
x y
n
n
n i
( , ) ( )[ ( )]
/
=
−







 ≥− +
= −
∞
∑ 1
2 1
2
1
(6.41)
Regenerator effectiveness ε, computed from Equation 6.31, as a function of NTUo and Cr
* is pre-
sented in Table 6.6. Note that the results are valid for C* = 1 and (hA)* = 1. It is emphasized again
that the regenerator effectiveness ε from Equation 6.23 is valid for 0.9 ≤ C* ≤ 1 and Cr
* 1.25 while
that of Equation 6.31 is valid not only for C* = 1 but for all values of Cr
*. Exact asymptotic values of
ε for Λ → ∞ and Π/Λ → 0, when ε = Λ/(2 + Λ) holds, are also included in Table 6.6.
6.8.7 Reduced Length–Reduced Period (Λ–Π) Method
6.8.7.1 Counterflow Regenerator
The asymmetric-unbalanced counterflow regenerator problem is solved by Baclic et al. [27] by
adopting Galerkin model. Based on these assumptions, an energy balance provides two equations
applicable during the hot gas flow period and two equations during the cold gas flow period:

1 1
Λh
h
h
r
r h
∂
∂
= −
∏
∂
∂
= −
t t
t t
ξ η
(6.42)

±
∂
∂
= −
∏
∂
∂
= −
1 1
Λ c
c
c
r
r c
t t
t t
ξ η
(6.43)
The regenerator can operate with either parallelflow (plus sign in Equation 6.43) or counterflow
arrangement (minus sign in Equation 6.43). In Equations 6.42 and 6.43, ξ is the fractional dis-
tance along the flow path in the regenerator matrix of length L and η is the fractional completion
of a respective gas flow period. Temperatures of the hotter gas, colder gas, and the solid matrix
are denoted by th, tc, and tr, respectively. The expressions for four parameters Λh and Λc (reduced
lengths), Πh and Πc (reduced periods) are given in Table 6.7.
The differential equations (6.42) and (6.43) describe the regenerator operation when the appro-
priate boundary conditions are specified. These are constant gas inlet temperatures th,i and tc,i at
the opposite ends (ξ = 0 and 1) of the regenerator matrix, and the condition stating that the matrix
temperature field at the end of one gas flow period is the initial matrix temperature distribution for
the subsequent gas flow period.
The subscript 1 is assigned to the weaker gas flow period such that the respective U1 = (Λ/Π)1
ratio is smaller of the two ratios Uh = (Λ/Π)h and Uc = (Λ/Π)C. The ratio (Λ/Π) is termed the uti-
lization factor. The main advantage of the utilization factors is the fact that these parameters do
not contain the fluid to matrix heat transfer coefficients of the respective flow periods. Thus, U1 is
defined as
U U U1 = min{ , }C h (6.44)

TABLE 6.6
Symmetric and Balanced Counterflow Regenerator Effectiveness ε = φ(Λ, Π) (as
Calculated from Equation 6.31)
Π/Λ
Λ
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.0 1/3 0.3332 0.3329 0.3323 0.3315 0.3304 0.3292 0.3277 0.3260 0.3241 0.3221
1.5 3/7 0.4283 0.4276 0.4264 0.4248 0.4227 0.4202 0.4173 0.4139 0.4102 0.4061
2.0 1/2 0.4996 0.4986 0.4968 0.4943 0.4912 0.4874 0.4830 0.4780 0.4725 0.4665
2.5 5/9 0.5551 0.5537 0.5513 0.5481 0.5440 0.5391 0.5333 0.5269 0.5197 0.5120
3.0 3/5 0.5994 0.5977 0.5949 0.5910 0.5861 0.5802 0.5733 0.5655 0.5570 0.5477
3.5 7/11 0.6357 0.6338 0.6305 0.6261 0.6204 0.6137 0.6058 0.5970 0.5872 0.5766
4.0 2/3 0.6659 0.6638 0.6602 0.6553 0.6490 0.6416 0.6329 0.6232 0.6124 0.6006
4.5 9/13 0.6915 0.6892 0.6853 0.6800 0.6732 0.6652 0.6559 0.6454 0.6337 0.6210
5.0 5/7 0.7134 0.7109 0.7068 0.7011 0.6940 0.6855 0.6756 0.6645 0.6521 0.6385
5.5 11/15 0.7324 0.7293 0.7255 0.7195 0.7121 0.7032 0.6928 0.6811 0.6681 0.6537
6.0 3/4 0.7491 0.7463 0.7418 0.7356 0.7279 0.7187 0.7080 0.6958 0.6822 0.6672
6.5 13/17 0.7637 0.7609 0.7562 0.7498 0.7419 0.7324 0.7215 0.7089 0.6948 0.6792
7.0 7/9 0.7768 0.7738 0.7690 0.7625 0.7544 0.7447 0.7335 0.7206 0.7061 0.6900
7.5 15/19 0.7884 0.7854 0.7804 0.7738 0.7656 0.7558 0.7444 0.7313 0.7164 0.6997
8.0 4/5 0.7989 0.7958 0.7908 0.7840 0.7757 0.7658 0.7543 0.7409 0.7257 0.7036
8.5 17/21 0.8084 0.8052 0.8001 0.7933 0.7849 0.7749 0.7633 0.7497 0.7342 0.7167
9.0 9/11 0.8171 0.8138 0.8086 0.8017 0.7933 0.7833 0.7715 0.7578 0.7421 0.7242
9.5 19/23 0.8250 0.8216 0.8164 0.8094 0.8010 0.7909 0.7791 0.7653 0.7493 0.7311
10.0 5/6 0.8322 0.8288 0.8235 0.8165 0.8080 0.7980 0.7862 0.7722 0.7560 0.7375
10.5 21/25 0.8388 0.8354 0.8300 0.8230 0.8146 0.8046 0.7927 0.7787 0.7623 0.7435
11.0 11/13 0.8450 0.8415 0.8361 0.8290 0.8206 0.8106 0.7988 0.7847 0.7681 0.7491
11.5 23/27 0.8506 0.8471 0.8417 0.8346 0.8262 0.8163 0.8044 0.7903 0.7736 0.7543
12.0 6/7 0.8559 0.8524 0.8469 0.8398 0.8315 0.8216 0.8098 0.7956 0.7788 0.7592
12.5 25/29 0.8603 0.8573 0.8517 0.8447 0.8364 0.8266 0.8147 0.8005 0.7836 0.7638
13.0 13/15 0.8654 0.8618 0.8562 0.8492 0.8410 0.8312 0.8194 0.8052 0.7882 0.7682
13.5 27/31 0.8697 0.8661 0.8605 0.8535 0.8453 0.8356 0.8239 0.8096 0.7925 0.7723
14.0 7/8 0.8737 0.8701 0.8644 0.8575 0.8494 0.8397 0.8280 0.8138 0.7966 0.7762
14.5 29/33 0.8775 0.8738 0.8682 0.8612 0.8532 0.8436 0.8320 0.8177 0.8004 0.7799
15.0 15/17 0.8811 0.8773 0.8717 0.8648 0.8568 0.8473 0.8358 0.8215 0.8041 0.7834
15.5 31/35 0.8844 0.8807 0.8750 0.8681 0.8602 0.8508 0.8393 0.8251 0.8076 0.7868
16.0 8/9 0.8876 0.8838 0.8781 0.8713 0.8635 0.8542 0.8427 0.8285 0.8110 0.7900
17.0 17/19 0.8934 0.8896 0.8839 0.8771 0.8695 0.8604 0.8490 0.8348 0.8172 0.7959
18.0 9/10 0.8967 0.8948 0.8891 0.8824 0.8749 0.8660 0.8548 0.8406 0.8229 0.8014
19.0 19/21 0.9034 0.8995 0.8938 0.8872 0.8799 0.8711 0.8601 0.8459 0.8282 0.8065
20.0 10/11 0.9077 0.9038 0.8981 0.8916 0.8844 0.8758 0.8649 0.8509 0.8331 0.8111
25 25/27 0.9245 0.9205 0.9148 0.9087 0.9024 0.8947 0.8844 0.8707 0.8528 0.8302
30 15/16 0.9360 0.9319 0.9263 0.9207 0.9151 0.9081 0.8984 0.8851 0.8673 0.8442
35 35/37 0.9445 0.9403 0.9347 0.9295 0.9246 0.9182 0.9090 0.8961 0.8785 0.8552
40 20/21 0.9509 0.9467 0.9411 0.9363 0.9320 0.9261 0.9174 0.9048 0.8875 0.8640
45 45/47 0.9559 0.9517 0.9462 0.9417 0.9379 0.9325 0.9241 0.9119 0.8948 0.8713
50 25/26 0.9600 0.9557 0.9503 0.9461 0.9427 0.9378 0.9297 0.9177 0.9009 0.8775
60 30/31 0.9662 0.9619 0.9565 0.9529 0.9502 0.9459 0.9383 0.9269 0.9106 0.8874
70 35/36 0.9707 0.9663 0.9611 0.9578 0.9558 0.9519 0.9447 0.9337 0.9180 0.8951
80 40/41 0.9740 0.9697 0.9645 0.9616 0.9600 0.9565 0.9497 0.9390 0.9239 0.9014
90 45/46 0.9767 0.9723 0.9672 0.9646 0.9634 0.9602 0.9536 0.9432 0.9236 0.9065

