NURUL AFIFAH BINTI MOHD YUSOFF

2013275464

EH110 4A

FACULTY OF CHEMICAL ENGINEERING

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

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 cocurrentflow

in the opposite direction - countercurrent flow or perpendicular to each other - cross flow

1

2

12

lnT

T

TTTLn

Co-current flow

∆ T1

∆ T2

∆ A

A

1 2 T 1 T 2T 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

Counter-current flow

T1

A

1 2

T2

T3

T6

T4 T6

T7T8

T9

T10

Wall

T 1T 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

LMTD Counter-Flow HX

icohch

ocihch

LMLM

TTTTT

TTTTT

TT

TTTTUAQ

,,2,2,2

,,1,1,1

)12

12

:FlowCounter for Where

/ln(

Tlm,CF > Tlm,PF FOR SAME U: ACF < APF

LMTD- Multi-Pass and Cross-FlowApply a correction factor to obtain LMTD

CFLMLMLM TFTTUAQ ,

t: Tube Side

LMTD Parallel-Flow HX

ocohch

icihch

LMLM

TTTTT

TTTTT

TT

TTTTUAQ

,,2,2,2

,,1,1,1

)12

12

:Flow Parallelfor Where

/ln(

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 passesV=linear velocity of the tube fluid

The total tube-side pressure drop is

∆PT = ∆Pt + ∆Pr

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

• 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 CC

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?

• Number of Transfer Units, NTU

min

UANTUC

A dimensionless parameter whose magnitude influences HX performance:

with q NTU

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

• 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

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