Summary of lmtd and e ntu
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The document discusses the Log Mean Temperature Difference (LMTD) method for heat exchangers, which is applicable for specific flow configurations like one shell pass and one tube pass. It explains how temperature differences vary with fluid flow and introduces the effectiveness-NTU method as an alternative for predicting outlet temperatures without complex numerical solutions. The document also covers key concepts like heat exchanger effectiveness and pressure drop calculations, emphasizing the equivalence of LMTD and effectiveness-NTU methods.
Summary of lmtd and e ntu
- 1. NURUL AFIFAH BINTI MOHD YUSOFF 2013275464 EH110 4A FACULTY OF CHEMICAL ENGINEERING
- 2. The Log Mean Temperature Difference Method (LMTD) The Logarithmic Mean Temperature Difference(LMTD) is valid only for heat exchanger with one shell pass and one tube pass. For multiple number of shell and tube passes the flow pattern in a heat exchanger is neither purely co-current nor purely counter-current. The temperature difference between the hot and cold fluids varies along the heat exchanger. It is convenient to have a mean temperature difference Tm for use in the relation. s mQ UA T
- 3. The mean temperature difference in a heat transfer process depends on the direction of fluid flows involved in the process. The primary and secondary fluid in an heat exchanger process may flow in the same direction - parallel flow or cocurrent flow in the opposite direction - countercurrent flow or perpendicular to each other - cross flow
- 5. 1 2 12 ln T T TT TLn Co-current flow ∆ T1 ∆ T2 ∆ A A 1 2 T 1 T 2 T 4 T 5 T 6T 3 T 7 T 8 T 9 T 10 P ara ll e l Fl ow 731 TTTTT in c in h 1062 TTTTT out c out h
- 6. Counter-current flow T1 A 1 2 T2 T3 T6 T4 T6 T7 T8 T9 T10 Wall T 1 T 2 T 4 T 5 T 3 T 7 T 8 T 9 T 10 T 6 Co un t e r - C u r re n t F l ow 731 TTTTT out c in h 1062 TTTTT in c out h
- 7. LMTD Counter-Flow HX icohch ocihch LMLM TTTTT TTTTT TT TT TTUAQ ,,2,2,2 ,,1,1,1 )12 12 :FlowCounterforWhere /ln( Tlm,CF > Tlm,PF FOR SAME U: ACF < APF
- 8. LMTD- Multi-Pass and Cross-Flow Apply a correction factor to obtain LMTD CFLMLMLM TFTTUAQ , t: Tube Side
- 10. In a multi-pass exchanger, in addition to frictional loss the head loss known as return loss has to be taken into account. The pressure drop owing to the return loss is given by- Where, n=the number of tube passes V=linear velocity of the tube fluid The total tube-side pressure drop is ∆PT = ∆Pt + ∆Pr
- 13. THE EFFECTIVENESS-NTU METHOD LMTD method is useful for determining the overall heat transfer coefficient U based on experimental values of the inlet and outlet temperatures and the fluid flow rates. A more convenient method for predicting the outlet temperatures is the effectiveness NTU method. This method can be derived from the LMTD method without introducing any additional assumptions. Therefore, the effectiveness-NTU and LMTD methods are equivalent. An advantage of the effectiveness-NTU method is its ability to predict the outlet temperatures without resorting to a numerical iterative solution of a system of nonlinear equations. The heat-exchanger effectiveness ε is defined as
- 14. • Heat exchanger effectiveness, : max q q 0 1 • Maximum possible heat rate: max min , ,h i c iq C T T min if or h h cC C C C Will the fluid characterized by Cmin or Cmax experience the largest possible temperature change in transit through the HX? Why is Cmin and not Cmax used in the definition of qmax?
- 15. • Number of Transfer Units, NTU min UANTU C A dimensionless parameter whose magnitude influences HX performance: withq NTU
- 16. Heat Exchanger Relations , , , , h i h oh h h i h o q m i i or q C T T • , , , , c c o c i c c o c i q m i i or q C T T min , ,h i c iq C T T • Performance Calculations: min max, /f NTU C C Cr Relations Table 11.3 or Figs. 11.14 - 11.19
- 17. • Design Calculations: min max, /NTU f C C Relations Table 11.4 or Figs. 11.14 - 11.19 • For all heat exchangers, with rC • For Cr = 0, to all HX types.a single relation appliesNTU 1 exp NTU or 1n 1NTU
- 19. References http://www.engineeringtoolbox.com/arithmetic-logarithmic- mean-temperature-d_436.html http://www-old.me.gatech.edu/energy/laura/node5.html http://www.che.ufl.edu/unit-ops-lab/experiments/HE/HE- theory.pdf http://web.iitd.ac.in/~prabal/MEL242/(30-31)-Heat-exchanger- part-2.pdf