COST MINIMIZATION OF SHELL AND TUBE HEAT EXCHANGER USING NON-TRADITIONAL OPTIMIZATION

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 9, Issue 11, November 2018, pp. 281–296, Article ID: IJMET_09_11_029
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=11
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
COST MINIMIZATION OF SHELL AND TUBE
HEAT EXCHANGER USING NON-TRADITIONAL
OPTIMIZATION
Dr.S.Elizabeth Amudhini Stephen
Associate Professor Mathematics,
Karunya Institute of Technology and Sciences Coimbatore, India,
ABSTRACT
Cost minimization of shell and tube heat exchanger is the key objective. Traditional
design approaches besides being time consuming, do not guarantee the reach of an
economically optimal solution. So, in this project, a new shell and tube heat exchanger
optimization design approach is developed based on four nontraditional optimization
algorithms Genetic algorithm, Simulated Annealing, Pattern search and fmincon
algorithm. In this study all the four optimization algorithms are applied to minimize the
total cost of equipment including capital investment and the sum of discounted annual
energy expenditures related to pumping of shell and tube heat exchanger by varying
various design variables such as length, tube outer diameter, pitch size, baffle spacing,
etc. Based on proposed methods, a full computer code was developed for optimal design
of shell and tube heat exchanger. Finally the results are compared to t
Keywords: Shell and Tube Heat Exchanger, Optimization Algorithm, Cost
Minimization, Energy Expenditures, Genetic Algorithm, Simulated Annealing, Pattern
Search and Fmincon
Cite this Article Dr.S.Elizabeth Amudhini Stephen, Cost Minimization of Shell and Tube
Heat Exchanger Using Non-Traditional Optimization, International Journal of Mechanical
Engineering and Technology, 9(11), 2018, pp. 281–296.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=11
1. INTRODUCTION
Heat exchangers are devices used to transfer heat between two or more fluids that are at different
temperatures and which in most of the cases they are separated by a solid wall. Shell and tube
heat exchangers (STHEs) are probably the most common type of heat exchangers applicable for
a wide range of operating temperatures and pressures. Shell and tube heat exchangers are widely
used in heating and air conditioning, power generation, refrigeration. Chemical processes,
manufacturing and medical applications. This widespread use can be justified by its versatility,
robustness and reliability.
The design of STHEs involves a large number of geometric and operating variables as a part
of the search for an exchanger geometry that meets the heat duty requirement and a given set of