369Regenerators
The effectiveness is given by

ε =
−
+
= …
=
∑
1
1
0 1 2 3
1
2 1
0
U
x x
m
m Mm m
m
M
( )!
, , , , ,for

(6.45)
The unknown coefficients x1m and x2m are determined from the following set of algebraic equations:

[ ( , ) ] , , , , ,− + = = …
=
∑ A x B x C k Mmk m mk m k
m
M
Π Λ1 1 1 2
0
0 1 2 3

(6.46)

[ ( , ) ] , , , , ,B x A x k Mmk m mk m
m
M
1 2 2 2
0
0 0 1 2 3− = = …
=
∑ Π Λ

(6.47)
where

A
k i
V
jmk j j
i
i m j j
j
i m
j
M
( , )
( )
( )!
( , )
,Π Λ
Π Λ
Λ
=
−
−
=+ +
+ +∑
1
1 22
1
0

(6.48)
Symmetric and Balanced Counterflow Regenerator Effectiveness ε = φ(Λ, Π) (as
Calculated from Equation 6.31)
Π/Λ
Λ
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
100 50/51 0.9788 0.9744 0.9693 0.9670 0.9662 0.9632 0.9568 0.9467 0.9325 0.9109
150 75/76 0.9852 0.9808 0.9759 0.9744 0.9747 0.9726 0.9667 0.9574 0.9452 0.9258
200 100/101 0.9835 0.9840 0.9792 0.9782 0.9791 0.9774 0.9719 0.9629 0.9520 0.9348
300 150/151 0.9917 0.9873 0.9826 0.9821 0.9837 0.9824 0.9772 0.9686 0.9592 0.9456
400 200/201 0.9934 0.9889 0.9843 0.9841 0.9860 0.9850 0.9799 0.9714 0.9629 0.9522
500 250/251 0.9944 0.9899 0.9853 0.9853 0.9874 0.9865 0.9815 0.9731 0.9651 0.9568
600 300/301 0.9950 0.9905 0.9860 0.9861 0.9884 0.9876 0.9826 0.9743 0.9665 0.9602
800 400/401 0.9959 0.9914 0.9869 0.9871 0.9896 0.9889 0.9840 0.9758 0.9682 0.9650
1000 500/501 0.9964 0.9919 0.9874 0.9877 0.9903 0.9897 0.9848 0.9766 0.9692 0.9634
2000 1000/1001 0.9974 0.9928 0.9884 0.9890 0.9917 0.9912 0.9865 0.9784 0.9711 0.9770
∞ 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Source: Baclic, B.S., Trans. ASME J. Heat Transfer, 107, 214, 1985.
Note: For the ε-NTUo method,
Π
Λ
Λ= =
1
2
Cr
o
*
and NTU .
TABLE 6.7
Expressions for Λh, Λc, Πc, and Πh
Πc
c
r r
=
( )hAτ
M C
Πh
h
r r
=
( )hAτ
M c
Λc
c
p c
=
( )
( )
hA
Mc
Λh
h
p h
=
( )
( )
hA
Mc


B
m k
mk =
+ +
1
1( )!
(6.49)

C
k k i
V
k
i
i
i
j
k
=
+
−
−
−
+
+
=
∑
1
1
1 2 1 1
1
1
0
( )!
( )
( )!
( , )Π Λ
Λ

(6.50)
For any fixed M, one needs 2(M + 1) equations for M + 1 unknowns x1m and for M + 1 unknowns
x2m. For any practical purpose M = 2 will be adequate.
6.8.8 Razelos Method for Asymmetric-Unbalanced Counterflow Regenerator
The forms produced by the Galerkin method of Baclic et al. [27] are not amenable for hand
calculation methods. They can be solved by either a computer or a programmable calcula-
tor. A hand calculation method was presented by Razelos [33]. In this approach, the unsym-
metric regenerator is approximated using an “equivalent” symmetric regenerator. The Razelos
approximate method can be used to calculate the counterflow regenerator effectiveness for
the complete range of C* and NTUo, and Cr
* ≥ 1, 0.25 ≤ (hA)* ≤ 4. The method follows the
following steps:
1. For the ε-NTUo method, compute the range of NTUo,m and Cr,m
* for an equivalent balanced
regenerator as follows from the specified values of NTUo, Cr
*, and C*.

