(30 31) heat exchanger part 2

7/22/2019 (30 31) Heat Exchanger Part 2

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HEAT EXCHANGERS-2

Associate Professor

IIT Delhi

E-mail: [email protected]

P.Talukdar/ Mech-IITD


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The subscripts 1 and 2 represent the inlet andoutlet, respectively..

T and t represent the shell- and tube-side


,


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T and t represent the shell-

- ,

respectively



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LMTD method is very suitable for determining the size of a heat

exc anger o rea ze prescr e ou e empera ures w en e mass ow

rates and the inlet and outlet temperatures of the hot and cold fluids arespecified.

With the LMTD method, the task is to select a heat exchanger that will

meet the prescribed heat transfer requirements. The procedure to be

Select-type Determine- Inlet, Oulet Calculate Tlm

o e aExchanger

emp, ea rans er ra eUsing energy balance

and F if neccessary


s


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determination of the heat transfer rate and the outlet temperatures of thehot and cold fluids for prescribed fluid mass flow rates and inlet temperatures

.

The heat transfer surface area A of the heat exchanger in this case is known,

but the outlet tem eratures are not. Here the task is to determine the heat

transfer performance of a specified heat exchanger or to determine if a heat

exchanger available in storage will do the job.

The LMTD method could still be used for this alternative problem, but theprocedure would require tedious iterations, and thus it is not practical. In an

attempt to eliminate the iterations from the solution of such problems, Kays


an on on came up w t a met o n ca e t e e ec veness

method, which greatly simplified heat exchanger analysis


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-Effectiveness

ratetransferheatpossibleMaximumratetransferheatActual

QQ

max

.

==

Actual heat transfer rate

. ==

Maximum temperature difference that can occurs

ou,n,n,cou,cc

Maximum possible heat transfer

n,cn,max

TTC.

=


,,


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The heat transfer in a heat exchanger will reach its maximum value

when

(1) the cold fluid is heated to the inlet temperature of the hot fluid or(2) The hot fluid is cooled to the inlet temperature of the cold fluid.

These two limiting conditions will not be reached simultaneously

unless the heat capacity rates of the hot and cold fluids are=. ., c h . c h, ,

the fluid with the smaller heat capacity rate will experience a larger

temperature change, and thus it will be the first to experience the

maximum tem erature at which oint the heat transfer will come to

a halt.Maximum possible heat transfer

.


,,minmax incinh


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Example-ontd.



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Example

- ont .

The temperature rise of the cold fluid in aheat exchanger will be equal to the

temperature drop of the hot fluid when the


the hot and cold fluids are identical.


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Effectiveness relationparallel-flow double-pipe heat exchanger

.)TT(C)TT(CQ out,hin,hhin,cout,cc == )TT(

C

TT in,cout,ch

cin,hout,h =

+=

h

c

c

s

in,cin,h

out,cout,h

C

C1

C

UA

TT

TTln

+=

pccphhsin,cin,h

out,cout,h

Cm

1

Cm

1

UATT

TT

ln &&

and after adding and subtractingTc, in gives

C

+=

+

h

c

c

s

in,cin,h

in,cout,ch

out,cin,cin,cin,h

C

C1

C

UA

TT

Cln


simplifies to

+=

+

h

c

c

s

in,cin,h

in,cout,c

h

c

C

C1

C

UA

TT

TT

C

C11ln


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We now manipulate the definition of effectiveness to obtain

c

min

in,cin,h

in,cout,c

in,cin,hmin

in,cout,cc

max

CC

TTTT

)TT(C)TT(C

Q

Q.

.

=

==

+=

+ h

c

c

s

incinh

in,cout,c

h

c

C

C

1C

UA

TT

TT

C

C

11lnTaking either Cc or Ch to be Cmin (both

results

approaches give the same result), the

relation above can be expressed more

conveniently as

+

+=cmin

hc

cs

flow_parallelC

1C

C1Cexp1

max

min

min

s

flowarallel

C

C1

C

UAexp1

+

=


hc

max

min_

C1+


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ss UAUA ==minp

min

)Cm(

C .

CCapacity ratio

maxCc=

s.Therefore,forspecifiedvaluesofUandCmin,thevalueofNTUisameasureoftheheattransfersurfaceareaAs.Thus, mins C1UAex1 +thelargertheNTU,thelargertheheatexchanger.

max

min

maxminflow_parallel

C

C1

CC

+

=


)c,NTU(function)C/C,C/UA(function maxminmins ==


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Effectiveness for heatexchangers (from Kays and London, Ref. 5).



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1. The value of the effectiveness ranges from 0 to 1.

to about NTU 1.5) but rather slowly for larger

values. Therefore, the use of a heat exchanger with

a large NTU (usually larger than 3) and thus a

arge s ze cannot e ust e econom ca y, s nce a

large increase in NTU in this case corresponds to a

small increase in effectiveness. Thus, a heat

exchan er with a ver hi h effectiveness ma be

highly desirable from a heat transfer point of view

but rather undesirable from an economical point of

view.

. v y =min

/Cmax, the counter-flow heat exchanger has the

highest effectiveness, followed closely by the

cross-flow heat exchangers with both fluids


unmixed.


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3. The effectiveness of a heat exchanger is

NTU values of less than about 0.3.4. The value of the capacity ratio c ranges between

. ,

becomes a maximum for c = 0 and a minimum

for c = 1. The case c = Cmin /Cmax0

corresponds to Cmax , which is realizedur ng a p ase-c ange process n a con enser or

boiler. All effectiveness relations in this case

reduce to = max = 1 - exp(NTU) regardless ofthe t e of heat exchan er. Note that the

temperature of the condensing or boiling fluidremains constant in this case. The effectiveness

is the lowest in the other limiting case of c =


min max = , w c s rea ze w en e ea

capacity rates of the two fluids are equal.


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Note that the analysis of heat exchangers with unknown outlet temperatures is

a straight forward matter with the effectivenessNTU method but requires

rather tedious iterations with the LMTD method.

en a e n e an ou e empera ures are spec e , e s ze o e ea

exchanger can easily be determined using the LMTD method.

,

by first evaluating the effectiveness from its definition and then the NTU

from the appropriate NTU relation given in tabular form.



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(30 31) heat exchanger part 2

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