design constrains. Usually a reference geometric configuration of the equipment is chosen at first
and an allowable pressure drop value is fixed. Then, the values of the design variables are defined
based on the design specifications and the assumption of several mechanical and thermodynamic
parameters in order to have a satisfactory heat transfer coefficient leading to a suitable utilization
of the heat exchange surface. The designer’s choices are then verified based on iterative
procedures involving many trials until a reasonable design is obtained which meets design
specifications with a satisfying compromise between pressure drops and thermal exchange
performances. (G.F.Hewitt, 1998) (R.K.Shah & K.J.Bell:, 2000) (D.Q.Kern, 1950) (Rosenhow
& Hartnett, 1973)
Due to the important role of shell-and-tube heat exchangers, a variety of techniques have been
proposed to the design optimization problem such as, numerical resolution of the stationary point
equations of a nonlinear objective function (M.Reppich & S.Zagermann, 1995) (F.O.Jegede &
G.T.Polley, 1992), graphical analysis of the search space (Poddar & G.T.Polley, 1996)
(K.Muralikrishna & U.V.Shenoy, 2000), simulated annealing (P.D.Chaudhuri, Diwekar, &
J.S.Logsdon, 1997), mixed integer nonlinear programming (F.T.Mizutani, Pessoa, Queriroz,
Hauan, & Grossmann, 2003), and systematic screening of tube count tables (Ravagnani, Silva, &
Andrade, 2003) (Y.A.Kara & O.Guraras, 2004). In addition, there are some studies based on
artificial intelligence techniques for the optimization of shell and tube heat exchangers. These
approaches overcome of some of the limitations of traditional design methods based on
mathematical programming techniques. Selbas et al., (R.Selbas, O.Kizilkan, & M.Reppich, 2006)
used genetic algorithm (GA) for optimal design of STHs, in which pressure drop was applied as
a constraint for achieving optimal design parameters. Caputo et al., (Caputo, P.M.Pelagagge, &
P.Salini, 2008) carried out heat exchanger design based on economic optimization using GA.
They minimized the total cost of the equipment including capital investment and the sum of
discounted annual energy expenditures related to pumping. Ponce-Ortega et al., (Ponce-Ortega,
Serna-Gonzalez, & Jimenez-Gutierrez, 2009) also have used genetic algorithms for the optimal
design of STHEs. The approach uses the Bell-Delaware method for the description of the shell-
side flow with no simplifications. Several other investigators also used strategies based on genetic
optimization algorithms (Ponce-Ortega, Serna-Gonzalez, & Jimenez-Gutierrez, 2009) (Ozkol &
Komurgoz, 2005) (Hilbert, Janiga, Baron, & Thevenin, 2006) (G.N.Xie, Sunden, & Wang, 2008)
(Sun, Y.Lu, & Yan, 1993) (Costa & Queiroz, 2008) (Wildi-Tremblay & Gosselin, 2007)
(B.V.Babu & Munawar, 2007) for various objectives like minimum entropy generation (Sun,
Y.Lu, & Yan, 1993)and minimum cost of STHEs (Ponce-Ortega, Serna-Gonzalez, & Jimenez-
Gutierrez, 2009) (Ozkol & Komurgoz, 2005) (Hilbert, Janiga, Baron, & Thevenin, 2006)
(G.N.Xie, Sunden, & Wang, 2008) (Wildi-Tremblay & Gosselin, 2007) (B.V.Babu & Munawar,
2007) to optimize heat exchanger design. Patel and Rao (B.K.Patel & R.V.Rao, 2010) applied
particle swarm optimization (PSO) for minimization of total annual cost of STHEs. In the study
the main focus was the analyses of the heat exchangers principles, while the optimization
approach was just a tool. Sahin et al., (A.S.Sahin, B.Kilic, & Kilic, 2011) presented an artificial
bee colony (ABC) algorithm for optimization of a shell and tube heat exchanger. Recently
Mariani et al., (Duck, Guerra, Coelho, & Rao, 2012)used a PSO method to optimal designing of
a shell and tube heat exchanger. They combined a quantum particle swarm optimization (QPSO)
approach with Zaslavskii (Zaslavskii, 1978) chaotic map sequences (QPSOZ) to shell and tube
heat exchanger optimization based on the minimization from economic view point. Some others
tried to optimize a variety of geometrical and operational parameter of the STHEs. However,
there is a need to investigate the potential of application of non-traditional optimization
techniques.
In the second chapter, the methodologies, such as Genetic Algorithm, Simulated Annealing,
Pattern Search and fmincon is explained with flow charts in detail. In the third chapter, the shell
and tube heat exchanger problem is explained with mathematical modeling. The exact cost

Cost Minimization of Shell and Tube Heat Exchanger Using Non-Traditional Optimization
minimization objective function with proper bounds is explained. The algorithm are used to find
Ds, do, B, total elapsed time and the cost is minimized. The results and conclusion are discussed
in chapter four.
NOMENCLATURE
a1 numerical constant
B baffles spacing (m)
Cl clearance (m)
Cp specific heat (kJ/kg k)
CE energy cost(€/kWh)
Co annual operating cost ( € /year)
CoDtotal discounted operating cost (€ )
Ctot total annual cost (€ )
d tube diameter (m)
D shell diameter (m)
f friction factor
F correction factor
h heat transfer coefficient (w/m2
k)
H annual operating time (h/year)
i annual discount rate(%)
k thermal conductivity (w/m k)
K1 numerical constant
L tube length (m)
m mass flow rate (kg/s)
n number of tubes passages
n1 numerical constant
ny equipment (year)
Nt number of tube
P pumping power (W)
P numerical constant
Pr Prandtl number
pt tube pitch (m)
Q heat duty (W)
Re Reynolds number
Rf fouling resistance (m2
k/W)
S heat transfer surface area (m2
)
T temperature
V fluid velocity(m/s)

