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College of Energy and Power Engineering JHH 1

3. Heat exchanger design

3.2 Evaluation of the mean temperature

difference in a heat exchangercont.)

College of Energy and Power Engineering JHH 2

Extended use of the LMTD

Limitations on the use of

LMTD

Restricted to the single-pass

parallel and counter-flow

configurations

For other configuration

LMTD need to be adjusted

Uis constant (more serious)

U(T, Configuration)

Regionally Uniform?

More severe in lager

exchanger

Less serious in compact

exchanger

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

A typical case of a heat exchanger

in which Uvaries dramatically.

Water side

Hot gas side

College of Energy and Power Engineering JHH 3

Extended use of the LMTD

Limitations Uvariation

The heat exchangesurface for a steamgenerator

This PFT-typeintegral-furnaceboiler,with a

surface area of 4560m2, is notparticularly large.

About 88% of thearea is in thefurnace tubing and12% is in the boiler.

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

College of Energy and Power Engineering JHH 4

Extended use of the LMTD

PFT-type boiler

Side view of PFT boiler

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

College of Energy and Power Engineering JHH 5

Extended use of the LMTD

LMTD correction factor,F

For common range of heat exchanger[Bowman 1940]

F is an LMTD correction factor

Tt temperature of tube flow, Ts temperature of shell flow

P is the relative influence of overall temperature difference

( on tube flow temperature,

If one flow remain constant T, then eitherP orR equal 0,F=1

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

=

R

intoutt

outsins

P

intins

intoutt

TT

TT

TT

TTFLMTDUAQ ,)(

st CCR /=

1

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College of Energy and Power Engineering JHH 7

Extended use of the LMTD

F for a one-shell-pass, four, six, tube-pass exchanger

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

)/1,(),( RPRFRPF = ForR > 1, Shamsundar noted

in out

out in

s s

t t

T TR

T T

=

College of Energy and Power Engineering JHH 8

Extended use of the LMTD

F for a two-shell-pass, four or more tube-pass exchanger

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

)/1,(),( RPRFRPF = ForR > 1, Shamsundar noted

in out

out in

s s

t t

T TR

T T

=

College of Energy and Power Engineering JHH 9

Extended use of the LMTD

F for a cross-flow exchanger with both passes unmixed

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

)/1,(),( RPRFRPF = ForR > 1, Shamsundar noted

in out

out in

s s

t t

T TR

T T

=

College of Energy and Power Engineering JHH 10

Extended use of the LMTD

F for a cross-flow exchanger with one passes mixed

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

)/1,(),( RPRFRPF = ForR > 1, Shamsundar noted

in out

out in

s s

t t

T TR

T T

=

College of Energy and Power Engineering JHH 11

Example 3.4

Known :Cpoil and U. To find: A=?

K

TT

TT

TTTT

incouth

outcinh

incouthoutcinh

76.40

3238

49181ln

)3238()49181(

)ln(

)()(LMTD

=

=

=Oil

Cooler

114.0P412.8 =

==

=

intins

intoutt

intoutt

outsins

TT

TT

TT

TTR

)/1,(),( RPRFRPF = AsR > 1

119.0/1,959.0 == RPR

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

Water

32oC

38oC

49oC

5.795kg/s Oil 181oC

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Example 3.4

AsR > 1 )/1,(),( RPRFRPF =

119.0/1,959.0 == RPR 92.0=F

)(LMTDUAFQ=

2121.2

)(

)(

)(

m

LMTDUF

TTcm

LMTDUF

QA

outsinsp

=

=

=

3. Heat exchanger design 3.2 Evaluation of t he mean t emperaturedifference in a heat exchanger

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College of Energy and Power Engineering JHH 19

Example 3.5

Known: parallel-flow heat exchanger, Tcin=49oC,Cc=20000W/K, Thin=150

oC, Ch=10000W/K,A=30 m2 ,

U=500W/m2K

To find: Q=?, Tcout=?, Thout=?

Cannot find LMTD

5.1NTUmin

==C

UA

5.0max

min =C

C

NTU

596.0=

kW6.655)(min

==incinh

TTCQ

C

C

QTT

CC

QTT

o

c

incoutc

o

h

inhouth

78.72

44.84

==

==

3. Heat exchanger design 3.3 Heat exchanger effectiveness

College of Energy and Power Engineering JHH 20

Example 3.6

Same kind of heat exchanger as Example 3.5.Thout=90

oC

To findA=?

NTU=1.15=UA/Cmin .

A=23.0m2 .

LMTD=52.79K

Q=UA(LMTD)

A=22.730m2

.

CC

TTCTT

o

c

inhouthh

incoutc70

)(=

=

5455.0)(

)(

min

=

incinh

outhinhh

TTC

TTC

NTU

3. Heat exchanger design 3.3 Heat exchanger effectiveness

Or

College of Energy and Power Engineering JHH 21

Heat exchanger design

Small exchanger, typically the kind of compact cross-

flow exchanger

The method described before

Larger exchanger pose difficulty in relation to U

The variation of Uthrough the exchanger

Hard to predict convective heat transfer coefficienth

Minimization of pumping power

Minimization of fixed costs

3. Heat exchanger design 3.4 Heat exchanger design

)(powerPumping Wpm

=

College of Energy and Power Engineering JHH 22

Heat exchanger design

Lager exchanger design process

Decide which fluid should flow in the shell side

which tube side

Pumping power, corrosion behavior, fouling, cleaning

Assess the cost of calculation

The converging accuracy of computation

The investment in the exchanger

The cost of miscalculation

Rough estimate of the size of the exchanger by using Uand

experience

Evaluate the Q, p, and the cost of various exchanger

configurations that appear reasonable for the application

Might involve 200 successive redesign

3. Heat exchanger design 3.4 Heat exchanger desi gn

College of Energy and Power Engineering JHH 23

Homework

3.20

3.28

300140 441241

2

3

2.25kg/s2000J/(kg*K)80560W/(m2K),8m21240

3. Heat exchanger design 3.4 Heat exchanger design