lect - 18 heat exchanger lecture 2 of 4.pptx

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'

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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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Temperatre )rofile *cross Heat Exchangers

-2 e"changer 

2-4 e"changer 

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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

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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 

= =

−

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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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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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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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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

∆=

∆ ∆ ∆= = =

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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= + + + +

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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

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5/12/16 | Slide 1

merical ranges of Heat transfer coefficientith respect to applications

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