GREEK SYMBOLS:
ΔP pressure drop (pa)
ΔTLM logarithmic mean temperature difference ( ̊c )
Π numerical constant
μ dynamic viscosity(pa s)
ν kinematic viscosity (m2
/s)
ρ density (kg/m3
)
SUBSCRIPTS:
e equivalent
i inlet
o outlet
s belonging to shell
t belonging to tube
w tube walls
2. SHELL AND TUBE HEAT EXCHANGER
Shell and tube heat exchangers in their various construction modifications are probably the most
widespread and commonly used basic heat exchanger configuration in the process industries. The
shell and tube heat exchanger provides a comparatively large ratio of heat transfer area to volume
and weight. It provides this surface in a form which is relatively easy to construct in a wide range
of sizes and which is mechanically rugged enough to withstand normal shop fabrication stresses,
shipping and field erection stresses, and normal operating conditions. There are many
modifications of the basic configuration, which can be used to solve special problems. The shell
and tube exchanger can be reasonably easily cleaned, and those components most subject to
failure-gaskets and tubes-can be easily replaced. Finally, good design methods exist, and the
expertise and shop facilities for the successful design and construction of shell and tube
exchangers are available throughout the world.
2.1. TUBES
The tubes are the basic component of the shell and tube exchanger, providing the heat transfer
surface between one fluid flowing inside the tube and the other fluid flowing across the outside
of the tubes. The tubes may be seamless or welded and most commonly made of copper or steel
alloys. Other alloys of nickel, titanium, or aluminum may also be required for specific
applications. The tubes may be either bare or with extended or enhanced surfaces of the outside.
Extended or enhanced surface tubes are used when one fluid has a substantially lower heat
transfer coefficient than the other fluid. Doubly enhanced tubes, that is, with enhancement both
inside and outside are available that can reduce the size and cost of the exchanger. Extended
surfaces,(finned tubes) provide two to four times as much heat transfer area on the outside as the
corresponding bare tube, and this area ratio helps to offset a lower outside heat transfer
coefficient.

Fig.1. Shell and Tube heat exchanger
2.2. TUBE SHEETS
The tubes are held in place by being inserted into holes in the tube sheet and there either expanded
into grooves cut into the holes or welded to the tube sheet where the tube protrudes from the
surface. The tube sheet is usually a single round plate of metal that has been suitably drilled and
grooved to take the tubes(in the desired pattern), the gaskets, the spacer rods, and the bolt circle
where it is fastened to the shell. However, where mixing between the two fluids(in the event of
leaks where the tube is sealed into the tube sheet) must be avoided, a double tube sheet. Triple
tube sheets(to allow each fluid to leak separately to the atmosphere without mixing) and even
more exotic designs with inert gas shrouds and leakage recycling systems are used in cases of
extreme hazard or high value of the fluid.The tube sheet,
2.3. SHELL AND SHELL-SIDE NOZZLES
The shell is simply the container for the shell-side fluid, and the nozzles are the inlet and exit
ports. The shell normally has a circular cross section and is commonly made by rolling a metal
plate of the appropriate dimensions into a cylinder and welding the longitudinal joint(“rolled
shells”). Small diameter shells (up to around 24 inches in diameter) can be made by cutting pipe
of the desired diameter to the correct length (“pipe shells”). The roundness of the shell is
important in fixing the maximum diameter of the baffles that can be inserted and therefore the
effect of shell-to-baffle leakage. The inlet nozzle often has an impingement plate set just below
to divert the incoming fluid jet from impacting directly at high velocity on the top row of tubes.
Such impact can cause erosion, cavitations, and vibration. In order to put the impingement plate
in and still leave enough flow area between the shell and plate for the flow to discharge without
excessive pressure loss, it may be necessary to omit some tubes from the full circle pattern. Other
more complex arrangements to distribute the entering flow, such as a slotted distributor plate and
an enlarged annular distributor section, are occasionally employed.
2.4. TUBE-SIDE CHANNELS AND NOZZLES
Tube-side channels and nozzles simply control the flow of the tube-side fluid into and out of the
tubes of the exchanger. Since the tube-side fluid is generally the more corrosive, these channels
and nozzles will often be made out of alloy materials (compatible with the tubes and tube sheets,
of course). They may be clad instead of solid alloy.
2.5. CHANNEL COVERS
The channel covers are round plates that bolt to the channel flanges an dcan be removed for tube
inspection without disturbing the tube-side piping. In smaller heat exchangers, bonnets with
flanged nozzles or threaded connections for the tube-side piping are often used instead of
channels and channel covers.