NTU
NTU
o,m
o
=
+
2
1
( *)
*
C
C
(6.51)

C
C C
C
r,m
r* =
+
2
1
* *
*

(6.52)
2. For the Λ–Π method, calculate Λm and Πm as

Π
Π Π
Λ
Π
Π Λ Π Λ
m
h c
m
m
h c/ /
=
+( )
=
+[ ]− −
2 2
1 1
( ) ( )

(6.53)
3. The equivalent balanced regenerator effectiveness εr is evaluated from Equation 6.23 or
6.31 for NTUo,m andCr,m
* or from Table 6.6 for Λm and Πm. For example, the equivalent form
of Equation 6.23 is given by

εr
o,m
o,m r,m
NTU
NTU
=
+
−







1
1
1
9 1 93
( * ) .
C

(6.54)
4. The actual regenerator effectiveness ε is then given by

ε
ε ε
εε
=
−
−
− −
− −
1
1
2
2
1 2 1
1 2 1
e
C e C C
{ ( )/[ ( )]}
{ ( )/[ ( )]}
* *
* * *
r r
r r
C C

(6.55)

371Regenerators
or

ε
ϕε ε
ϕε ε
=
−
−[ ]
−
−
1
1
1
1
e
e
[ ( )]
/( )
( ) ( )
r r
r r
/
h c/ / /Λ Π Λ Π

(6.56)
where

φ =
−[( ) ( ) ]
( ) ( )
Λ Π Λ Π
Λ Π Λ Π
/ /
/ /
h c
h c
2 2
2
(6.57)
where C* is the original specified value, which is less than unity.
A sample calculation [17] for Λh = 18, Λc = 15.5, Πh = 16, and (Λ/Π)c = 1.2 yields Πm = 4960/347
and Λm = 5760/347. From Table 6.6, by linear interpolation, one obtains εr = 0.8215, since (Λ/Π)m =
31/36 for this case, while ϕ = −0.0645833 from the equation. With these values, ε = 0.847047 from
the equation. The exact value of the effectiveness for this example is 0.847311, which is just 0.03%
higher than the result obtained from this approximate procedure.
6.8.9 Influence of Longitudinal Heat Conduction in the Wall
In the foregoing analysis, the influence of longitudinal heat conduction was neglected. For a high-
thermal-effectiveness regenerator with a large axial temperature gradient in the wall, longitudinal
heat conduction reduces the regenerator effectiveness and the overall heat transfer rate. Bahnke and
Howard [22] showed that an additional parameter λ, the longitudinal conduction parameter, would
account for the influence of longitudinal heat conduction in the wall. Here, λ is defined as

λ =
k A
LC
w k,t
min
(6.58)
where
kw is the thermal conductivity of the matrix wall
Ak,t is the total solid area available for longitudinal conduction
Ak,t is given by [14]

A A A A A Ak,t k,h k,c fr o fr= + = − = −( )1 σ
(6.59)
Introducing the longitudinal conduction parameter, a generalized expression for thermal effective-
ness in the functional form is given by
ε λ= { , *, *,( )*, }NTUo rC C hA (6.60)
Lowered effectiveness because of longitudinal conduction, ∆ε, can be calculated in several ways.
Parameter definitions for λ and its equivalents for the stationary and rotary regenerators are given
in Table 6.8.
TABLE 6.8
Parameter Definitions for λ
Stationary Rotary
λ k A
L MC
w k,t
p c
c h
c( )
τ τ
τ
+



k A
L Mc
w k,t
p c( )

6.8.9.1 Bahnke and Howard Method
Bahnke and Howard [22] illustrated the influence of the thermal conductivity on thermal effective-
ness by a factor called the conduction effect. The conduction effect is defined as the ratio of the
difference between effectiveness with no conduction effect and with conduction effect to the no
conduction effectiveness, as given by

∆
=
−=
=
ε
ε
ε ε
ε
λ λ
λ
0
0
(6.61)
Bahnke and Howard tabulated results for ε for a wide range of NTUo, Cr
*, Cr, and λ. Their results
are valid over the following range of dimensionless parameters:

1 0 90
1 0
1 100
1 0 0 25
1 0
≥ ≥
≤ ≤ ∞
≤ ≤
≥ ≥
≥
C
C
C
C
A
min
max
min
.
.
. ( )* .
. *
r
o
s
NTU
hA
≥≥
≤ ≤
0 25
0 01 0 32
.
. .λ
Bahnke and Howard’s results for C* = 1 can be accurately expressed by [29]:
ε ελ λ= C =0 (6.62)
where ελ = 0 is given by Equation 6.23 or 6.31, and Cλ is given by

Cλ
λψ λ
=
+
−
+ + +






1
1
1
1 1 1
NTU
NTU NTU / NTU
o
o o o( ) ( )

(6.63)
in which

ψ
λ
λ λ λ
=
+



 +






NTU
NTU
NTU
NTU / NTU
o
o
o
o o1 1
0 5
0 5
.
.
tanh
[ ( )]

(6.64a)

NTU
NTU
for NTUo
o
o≈
+



 ≥
λ
λ1
3
0 5.

(6.64b)
6.8.9.2 Romie’s Solution
Romie [34] expressed the effects of longitudinal heat conduction on thermal effectiveness in terms
of a parameter GL. The factor GL is derived from the analysis of axial conduction in counterflow
recuperators by Hahnemann [35]. GL is given by

G
b
b b
CL
NTU
for )* 1= − −









 = =1 1 1
2
tanh( ) * , (hA

(6.65)

373Regenerators
where

b = +





NTU
NTU
o
o
1
1
0 5
( )
.
λ

(6.66)
The expression for ελ = 0 is given by

ελ≠
− −
− −
=
−
−
0
1
1
1
1
1
0
e
C e
C
G C
G C
L
L o
NTU
NTU
( )
( )
*
* *
*

(6.67a)

=
+
=
G
G
CL o
o
NTU
NTU( , )
*
1
1
L
(6.67b)
Figure 6.17 shows GL as a function of the product NTUo for several values of NTUo. The curves are
for (hA)* = 1 and C* = 0.9 and 1. The same curves were obtained using (hA)* = 0.5, thus indicating
that GL is a very weak function of (hA)* [34].
6.8.9.3 Shah’s Solution to Account for the Longitudinal Conduction Effect
For 0.9 ≤ C* ≤ 1, Shah [36] has provided a closed-form formula to take into account the longitu-
dinal conduction effect. However, the following more general method is recommended for C* 1
by Shah [14]:
1. Use the Razelos method to compute εr,λ = 0 for an equivalent balanced regenerator using the
procedure from Equations 6.51, 6.52, and 6.54.
2. Compute Cλ from Equation 6.63 using NTUo,m and λ.
3. Calculate εr,λ≠0 = Cλεr,λ = 0.
4. Finally, ε is determined from Equation 6.55 or 6.56 with ελ, replaced by εr,λ ≠ 0.
1.0
0.9
0.8
0.7
GL
0.6
0.5
0.0 0.5
λ NTUo
NTUo ≥64
1.0
8
4
2
1
NTUo
1.5
hA*= 1
C *
1.0
0.9
FIGURE 6.17 Parameter GL for longitudinal conduction effect. (From Romie, F.E., Trans. ASME J. Heat
Transfer, 113, 247, 1991.)

