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HEAT EXCHANGERS-2
Associate Professor
IIT Delhi
E-mail: [email protected]
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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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,
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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
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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
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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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,,
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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
.
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,,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
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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
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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
+
=
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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
+
=
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)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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Effectiveness for heatexchangers (from Kays and London, Ref. 5).
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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
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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 =
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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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