2.6. PASS DIVIDER
A pass divider is needed in one channel or bonnet for an exchanger having two tube-side passes,
and they are needed in both channels and bonnets for an exchanger having more than two passes.
If the channels or bonnets are cast, the dividers are integrally cast and then faced to give a smooth
bearing surface on the gasket between the divider and the tube sheet. If the channels are rolled
from plate or built up from pipe, the dividers are welded in place. The arrangement of the dividers
in multiple-pass exchangers is somewhat arbitrary, the usual intent being to provide nearly the
same number of tubes in each pass, to minimize the number of tubes lost from the tube count, to
minimize the pressure difference across any one pass divider (to minimize leakage and therefore
the violation of the MTD derivation), to provide adequate bearing surface for the gasket and to
minimize fabrication complexity and cost.
2.7. BAFFLES
Baffles serve two functions: Most importantly, they support the tubes in the proper position
during assembly and operation and prevent vibration of the tubes caused by flow-induced eddies,
and secondly, they guide the shell-side flow back and forth across the tube field, increasing the
velocity and the heat transfer coefficient. The most common baffle shape is the single segmental.
For liquid flows on the shell side, a baffle cut of 20 to 25 percent of the diameter is common; for
low pressure gas flows, 40 to 45 percent(i.e. close to the maximum allowable cut) is more
common, in order to minimize pressure drop. The baffle spacing should be correspondingly
chosen to make the free flow areas through the “window”(the area between the baffle edge and
shell) and across the tube bank roughly equal.For many high velocity gas flows, the single
segmental baffle configuration results in an undesirably high shell-side pressure drop. One way
to retain the structural advantages of the segmental baffle and reduce the pressure drop(and
regrettably, to some extent, the heat transfer coefficient, too) is to use the double segmental baffle.
3. MATHEMATICAL MODELLING
The Objective function is to minimize the total cost Ctot. Total cost Ctot is taken as the objective
function, which includes capital investment (Ci), energy cost (Ce), annual operating cost(Co) and
total discounted operating cost (CoD) (Caputo, P.M.Pelagagge, & P.Salini, 2008)
oDitot CCC +=
(1)
Ctot= Total cost
Ci= Capital investment
CoD= total discounted operating cost
The capital investment Ci is computed as a function of the exchanger surface adopting Hall’s
correlation (M.Taal, J.Bulatove, J.Klemes, & P.Stehlik, 2003)
3
21
a
i saaC +=
(2)
Where
a1,a2,a3= numerical constant (M.Taal, J.Bulatove, J.Klemes, & P.Stehlik, 2003)
For exchangers made with stainless steel for both shells and tubes
= 8000 + 2592 91.0
s
The heat exchange surface area S (D.Q.Kern, 1950) (Sinnot) is calculated by
S =
Ft
Q
LM∆U
(3)

Q = heat duty (w) =0.415 6
10×
U= overall heat transfer coefficient(w/m2
k)
( ) ( )




















−
−
−−−
=∆
itos
otis
n
itosotis
LM
TT
TT
l
TTTT
T
(4)
LMT∆ = logarithmic mean temperature difference (o
C)
.25,40,40,95 ==== itosotis TTTT
Tis =95 = inlet temperature belonging to shell
Tot =40 = outlet temperature belonging to tube
Tos =40 = outlet temperature belonging to shell
Tit =25 = inlet temperature belonging to tube
= 30.78621092
The correction factor F for the flow configuration involved is found as a function of
dimensionless temperature ratio for most flow configuration of interest (A.P.Frass, 1989)
(M.M.Ohadi, 2000)
R = correction coefficient =
itot
osis
TT
TT
−
−
=
3
11
= 3.6667
P = efficiency =
itis
itot
TT
TT
−
−
=
70
15
= 0.2143
F = correction factor =
1
12
−
+
R
R
=
( )
16667.3
1666.3
2
−
+
. = 0.81207 (5)
S =
81207.07862.30
10415.0 6
××
×
U
The overall heat transfer coefficient, U depends on both the tube side and shell side heat
transfer coefficients and fouling resistances (Caputo, P.M.Pelagagge, & P.Salini, 2008)
U=






+++
t
t
i
s
s h
Rf
d
d
Rf
h
11
1
0
(6)
Rfs=0.00033 =fouling resistance of the shell
Rft=0.0002 = fouling resistance of the tube
di=0.8do
di = inlet diameter of the tube
do= outlet diameter of the tube