This procedure yields a value of ε accurate within 1% for 1 ≤ NTUo ≤ 20 and Cr
* ≥ 1 when com-
pared to Bahnke and Howard’s results.
6.8.10 Fluid Bypass and Carryover on Thermal Effectiveness
Fluid bypass and carryover on thermal effectiveness are discussed in Refs. [14,37].
6.8.11 Regenerator Design Methodology
To design a successful regenerator, the engineer must consider many design factors including the
following [2]:
1. Describe the different types of regenerative heat exchangers
2. Discuss the basic heat transfer process and the correlation of cyclic temperature distribu-
tions resulting from storage of thermal energy
3. Relate the regenerator to classical counterflow arrangements to enable trade-offs of heat
transfer, pressure drop, size, and alternative surfaces
4. Discuss the effects of leakage on both performance and design
5. Consider the effects of pressure loads, leakage control, and rotation on mechanical design
6.8.12 Primary Considerations Influencing Design
Primary considerations influencing the design of a regenerator especially for aircraft/vehicular gas
turbine applications may be summarized as follows [38]:
1. Manufacturing limitations
2. Cost limitations
3. Maintenance and cleaning requirements
4. Mechanical design problems
5. Weight, shape, and size limitations
6. Limitations on flow friction-power expenditure
7. Desired exchanger heat transfer effectiveness
6.8.13 Rating of Rotary Regenerators
The basic steps involved in the analysis of a rating problem are the determination of surface geo-
metrical properties, matrix wall properties, fluid physical properties, Reynolds numbers, j (or Nu)
and f factors corrected for property variations, heat transfer coefficients, NTUo, C*, Cr
*, and pres-
sure drops. The procedure presented for regenerators parallels that for a compact heat exchanger.
Therefore, the rating procedure is not repeated here. However, for details on a rating procedure from
first principles consult Shah [14].
6.8.14 Sizing of Rotary Regenerators
The sizing problem for a rotary regenerator is more difficult. Similar to recuperator design, the
sizing of a regenerator involves decisions on material, surface geometry selection, and mechani-
cal design considerations. Once these are decided, the problem reduces to the determination of
the disk diameter, division of flow area, disk depth, and disk rotational speed to meet the speci-
fied heat transfer and pressure drops [14]. Sometimes a limitation on the size is also imposed.
One method for a new design would be to assume a regenerator size, consider it as a rating

375Regenerators
problem, and evaluate the performance as outlined for compact recuperators. Iterate on the size
until the computed performance matches the specified performance. A detailed sizing procedure
is outline in Ref. [14].
6.9 MECHANICAL DESIGN
After the heat transfer surface has been chosen, sizing studies completed, and the regenerator
selected to be compatible with the overall system requirements, the next step involves mechanical
design. Mechanical designs must consider items such as [2] (1) thermal distortions, (2) leakages,
(3) pressure loadings, and in the case of the rotary types, (4) a drive system, and (5) sealing. An
important source book on regenerator mechanical design is Mondt [2].
6.9.1 Single-Bed and Dual-Bed Fixed Regenerators
Single-bed and dual-bed regenerators can be relatively simple to design. If the bed is composed of
loose pellets, grids or screens are necessary to retain the pellets within a container. The grid mesh
must be fine enough to retain the smallest pellet in the bed, yet the mesh must be porous enough to
keep pressure drops low. If the retaining grids are not strong enough at the operating temperature,
the bed will “sag” and loosen the packing.
Leakages: Both the single-bed and dual-bed valved regenerators have displacement leakage,
that is, displacement of the fluid entrained in the matrix voids at the switching instant. This fluid is
trapped and “displaced” into the other fluid stream and hence is known as displacement leakage. In
addition to displacement leakage, fixed-bed regenerators may have small primary leakage of one
fluid into the other through leaks in closed switching valves.
6.9.2 Rotary Regenerators
The mechanical design of a rotary regenerator requires (additionally to the recuperator) the follow-
ing items [39]:
1. A subdivision of the casing into a rotor and a stator
2. Leakage and an effective seal between the two gases
3. Means for supporting the rotor in the stator
4. A drive for the rotor
Items (2) and (4) are discussed next.
6.9.2.1 Leakages
Primary leakages in a rotary regenerator can be classified as (1) labyrinth leakage, (2) carryover or
displacement leakage, and (3) structural leakage.
Labyrinth or seal leakage: This is leakage through the seal stem from the fact that the cold gases
are at much higher pressures than the hot gases. This is especially true in the case of gas turbine
with high-pressure ratio.
Carryover or displacement leakage: In addition to direct leakage through seals, there is inevita-
bly a “carryover” or displacement leakage due to air trapped in the matrix as it passes through the
gas side.
Structural primary leakage: Structural leakages take place through any gaps existing in the
matrix and the housing.
Any leakage is a serious loss, because it is the air that has absorbed compressor work but escapes
to the atmosphere without passing through the turbine. It is more important than pressure loss, as it
affects the net work severely [40]. Leakage is dependent mainly on pressure ratio and carryover on
matrix rpm. Leakage due to seal leakage and displacement leakage can amount to 3%–4% of the

airflow out of the compressor [41]. The effect of a given fractional leakage depends on the values of
exchanger effectiveness and cycle pressure ratio. As an example, for a cycle with typical tempera-
tures, component efficiencies, and regenerator effectiveness of 90%, a leakage of 5% will reduce the
net output by about 11% while a leakage of 10% will reduce it by twice that amount [40].
6.9.2.2 Seal Design
In a rotary regenerator, the stationary seal locations control the desired frontal areas for each fluid
and also serve to minimize the primary leakage from the high-pressure side to the low-pressure
side. The sealing arrangement must adequately prevent leakage flow, and at the same time not
introduce high frictional resistance for rotation. Because the matrix is alternately exposed to hot
and cold gases, thermal expansion and contraction add to the sealing problem. Typical seals used
in rotary regenerator include radial seals, axial seals, and circumferential seals. While designing
seals, the pressure forces under the seal faces, which must be balanced, and allowances to be made
for the thermal distortion of the rotor [42]. Sealing arrangements are illustrated diagrammatically
in Figure 6.18. Certain considerations for seal design are [43] as follows:
1. The seals must be efficient at very high temperature and pressures but still allow freedom
of movement.
2. The seals must accommodate the expansion and contraction accompanying temperature
variations and still prevent leakage.
6.9.2.3 Drive for the Rotor
A design problem encountered with the regenerator is that of supporting and driving the matrix at
low speed. The regenerator usually rotates at a speed of approximately 20–30 rpm [41]. An electric
drive will be ideal, because of its low rpm and small power requirement.
Seal
shoes
Matrix(a)
(b) (c)
Radial
sealing plate
Radial seals
Circumferential
by-pass sealRadial
seal
Radial
seal
Axial seal
Axial sealing plate
Axial seals
Axial seal plate
Air
side
Gas
side
Sealing surface
adjuster
FIGURE 6.18 Seals for rotary regenerator.

