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8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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Heat ExchangersDr. Senthilmurugan S. Department of Chemical Engineering IIT Guwahati - CL204 - Part !
Overall heat transfer coefficient
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide 2
Content
Temperatre profile across H!
Over all heat transfer coefficient
"lat plat configration
T#lar pipe configration
$efine %ith respect to heat transfer area
&inside/otside'
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide (
Temperatre )rofile *cross Heat Exchangers
Conter Crrent
Concrrent
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide +
Temperatre )rofile *cross Heat Exchangers
-2 e"changer
2-4 e"changer
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide 5
Temperatre )rofile *cross Heat ExchangersCross "lo% Exchangers
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5/12/16 | Slide 6
Temperatre )rofile *cross Heat Exchangers
Condenser
Sper heated ,apor
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide -
Heat Transfer CoefficientCalclation of overall coefficients from individal coefficients.
here0
d/d* local heat flx0 #ased on the area in
contact %ith flidT local average temperatre of flid
T% temperatre of %all in contact %ith flid
The individal0 or srface0 heat3transfer coefficient h
w
dq dAh
T T =
−
1
1
h wh
dq dAh
T T =
−
2
2
wc c
dq dAh
T T =
−
wwh wc
w w
xT T dq
dA k
− =
1 1
h wh
dqT T
dA h− =
2 2
wc c
dqT T
dA h− =
w ww
w wh wc
k dq dAh
x T T
= =
−
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide 4
Heat Transfer CoefficientCalclation of overall coefficients from individal coefficients.
"lat plate Configration H!
2 2 1 1
1 1
h wh wh wc wc c h c
w
w w
T T T T T T T T
xdq
dA h dA k dA h
− + − + − = −
= + + ÷
overall q UA T = ∆
2 1 wdA dA dA= =
2 2 1 1
1 1w
h cw w
x
T T dq dA h dA k dA h
− = + + ÷
( )
0 0
2 1
1 1
q A
h c
w
w
T T dq dA
x
h k h
−=
+ + ÷
∫ ∫
( )
2 1
1 1
h c
w
w
A T T q
x
h k h
−=
+ + ÷
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5/12/16 | Slide
Heat Transfer Coefficient"lat plate Configration H!
ncorporate the foling 7esistance
overall q UA T = ∆
1 2
1
1 1U
x
h k h
=∆
+ +
1 2
1 1 1 x
U h k h
∆= + +
1 1 2 2
1 1 1 1 1
f f
x
U h h k h h
∆= + + + +
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5/12/16 | Slide 18
Heat Transfer CoefficientT#lar Configration H!
Double-pipe heat exchanger
*ssme that the heat3transfer rate is ar#itraril9 #ased
on the otside area
2 2 1 1
1 1wh c
w w
x
T T dq dA h dA k dA h
− = + + ÷
1 1
h c
o wo
o o L w i i
T T dq
dA xdA
dA h dA k dA h
−
= + + ÷
id
od
1 1
h c
o o w o
o L w i i
T T dq
dA dA x dAh dA k dA h
−=
+ + ÷
o o
i i
dA d
dA d = o o
L L
dA d
dA d =
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5/12/16 | Slide 11
Heat Transfer CoefficientT#lar Configration H!
Double-pipe heat exchanger
id
od
01 1
o Aqh c
o
o o w o
o L w i i
T T dq dA
d x d
h d k d h
−=
+ + ÷
∫ ∫
( )1 1
o h c
o w o
o L w i i
A T T qd x d
h d k d h
−=
+ + ÷
( )
ln
o i
L
o
i
d d d
d d
−=
÷ 1 1 1o w o
o o L i i
d x d
U h d k d h= + +
o o overall q U A T = ∆
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5/12/16 | Slide 12
Heat Transfer CoefficientT#lar Configration H!