U=






+++
ts hd
d
h
1
0002.0
8.0
00033.0
1
1
0
0
(7)
hs= heat transfer coefficient of the shell (w/m2
k) (D.Q.Kern, 1950)
( ) ( )
14.0
3
155.0
PrRe
36.0






=
w
t
ss
e
s
s
D
k
h
µ
µ
ks=thermal conductivity of the shell(w/m k) =0.19
tµ =dynamic viscosity of the tube (pas) =0.0008
sµ =dynamic viscosity of the shell (pas) =0.00034
wµ =dynamic viscosity of the tube wall (pas) =0.00057
For a triangle pitch (D.Q.Kern, 1950) (Sinnot)
0
2
02
5.0
4
5.0
43.04
d
d
p
D
t
e
π
π














−
=
(8)
De=equivalent shell diameter(m)
Pt=1.25do = tube pitch(m)
( )





 −
=
0
2
0
2
0
2
5.0
5.025.143.0
4
d
dd
De
π
π
=0.7 0d
1.5
19.0
100084.200034.0
=
××
==
s
pss
rs
k
C
P
µ
7213.131
=rsP
Prs= Prandtl number of the shell
Cps= specific heat of the shell (kJ/kg k)
hs= heat transfer coefficient (w/m2
k)
( ) ( )
14.0
55.0
0 00057.0
0008.0
7213.1Re
7.0
07172.0






×
= ss
d
h
(9)
=
( ) 55.0
0
Re1764.0
d
s
Res= Reynolds number of the shell (D.Q.Kern, 1950) (Sinnot)
Cl=clearance(m)

t
ls
s
P
CBD
a
××
=
(D.Q.Kern, 1950) (10)
B= baffles spacing(m)
=
( )
o
oos
d
ddBD
25.1
25.1 −×
(11)
10
BDs ×
=
ss
s
s
a
m
V
ρ
= =fluid velocity of the shell(m/s) (D.Q.Kern, 1950) (Sinnot) (12)
ms= mass flow rate of the shell(kg/s) =27.8
sρ = density of the shell(kg/m3
) =750
s
s
a
V
××
=
7502
8.27
=
BDs ×
1853.0
s
ess
s
DV
µ
ρ ××
=Re = 00034.0
7.0
1853.0
750 o
s
d
BD
×
×
×
(13)
471.286176Re ×
×
=
BD
d
s
o
s
ht= heat transfer coefficient(w/m2
k) (D.Q.Kern, 1950)
No. of tubes
1
1
n
o
s
t
d
D
KN 





=
(R.K.Shah & K.J.Bell:, 2000) (Rosenhow & Hartnett, 1973)
(Sinnot)
k1= numerical constant =0.249
n1= numerical constant =2.207
207.2
0
249.0 





=
d
D
N s
t
Length of tubes sDL ×= 5
=tV Velocity inside the tube =
t
t
i
t
N
n
d
m
×
ρ
π
4
2
(D.Q.Kern, 1950) (14)
n= no. of passes =2
08.0 ddi =
mt= mass flow rate of the tube(kg/s) =68.9

tρ = density of the tube (kg/m3
) =995
Vt= fluid velocity of the tube (m/s) =
2
0
207.2
0
1068.1
d
d
Ds
×





Ret = Reynolds number of the tube =
t
itt dV
µ
ρ ××
(15)
=
207.2
0
0
552.1101275






d
D
d s
7.5
59.0
10002.40008.0
Pr
=
××
=
=
t
tt
t
K
CP
tubetheofnumberprandtl
µ
According to flow regime the tube side heat transfer coefficient ht is computed from the
following correlation (D.Q.Kern, 1950) (A.P.Frass, 1989)




















+






+= 3.0
33.1
RePr1.01
PrRe0677.0
657.3.
L
d
L
d
d
k
h
i
tt
i
tt
i
t
t tRe <2300 (16)
( )






























+








−+
−
=
67.0
3
2
1
1Pr
8
7.121
Pr1000Re
8
L
d
f
f
d
k
h i
t
t
tt
t
i
t
t 2300< tRe <10000 (17)
14.0
3
1
8.0
PrRe027.0 





=
w
t
tt
i
t
t
d
k
h
µ
µ
tRe >10000 (18)
t
s
hd
BDd
U
8.0
1
00058.0
479.411
1
55.0
0
0
++