377Regenerators
6.9.2.4 Thermal Distortion and Transients
A regenerator is subjected to thermal shock and thermal distortion due to unsteady thermal condi-
tions. However, this can be minimized by the use of ceramic material. A regenerator cannot be
designed assuming that all operations will be at steady-state conditions. In vehicular gas turbines
system, transients are common. Even industrial regenerators are occasionally exposed to starting
and stopping transients. Gentle or long-duration transients are desirable to minimize thermal dis-
tortions and potential thermal stresses [2]. More problems are usually faced during the warm-up of
a regenerator than during stopping because on starting, the matrix and rotor respond much faster
than the surrounding housing. If the housing does not accommodate the matrix and the rotor to
expand during warm-up, the housing may constrain the matrix growth and cause thermal stresses.
6.9.2.5 Pressure Forces
Pressures in the regenerator system exert forces on the matrix or structure. There are two sources of
pressure forces in a rotary regenerator [2]: One source of pressure forces is due to pressure differ-
ence between the high-pressure cold air and the low-pressure hot gases. This pressure force depends
on the seal arrangement. The seals for a disk can be arranged so that the net force on the support
is essentially zero. The second source results from pressure drop of the fluids flowing through the
matrix. This pressure force is the product of the total pressure drop and the frontal area.
6.10 INDUSTRIAL REGENERATORS AND HEAT RECOVERY DEVICES
Apart from recuperators and regenerators, various types of heat recovery devices are available for
many years. Commercially available heat recovery devices for combustion air preheaters include
the following [44]:
1. Fluid-bed regenerative heat exchanger
2. Fluidized-bed waste heat recovery system
3. Vortex-flow direct-contact heat exchanger
4. Ceramic bayonet tube heat exchanger or high-temperature burner duct recuperators
5. Regenerative burner
6. Porcelain-enameled flat-plate heat exchanger
7. Radiation recuperators
8. Heat-pipe exchangers
9. Economizer
10. Thermocompressor
11. Plate heat exchanger energy bank
Because of the multitude of different industrial heating processes and exhaust system designs, there
is no one universal type of heat transfer device best suited for all applications. Various types of
industrial air preheaters are discussed here under and readers may refer for more details to Ref. [44].
6.10.1 Fluid-Bed Regenerative Heat Exchangers
In fluid-bed regenerative heat exchangers, fluidized beds of pellets recover heat from hot exhaust
gas and transfer this heat to cold combustion air [45]. The basic fluid-bed heat exchanger consists of
an insulated cylindrical tower incorporating an upper and a lower chamber as shown in Figure 6.19.
Each chamber is fitted with several horizontal perforated trays. Hot exhaust gases enter the upper
chamber near its base and rise to the outlet near the top, heating counterflow alumina pellets as
they fall. The heated pellets pass through an aperture into the lower chamber, where they give up
their heat to the cold air. Air enters the lower chamber near the base and exits near the top. Direct

contact of gas and air streams with the heat exchange media, namely, the alumina pellets, coupled
with controlled dwell time at the trays, results in high heat transfer rates. By controlling the rate of
pellet recycling, the temperature of the air being heated can be held constant within wide variations
of gas inlet temperature and volume. As a part of this heat exchange system, an auxiliary pneumatic
system is incorporated for recycling alumina pellets.
6.10.2 Fluidized-Bed Waste Heat Recovery
Fluidized-bed waste heat recovery (FBWHR) systems are being developed to preheat combus-
tion air for industrial furnaces. FBWHR systems employ a heat transfer particulate media, which
is heated as it falls through the upward-flowing flue gases in a raining bed heat exchanger
[9,46]. This type of heat exchanger is known as a fluidized-bed heat exchanger (FBHE). FBHE offer
the potential for economic recovery of high-temperature (2000°F–3000°F) heat from the flue
gases of industrial processes such as steel soaking pits, aluminum remelt furnaces, and glass
melting furnaces.
An FBHE consists of horizontal finned heat exchanger tubes with a shallow bed of fine inert
particles, which move upward with gas flow and give up the heat to the finned tubes, which in turn
transfer heat to cold air passing through them. A thin steel plate with small perforations supports
the bed and distributes the hot gas evenly. The perforations are uniform with a hole size of 1.5 mm
diameter or less, and the holes are spaced to provide a free flow area of 3%–10%. For many applica-
tions, only ceramic distributor plates will withstand the temperatures and corrosive environments
of flue gases. Among the FBHE advantages are enduring the hostile environments such as elevated
temperature, fouling particulates, corrosive gases, corrosive particulates, and thermal cycling [9].
Most surfaces are kept clean by fluidizing action.
Cold gas out
Fluidized-bed
pellet heating
Hot gas in
Preheated air out
Distributor plate
Distributor plate
Fluidized-bed
heat recovery
Cold air in
Pellet recycling
system
FIGURE 6.19 Fluid-bed regenerator.

