Summary of lmtd and e ntu. 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

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

9. LMTD Parallel-Flow HX
ocohch
icihch
LMLM
TTTTT
TTTTT
TT
TT
TTUAQ
,,2,2,2
,,1,1,1
)12
12
:FlowParallelforWhere
/ln(






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