 ×
=








++




 ×





××
=
to
so
hd
BDd
S
8.0
1
00058.0
479.41100055.25
00143.010415.0
55.0
6
The total discounted operating cost related to pumping power to overcome friction losses is
instead computed from the following equations (Caputo, P.M.Pelagagge, & P.Salini, 2008)

( )∑= +
=
yn
k
k
o
oD
i
C
C
1 1
(19)
HPCC EO =
(20)
kwhCE /12.0 ∈=
H=7000 h/ys






∆+∆= s
s
s
t
t
t
P
m
P
m
P
ρρη
1
(21)
npf
d
LV
P t
o
tt
t 





+=∆
8.02
2
ρ
(D.Q.Kern, 1950) (22)






+= 4
8.0
5
995 2
t
o
s
t f
d
D
V
( ) 15.0
Re2
−
= sos bf 15.0
Re44.1 −
= s


















=∆
e
sss
ss
D
D
B
LV
fP
2
2
ρ
(D.Q.Kern, 1950) (Caputo, P.M.Pelagagge, & P.Salini, 2008) (23)


















=
o
ss
ss
d
D
B
D
Vf
7.0
5
2
750 2
o
sss
Bd
DVf 22
5714.2678=






∆+∆= s
s
s
t
t
t
P
m
P
m
P
ρρ8.0
1
( )st PP ∆+∆= 0371.007.025.1
n=no.of passes=2
efficiencypumping−η = 0.8
08.0 ddi = 8.27=sm 9.68=tm 995=tρ 750=sρ 72.00 =b
BD
d
s
s
0471.286176
Re = ;
sDL 5=
;
2
0
207.2
0
1068.1
d
d
D
V
s
t






=
07.0 dDe =
BD
V
s
s
1853.0
= Darcy friction factor (G.F.Hewitt, 1998)
( ) 2
10 64.1Relog82.1
−
−= ttf

207.2
0
0
552.1101275
Re






=
d
D
d s
t ;
( )st PPP ∆+∆= 0371.007.025.1
;
PCo ××= 700012.0
( )∑= +
=
10
1 1k
k
o
oD
i
C
C
Therefore the problem is to minimize Ctot
( )∑= +
++=
10
1
91.0
1
2.2598000
k
k
o
tot
i
C
SC
(3.24)
Subject to the condition,
1. The Shell internal diameter Ds , 0.1 m ≤ Ds ≤ 1.5 m
2. Tube outside diameter do ; 0.01 m ≤ do ≤ 0.051m
3. Baffles spacing B ; 0.05 m ≤ B ≤ 0.5 m
4. PARAMETERS.
The problem is solved using all the four nontraditional optimization methods and the parameters
are tabulated for comparison purpose
Table 1 Parameters of the optimal shell and tube heat exchangers
using four different optimization methods
Original Design Ga SA PS Fmincon
Ds(m) 0.894 0.617279 0.615774 0.615777 0.615775
L(m) 4.83 3.0864 3.0789 3.0789 3.0789
B(m) 0.356 0.499952 0.5 0.4977798 0.5
d0(m) 0.02 0.01254 0.01228 0.011181 0.01228
Pt(m) 0.025 0.0157 0.0154 0.0123 0.0153
Cl(m) 0.005 0.0031 0.0031 0.0011 0.0031
Nt 918 1352 1408 1333 1408
Vt(m/s) 0.75 1.2963 1.2977 1.2876 1.2977
Ret 14925 16179 15860 16861 15860
Prt 5.7 5.7 5.7 5.7 5.7
ht(W/m2K) 3812 7428.8 7466.3 7422.2 7466.3
ft 0.028 0.0276 0.0277 0.0275 0.0277
Del-Pt(Pa) 6251 6693.9 6707.9 6690 6707.8
as(m2) 0.032 0.0309 0.0308 0.0309 0.0308
De(m) 0.014 0.0088 0.0086 0.0086 0.0086
Vs(m/s) 0.58 0.6005 0.602 0.6002 0.602
Res 18381 11629 11414 11665 11414
Prs 5.1 5.1 5.1 5.1 5.1
hs(W/m2K) 1573 2422.3 2448.5 2421.4 2448.5
fs 0.33 0.3536 0.3546 0.3546 0.3546
Del-Ps(Pa) 35789 20754 21247 21245 21247
U(W/m2K) 615 861.2594 865.1725 850.1595 865.1718
S(m2) 278.6 173.0224 172.2398 174.2424 172.24
Ci(euro) 51507 36204 36088 36224 36088
Co(euro/yr) 2111 1300.5 1320.7 1399.6 1320.7
CoD(euro) 12973 7990.7 8115.1 7850.7 8115.1
Ctot(euro) 64480 44195 44203 44075 44203