379Regenerators
6.10.3 Vortex-Flow Direct-Contact Heat Exchangers
The vortex-flow direct-contact heat exchanger represents a new approach for high-temperature
(2500°F) heat recovery from industrial waste heat flue gas with a simple payback period. In the vor-
tex-flow direct-contact heat exchanger, the heat conduction material wall of conventional metal or
high-temperature ceramic material is replaced by a vortex-induced fluid dynamic gas boundary, which
separates the tangentially rotating hot and cold gas flows between which heat exchange is desired [47].
The VFHE is a cylindrical cavity into which separate hot flue gas and cold preheat air gas flows are
injected. Injection of the gases is such that a vortex-flow pattern is established in the cavity, providing
confinement of hot fluid to the central region of the cavity surrounded by cold air stream. Solid particles
of 20–200 μm diameters as a medium to exchange heat between hot and cold streams are injected into
the hot spiraling gas stream. Due to centrifugal action, these particles pass into the surrounding cold gas
rotating flow, to which the particles transfer heat. Upon reaching the outside cavity surface, the particles
are entrained in the outermost region of the vortex flow and removed with a portion of the cold flow, which
exits at the periphery (exhaust end wall). The VFHE requires a particle injection and separation subsystem
to collect and recycle the particle to the vortex chamber for continued heating and cooling cycles.
6.10.4 Ceramic Bayonet Tube Heat Exchangers
Babcock and Wilcox (BW) and the Department of Energy (DOE) developed high-temperature
burner duct recuperator (HTBDR) systems capable of recovering waste heat from high-temperature
flue gas using ceramic bayonet elements [48,49]. The HTBDRs consist of silicon carbide ceramic
bayonet tubes suspended into the exhaust gas flow stream, where they recover the heat from the
exhaust and preheat the combustion air up to a temperature of 1090°C (2000°F). The ceramic bayo-
net elements consist of an assembly of two concentric tubes of each bayonet element suspended from
metallic, air-cooled tubesheets at the top end of the element. Combustion air is directed through the
elements at the inner tube or the annulus from heavily insulated plena located above the tubesheets.
The tubes of each element are free to expand or contract under the influence of temperature varia-
tions. The ceramic bayonet elements are also expected to ease maintenance and to best deal with
problems associated with thermal stress, leakage, and stress-related corrosion.
6.10.5 Regenerative Burners
The reGen regenerative burner, an all-ceramic high-temperature burner, close coupled to a compact,
fast-cycle, ceramic regenerator, provides air preheats in excess of 85% of the process temperature
in fuel-fired applications up to 1399°C (2550°F) [7]. Figure 6.20 shows one complete regenerative
Mode-1
Regen-1
Mode-2
Regen-2 Regen-1 Regen-2
CollectingCollecting Firing
Process fluid heating
Firing
Exhaust
gas
Combustion
air
Exhaust
gas
Combustion
air
Process fluid heating
FIGURE 6.20 Regenerative burner.

unit comprised of two burners, two regenerators, a reversing valve, and the related pipings. While
one of the burners fires, drawing the preheated air fed through its regenerator, exhaust gas is drawn
through the other burner and down into its associated regenerator, then discharged to the atmo-
sphere. After a sufficient interval, the reversing operation takes place.
6.10.6 Porcelain-Enameled Flat-Plate Heat Exchangers
Porcelain-enameled heat exchangers offer cost-effective solutions to problems of heat recovery from
extremely corrosive gases that preclude the use of carbon steel or common types of stainless steels [50].
Porcelain enamel is a glass coating material that is applied to a metal substrate to protect the base metal.
The base metal gives strength and rigidity; the metal can be steel, cast iron, aluminum, or copper, but
mostly steel is used on a larger scale. The glass coating offers significant corrosion resistance to the cor-
rosive flue gas. The porcelain-enameled coating finds application in flat-plate heat exchangers of the open
channel air preheater (OCAP) type for advanced heat recovery. The OCAP is a plate-type exchanger
characterized by a nonweld construction of the heat transfer core. The enameled plates are assembled into
a floating construction. Elastic springs are used between all adjacent plates to ensure a uniform distribu-
tion of the dead weights and to allow for the thermal expansion and contraction in operation. This floating
core is enclosed in a rigid frame, again without any welding or any damage to the porcelain enamel layer.
6.10.7 Radiation Recuperators
Metallic recuperators for industrial furnaces are generally of the following types [51]:
1. Convective units, operating at flue gas temperatures up to a maximum of 1100°C (2000°F).
2. Radiation-type units, that is, the heat transfer mode is by radiation, operating at tempera-
ture ranges of nearly 900°C–1500°C (2700°F). In radiation-type recuperators, parallelflow
is essential to control the operating temperatures of the heating surface. A combination
of parallelflow and counterflow is required to reach the highest recuperator efficien-
cies of air temperature of above 800°C (1500°F). Typical radiation recuperators include
a double-shell parallelflow radiation recuperator consisting of two concentric cylinders
(Figure 6.21)—through the inner shell the flue gas flows and through the annulus the cold
air flows in a parallel direction—as well as cage-type radiation recuperators for very large
high-temperature furnaces, with a combination of parallelflow and counterflow units.
Cold gas out
Hot air out
Cold air in
Hot gas in
FIGURE 6.21 Radiation recuperator.

381Regenerators
6.10.8 Heat-Pipe Heat Exchangers
The heat-pipe heat exchanger used for gas–gas heat recovery is essentially a bundle of finned heat
pipes assembled like a conventional air-cooled heat exchanger. The heat pipe consists of three ele-
ments (1) a working fluid inside the tubes, (2) a wick lining inside the wall, and (3) a vacuum sealed
finned tube. Because the pipe is sealed under a vacuum, the working fluid is in equilibrium with its
own vapor. The purpose of the wick is to transport the working fluid contained within the heat pipe,
from one end to the other by capillary action.
The heat-pipe heat exchanger consists of an evaporative section through which the hot exhaust gas
flows and a condensation section through which the cold air flows. These two sections are separated by
a separating wall as shown in Figure 6.22 [52]. The working of a heat-pipe heat exchanger is as follows.
Heat transfer by the hot flue gas at the evaporative section causes the working fluid contained within
the wick to evaporate and the increase in pressure causes the vapor to flow along the central vapor
region to the condensation section, where it condenses, and gives up the latent heat to the cold air. The
condensate then drains back to the evaporative section by capillary action in the wick. Figure 6.23
shows heat-pipe heat exchanger finned U-tube. In cases where gravity aids return of the condensate
to the evaporative section, it is possible to operate without a wick; the device then becomes a simple
two-phase thermosyphon.
T2 t1
t2
Wick structure
(a)
Evaporation
Sealed fin-tube
(vacuum)
Cold fluid in
Vapor flow Condensation Working
fluid
Seal
T1
Heat in
Separator plate
(b) (c)T1
T2
T2
T1
t2
t1
t1
t2
Center portion
separates fluids
FIGURE 6.22 Heat-pipe heat exchanger. (a) Principle of working, (b) heat-pipe tube arrangement, and
(c) heat-pipe heat exchanger (schematic).