Double-pipe heat exchanger
*ssme that the heat3transfer rate is ar#itraril9 #ased on
the otside area
id
od
01 1
i Aq
h ci
o i i w
o o L w i
T T dq dA
d d x
d h d k h
−=
+ + ÷
∫ ∫
( )
0
1 1
i h c
i i w
o L w i
A T T qd d x
d h d k h
−=
+ + ÷
( )
ln
o i
L
o
i
d d d
d d
−=
÷
0
1 1 1i i w
i o L w i
d d x
U d h d k h= + +
i i overall q U A T
= ∆
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5/12/16 | Slide 1(
7esistance form of overall coefficient.
The overall temperatre drop is proportional to 1/:0and the temperatre drops in the t%o flids and the
%all are proportional to the individal resistances
%here ;T overall temperatre drop
;Ti temperatre drop throgh inside flid
;T% temperatre drop throgh metal %all
;To temperatre drop throgh otside flid
( ) ( ) ( ) ( )0
1
1
i i
o w i
i o i L w w i
q T
A U T T T
d d h d d x k h
∆=
∆ ∆ ∆= = =
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide 1+
"oling 7esistance
Heat3transfer srfaces do not remain clean. Scale0 dirt0 and other solid deposits form
on one or #oth sides of the t#es0 provide additional resistances to heat flo%0 and
redce the overall coefficient.
The effect of sch deposits is ta<en into accont #9 adding foling resistance in over
all Heat transfer coefficient
Overall coefficients #ased on otside and inside areas0 respectivel9
Ho% to accont %ith over all Heat transfer coefficient
0 0
1 1 1 1 1i i i w
i o fo L w i f i
d d d x
U d h d h d k h h= + + + +
1 1 1 1 1o w o o
o o fo L i i i fi
d x d d
U h h d k d h d h= + + + +
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide 15
"oling "actor Estimation
"oling factors mst #e o#tained experimentall9 #9 determining the vales of U for
#oth clean and dirt9 conditions in the heat exchanger. The foling factor is ths
defined as
0
1 1 1 1i f
f clean fo f i
d R
U U d h h= − = +
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5/12/16 | Slide 16
$9namic natre of "oling "actor 7ate of foling 3 d9namic models
=<>0 =a>0 =#> and =c> are foling thic<ness parameters.
ε 3 foling rate coefficient0
Tf 3 foling thic<ness vale0
?1 and ?2 @ foling thic<ness parameters0
?T @ coefficient of foling temperatre
parameter0 AS3 mass fraction of solids in the
mixtre of one or more components0Tl3 temperatre of the mixtre of one or more
components in the cold cham#er at heat
transfer srface0
*3 *rea of heat transfer0
ρ3 initial densit9 of the mixtre of the one or
more components.
( ) 2
3*exp f sT
f l
dt Z A K t K
T dt ε
ρ
= − − − ÷
[ ]
5
3
2
3
0.01
0.003 m
273.15 K
A=100 m
0.01
1000
T
s
kg
m
K
K
Z Kg
m
ε
ρ
=
==
= −=
( ) f f
dt f t dt
= ( )2, f
f f dt f t t dt
= ( )2*exp * * f f f dt k b t a t c
dt = − +
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5/12/16 | Slide 1-
Significance of srface area section
*lthogh the choice of area to #e sed as the #asis of an overall coefficient is
ar#itrar90 sometimes one particlar area is more convenient than others. "or
example
hen hi BB ho and <%/x% BB ho then :ho
hen ho BB hi and <%/x% BB hi then :hi
hen "oling effects are negligi#le0
The ratios do /d i and d o /d L have so little significance that the9 can #e disregarded0
.e. for large3diameter thin3%alled t#es0 flat plates or an9 other case %here a
negligi#le error is cased #9 sing area factor i.e. U i and U o are identical
Overall Heat Transfer Coefficient
1 1 1w
o i
x
U h k h= + +
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5/12/16 | Slide 14
Classification of ndividal Heat3transfer Coefficients
Heat flo% to or from flids inside t#es0 %ithot phase change
Heat flo% to or from flids otside t#es0 %ithot phase change
Heat flo% from condensing flids
Heat flo% to #oiling liids
8/17/2019 Lect - 18 Heat Exchanger Lecture 2 of 4.pptx
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5/12/16 | Slide 1
merical ranges of Heat transfer coefficientith respect to applications
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