5 .RESULTS AND DISCUSSION.
The effectiveness and validity of the suggested approach in this project was assessed by analyzing
some relevant case studies taken from literature. The study of this project is a heat exchanger for
distilled water-raw water heat exchanger from (Sinnot). The heat load is 0.415Mw. This heat
exchanger has two tube side passages with triangle pitch pattern and one shell side passage. For
the original design specifications were supplied as input to the optimization algorithm and the
resulting optimal exchanger cost given by four optimization methods were compared with the
original design solution given by the reference author and literature values.
The following upper and lower bounds for the optimization variables were imposed. Shell
internal diameter Ds ranging between 0.1m and 1.5m; tubes outside diameter do ranging from
0.01m to 0.051m; baffles spacing B ranging from 0.05m to 0.5m. All values of discounted
operating costs were computed with ny =10 years, annual discount rate i=10%, energy cost
CE=0.12∈/ kw h and an annual amount of work hours H=7000h/years similar to other researches
( (Caputo, P.M.Pelagagge, & P.Salini, 2008); (B.K.Patel & R.V.Rao, 2010); (Duck, Guerra,
Coelho, & Rao, 2012), (Sinnot))
Figure 2 Overall costs comparison
Table 2 Comparative table for parameters in all 4 methods
Variables GA SA PS Fmincon
Ds X X 0.615 0.615
d 0 X X 0.122 0.122
B X 0.5 0.5 0.5
Ci 1300.5 1320.7 36224 1320.7
Cod 7990.7 8115.1 7850.7 8115.1
Ctot 44195 44203 44075 44203
Elapsed Time
(sec)
0.39 X 5.08 0.24 3.25
- Represents the parameters which are consistent for all the 20 trials and the corresponding
parameter values are given in the respective cell.
X - Represents the parameters which are not consistent for all the 20 trials In case of elapsed
time only the two or three minimum values alone are given.

With the two extreme values of parameters from survey, the optimization is carried out with
different solvers. As they are of stochastic type, their results may vary from trial to trial and so
the problem is made to run for 20 trials and an average of all trials is taken as the final value of
the parameter, by the solver. The solvers are compared with three different criteria.
Consistency
The consistency table gives the parameters that remain constant for all the trails. All the
solvers give the same value for all the runs, which in turn indicates that the cost requirements are
acceptable. So we see that the solvers Pattern Search, Fmincon remain constant throughout their
runs.
Minimum Run Time
For a minimum run time of the problem we got PS (0.24seconds), GA (0.39 seconds).
Simplicity of Algorithm
Of all the algorithms we have taken the Pattern Search algorithm is the simplest followed by
GA, Simulated Annealing, and fmincon.
Thus it is seen that the cost is minimum for Pattern search. The Pattern Search solver satisfies
all the other criteria, it is consistent, the total elapsed time is just 0.24 seconds and the algorithm
is the simplest, so the appropriate algorithm, for optimization of thermal comfort is suggested as
Direct search algorithm & the solver is PATTERN SEARCH.
6. CONCLUSION
Heat exchanger design can be a complex task and advanced optimization tools are useful to
identify the best and cheapest heat exchanger. In this project, a solution method of the shell and
tube heat exchanger design optimization problem was proposed based on four optimization
algorithms. Based on this mathematical model is proposed, a computer code is developed in
Matlab, and it is solved using four optimization algorithm. It is found that the cost is minimized
and the appropriate algorithm for optimizing of cost is suggested as Direct Search Algorithm and
the solver is Pattern Search.
FUTURE WORK.
While there are many research needs related to the subject discussed here, the following is
suggested as high priority research needs which can be taken as future work. In continuation,
optimization of Cost minimization of Shell- and- Tube heat exchangers using non-traditional
optimization few other nontraditional optimization methods can be used to check which methods
yields the best result other than what is existing in the Literature
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