6.10.8.1 Merits of Heat-Pipe Heat Exchanger
The heat-pipe exchanger is a lightweight compact heat recovery system. It does not need mechanical
maintenance, as there are no moving parts. It does not need input power for its operation.
6.10.8.2 Application
The heat pipes are used in following industrial applications such as (1) process fluid to preheat-
ing of air; (2) preheating of boiler combustion air; (3) heating, ventilating, and air-conditioning
(HVAC) systems; (4) recovery of waste heat from furnaces; (5) reheating of fresh air for hot air
driers; (6) preheating of boiler feed water with waste heat recovery from flue gases in the heat-pipe
economizers; and (7) reverberatory furnaces (secondary recovery).
6.10.9 Economizer
In case of boiler system, economizer is provided to utilize the flue gas heat either for preheating the
boiler feed water or the combustion air. In both the cases, there is a corresponding reduction in the
fuel requirements of the boiler. For every 22°C reduction in flue gas temperature by passing through
an economizer or a preheater, there is 1% saving of fuel in the boiler. In other words, for every 6°C
rise in feed water temperature through an economizer or 20°C rise in combustion air temperature
through an air preheater, there is 1% saving of fuel in the boiler [52]. Few types of industrial econo-
mizers are shown in Figure 6.24.
6.10.10 Thermocompressor
In many cases, very low-pressure steams are reused as water after condensation for lack of any
better option of reuse. Also, it becomes feasible to compress low-pressure steam by very high-
pressure steam and reuse it as a medium pressure steam. The major energy in steam is its latent
heat value and thus thermocompressing would give a large improvement in waste heat recovery.
The thermocompressor is a simple equipment with a nozzle where high-pressure steam is acceler-
ated into a high-velocity fluid (Figure 6.25). This entrains the low-pressure steam by momentum
transfer and then recompresses in a divergent venturi. It is typically used in evaporators where the
boiling steam is recompressed and used as heating steam.
FIGURE 6.23 Heat-pipe heat exchanger finned U-tube. (From Thermofin, www.thermofin.net)

383Regenerators
6.10.11 Mueller Temp-Plate® Energy Recovery Banks
A Mueller Temp-Plate energy recovery bank (Figure 6.26) transfers the heat content of the waste
gas to the media used in the process or to an intermediate heat transfer solution. High grade heat can
be efficiently recovered using a Mueller Temp-Plate energy recovery bank.
6.11 ROTARY HEAT EXCHANGERS FOR SPACE HEATING
The ventilation losses account for the major part of energy use in HVAC, it is imperative to
reduce these losses as much as possible. Rotary heat exchangers are well-proven means of high
efficiency energy recovery, typically recovering up to 80% in typical HVAC (space heating
and ventilation) applications. The combination of heat and humidity recovery by rotary heat
exchangers is a highly efficient energy-saving method. Typical summer application is dehumidi-
fication of warm and humid supply air to reduce the energy consumption of the downstream
cooling equipment. During winter, operation of this feature recovers moisture from the exhaust
air to reduce the humidification load.
Leading rotary heat exchanger manufacturers for HVAC applications include Hovalwerk AG,
9490 Vaduz, Liechtenstein, Reznor UK Ltd, Klingenburg GmbH, Germany, Munters International
Inc., FL and Fläkt Woods AB, SE-551 84 Jönköping.
(a) (b) (c)
FIGURE 6.24 Economizer. (a) Coiled-tube economizer, (b) rectangular economizer, and (c) cylindrical
economizer. (Courtesy of Fintube, LLC, Tulsa, OK; www.fintubellc.com)
High pressure
steam
Suction steam
(low pressure)
Discharge steam
(medium pressure)
FIGURE 6.25 Thermocompressor.

6.11.1 Working Principle
The rotor with its axial, smooth air channels serves as a storage mass, half of which is heated by the
warm air stream and half of which is cooled by the cold air stream, in a counterflow arrangement.
Consequently, the temperature of the storage mass varies depending on the rotor depth in the axial direc-
tion and on the angle of rotation. In a counterflow arrangement, the rotating, air permeable storage mass
is heated and cooled alternately by the heat-releasing and heat-absorbing air streams. Depending on the
air conditions and on the surface of the storage mass, also moisture may be transferred in this process.
The supply and extract air streams must be adjacent and pass through the heat exchanger simultaneously.
A typical rotary wheel for HVAC applications is shown in Figure 6.27. (Also refer to Figure 1.15.)
FIGURE 6.27 Rotary wheel for HVAC application.
FIGURE 6.26 Mueller Temp-Plate energy recovery banks. (Courtesy of Mueller, Heat Transfer Products,
Springfield, MO.)

385Regenerators
6.11.2 Construction
Rotor wheel—The rotor wheel shall be made of layers of corrugated and intervening flat compos-
ite material or aluminum foil of uniform width to ensure a smooth surface. This wheel material
is bonded together to form a rigid heat transfer matrix forming a multitude of narrow triangular
air channels in an axial direction. Rotors with straight oriented waves guarantee a laminar flow
through the heat exchanger with an optimum degree of efficiency and favorable pressure drops as
well as a high level of self-cleaning. The thickness of the material (usually aluminum) is 0.06–1.2
mm. The standard range of airway wave height available is 1.6–2.9 mm depending on the applica-
tion. Depending on the heights of the waves in the aluminum foil, air channels of different sizes can
be supplied, smaller air channels increase operating efficiency but increase the pressure drop. The
depth of the storage mass in the direction of air flow is usually 200 mm. Rotors are available from
0.25 to 6.0 m diameter and it can handle air flow rates up to 150,000 m3/h.
The wheel can be fully wound or on larger units, sectorized, i.e., assembled in segments for
the ease of transport, stability, and insertion into building. The segments are assembled between
rigid spokes, thus ensuring structural rigidity and longevity and allowing replacement of one or
specific segments or all of the segments without having to remove any spokes. The segments
need to be installed inside the divided casing at the final site. At the perimeter the rotor is
enclosed by a welded aluminum shell, ensuring true running and allowing maximum use of the
wheel face area. The wheels shall be tested in accordance with ASHRAE-78 method. Rotary
heat exchangers can transfer moisture as well as heat. The decisive criterion for the transfer of
moisture is the material or surface of the storage mass. The following are the major designs
available in the market:
1. Condensation rotor or non-hygroscopic aluminum wheel for recovering principally sen-
sible heat. The storage mass consists of smooth untreated aluminum foil transferring mois-
ture only when condensation occurs on the warm air side and (part of) this is taken up by
the cold air. Condensation may be carried along with the air flow.
2. Enthalpy rotors or hygroscopic aluminum wheel for recovering sensible and latent heat.
3. Sorption wheel consisting of aluminum backing foil which is coated with a sorbent (e.g.,
silicagel) to accomplish vapor transfer without condensation.
6.11.3 Rotor Materials
Normally, the rotor wheel shall be made of aluminum foil. Operating conditions with high degrees
of fouling and corrosion have led to the development of aluminum plated steel foil, chrome steel,
and chrome nickel steel foils of various thicknesses. Rotors are also available with epoxy-coated
aluminum matrix in order to increase the corrosion resistance.
6.11.3.1 Construction
Casing: The casing shall be constructed as a single skin, self-supporting from galvanized steel and
include rotary wheel support beams and a purging sector.
6.11.3.2 Carryover
To a minor degree, the two air flows mix due to the rotating storage mass. Depending on the air
velocity and rotation speed, carryover amounts to about 2%–4% of the airflow rate. Carryover of
exhaust air to the fresh air side can be minimized by installing a purge sector.
6.11.3.3 Seals
The casing shall be equipped with adjustable brush seals which minimize carryover loss. Sealing at
the periphery is important for the internal leakage of the rotary heat exchanger. A plastic seal tape

being pressed onto the storage mass by means of springs. This design keeps cross-contamination via
the inside of the rotor casing to a minimum. Transverse seal is also required between the warm air
and the cold air. Manufacturers use an adjustable threefold lip seal, ensuring a minimal air gap to the
storage mass. This reduces direct carryover from warm air to cold air (and vice versa) to a minimum.
6.11.4 Drive System and Control Unit
The rotor shall be belt or gear driven along its periphery. A constant speed or variable speed drive
motor shall be used. The motor shall be mounted on a self-adjusting base to provide correct belt ten-
sion. The drive unit shall be available with a differential thermostat for summer/winter changeover,
a speed detector with alarm function, an interface for central energy management control system
and for climate zones a frequency converter to control and regulate the efficiency of fan by varying
its rpm. Rotary heat exchangers have optimized efficiency around 12–20 rpm.
6.11.5 Cleaning Devices
For the regenerative heat exchangers, there are several types of cleaning devices. They are selected
according to the degree of fouling of the rotor. Under normal conditions, the rotor has a high self-
cleaning effect, on account of the continuously changing directions of air flow. The cleaning meth-
ods include (1) compressed air cleaning, (2) compressed air and water cleaning, (3) steam cleaning,
and (4) compressed air and warm water cleaning.
NOMENCLATURE
AC matrix transfer area on cold side, m2 (ft2)
Afr frontal area, m2 (ft2) = Afr,h + Afr,c
Afr,c frontal area on cold side, m2 (ft2)
Afr,h frontal area on hot side, m2 (ft2)
Afr,t total face area, m2 (ft2)
Ah matrix transfer area on hot side, m2 (ft2)
Ak,l total solid area for longitudinal conduction, m2 (ft2)
Amk constants defined by Equation 6.48
ajk constants defined by Equation 6.29
Ao minimum free flow area, m2 (ft2) = σAfr
%a face seal and hub coverage
Bj constants defined by Equation 6.28
Bmk constants defined by Equation 6.49
b cell geometry dimension, m (ft); or function defined by Equation 6. 66
C heat capacity rate (Mcp), J/°C (Btu/h · °F)
C* heat capacity rate ratio (it should be less than or equal to 1) = Cmin/Cmax
Cc fluid stream capacity rate (Mcp) for cold gas, W/°C (Btu/h · °F)
Ch fluid stream capacity rate (Mcp) for hot gas, W/°C (Btu/h · °F)
Ck constant defined by Equation 6.50
Cmax maximum of Cc or Ch, W/°C (Btu/h · °F)
Cmin minimum of Cc or Ch, W/°C (Btu/h · °F)
cp,c specific heat of cold gas, J/kg · °C (Btu/lbm · °F)
cp,h specific heat of hot gas, J/kg · °C (Btu/lbm · °F)
Cr = capacity rate of the rotor matrix (Mrcr), W/°C (Btu/h · °F)
= MrcrN for rotary regenerator, W/°C (Btu/h · °F)
cr specific heat of the matrix material, J/kg · °C (Btu/lbm · °F)

387Regenerators
C* matrix heat capacity rate ratio
Cr,m
* = matrix heat capacity rate ratio
= (Mrcr)/Cmin
Cr,m
* = Cr
* for equivalent balanced regenerator
Cλ longitudinal conduction correction factor
D regenerator disk outer diameter at the end of the heat transfer surface, m (ft)
d hub diameter, m (ft)
d* cell height/width
GL parameter to account the effects of longitudinal heat conduction on thermal effective-
ness as defined in Equation 6.65
hA thermal conductance W/°C (Btu/h · °F)
(hA)* ratio of the convective conductance on the Cmin side to Cmax side = (hA)c/(hA)h
hc convective conductance for cold gas, W/m2 °C (Btu/h ft2 °F)
hh convective conductance for hot gas, W/m2 · °C (Btu/h · ft2 · °F)
In(·) modified Bessel function of the first kind and nth order
j Colburn factor for heat transfer
i, j, k, n integers
kw thermal conductivity of the matrix wall
L matrix flow length, m (ft)
M order of the trial solution, Equation 6.45
Mc mass flow rate of cold gas, kg/s (lbm/h)
mc mass of the cold gas retained in the matrix flow length dx, kg (lbm)
(Mcp)c capacity rate of cold gas, W/°C (Btu/h · °F)
(Mcp)h capacity rate of hot gas, W/°C (Btu/h · °F)
Mh mass flow rate of hot gas, kg/s (lbm/h)
m′h mass of the hot gas retained in the matrix flow length dx, kg (lbm)
Mr matrix mass, kg (lbm)
Mrcr thermal capacitance of matrix, W/°C (Btu/h · °F)
N rpm of the rotary matrix
Nc cell density
Nu Nusselt number, hDh/k
NTU number of transfer units, hA/C
NTUc number of transfer units on the cold side (≈twice NTUo)
NTUh number of transfer units on the hot side (≈twice NTUo)
NTUo modified number of transfer units
NTUo,m NTUo for an equivalent balanced regenerator
Q total heat duty of the exchanger, W s (Btu)
Re Reynolds number
tc temperature of the cold gas, °C (°F)
th temperature of the hot gas, °C (°F)
tr temperature of the matrix, °C (°F)
tc,i, tc,o cold fluid terminal temperatures, °C (°F)
th,i, th,o hot fluid terminal temperatures, °C (°F)
Uc utilization factor on the cold side (Λ/Π)c
Uh utilization factor on the cold side (Λ/Π)h
U1 (Λ/Π)1, the smaller of the two ratios UC and Uh

x1m, x2m unknown coefficients defined by Equation 6.45
x, y variables as defined in Equation 6.2
V = (Afr,h + Afr,c)L, m3 (ft3), volume of regenerator
Vi(x, y) special functions defined by Equation 6.41
ß area density, m2/m3(ft2/ft3)
δ matrix stock thickness, m (ft)
εcf counterflow regenerator thermal effectiveness
εr thermal effectiveness of reference regenerator
∆ε lowered effectiveness because of longitudinal conduction
εr,λ = 0 equivalent balanced regenerator neglecting longitudinal heat conduction
εr,λ≠0 = Cλεr,λ = 0
ξ fractional distance along the flow path in the regenerator matrix of length L
η fractional completion of a respective gas flow period
Λ reduced length
Λm mean reduced length
λ longitudinal conduction parameter
λc longitudinal conduction on the cold side
λh longitudinal conduction on the hot side
Π reduced period
Πm mean reduced period
ρr matrix material density
φ function defined by Equation 6.57
ψ function defined by Equation 6.64
σ porosity = Ao/Afr
τ flow period, s
τc duration of cold flow period, s
τh duration of hot flow period, s
τL time for one revolution, τc + τh,s
Subscripts
c

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