Lect - 20 Heat Exchanger Lecture 4 of 4.pptx

8/17/2019 Lect - 20 Heat Exchanger Lecture 4 of 4.pptx

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Heat ExchangersDr. Senthilmurugan S. Department of Chemical Engineering IIT Guwahati - CL204 - Part 20

Effectiveness-NTU method


2/18

5/12/16 | Slide 2

Need of Effectiveness - NTU method

The !T" a##roach to heat-exchanger anal$sis is %sef%l &hen the inlet and o%tlet

tem#erat%res are 'no&n or are easil$ determined(

The !T" is then easil$ calc%lated) and the heat flo&) s%rface area) or overall heat-

transfer coefficient ma$ *e determined

+hen the inlet or exit tem#erat%res are to *e eval%ated for a given heat exchanger)

the anal$sis fre,%entl$ involves an iterative #roced%re *eca%se of the logarithmicf%nction in the !T"

n these cases the anal$sis is #erformed more easil$ *$ %tili.ing a method *ased on

the effectiveness of the heat exchanger in transferring a given amo%nt of heat

The effectiveness method also offers man$ advantages for anal$sis of #ro*lems in

&hich a com#arison *et&een vario%s t$#es of heat exchangers m%st *e made for

#%r#oses of selecting the t$#e *est s%ited to accom#lish a #artic%lar heat-transfer

o*ective(

Effectiveness 0


3/18

5/12/16 | Slide

ct%al Heat transfer for 3o%nter flo& H4

verall enthal#$ *alance

or 3o%nter lo& H4

&here c#c 0 s#ecific heat of cold fl%id

c#h 0 s#ecific heat of &arm fl%id

3o%nter lo& H4

Tc*

Tca

h cq q=

( ) ( )h ph ha hb c pc ca cbq m c T T m c T T = − = −& &


4/18

5/12/16 | Slide 7

ct%al Heat transfer for #arallel flo& H4

or 3o%nter lo& H4

!axim%m #ossi*le heat transfer is

ex#ressed as

The minim%m fl%id ma$ *e either the hotor cold fl%id) de#ending on the mass-

flo& rates and s#ecific heats(

3onc%rrent flo&

( ) ( )h ph ha hb c pc cb caq m c T T m c T T = − = −& &

( ) ( )max min inlet inlet p h C q mc T T = −&


5/18

5/12/16 | Slide 5

Effectiveness - NTU method

or #arallel flo& Heat Exchanger

f hot fl%id is fl%id then

f cold fl%id is fl%id then

or co%nter flo& Heat Exchanger

f hot fl%id is fl%id then


( )

( )

( )

( )

h ph ha hb ha hb

h h ph ha ca ha ca

m c T T T T

m c T T T T

− −∈ = =

− −

&

&

( )

( )

( )

( )c pc cb ca cb ca

c

c pc ha ca ha ca

m c T T T T

m c T T T T

− −∈ = =− −

&

&

( )

( )

( )

( )

h ph ha hb ha hb

h

h ph ha ca ha ca

m c T T T T

m c T T T T

− −∈ = =

− −

&

&

( )

( )( )

( )) )c pc ca cb ca cb

c

c pc ha ca ha ca

m c T T T T

m c T T T T

− −

∈ = =− −

&

&


6/18

5/12/16 | Slide 6


8$ ntegration of heat fl%x across H4 or #arallel flo& Heat Exchanger


Enthal#$ *alance

1 1ln hb cb o o

ha ca c pc h ph

T T U A

T T m c m c

−= − + ÷ ÷ ÷− & &

1 c pco o

c pc h ph

m cU A

m c m c

−= + ÷

÷

&

& &

exp 1 c pchb cb o o

ha ca c pc h ph

m cT T U A

T T m c m c

− −= + ÷ ÷−

&

& &

( )

( )cb ca

ha ca

T T

T T

−∈=

−

( )c pc

ha ca cb cb

h phhb cb

ha ca ha ca

m cT T T T m cT T

T T T T

− − −−

=− −

&

&

( )c pc

hb ha ca cb

h ph

m cT T T T

m c

= − − ÷ ÷

&

&


7/18

5/12/16 | Slide 9


( )c pc

ha ca cb cb

h phhb cb

ha ca ha ca

m c

T T T T m cT T

T T T T

− − −−=

− −

&

&

( ) ( ) ( )1 1

c pc

ha ca ca cb ca cb

h ph c pchb cb

ha ca ha ca h ph

m c

T T T T T T m c m cT T

T T T T m c

− − − + − −= = − + ∈ ÷ ÷− −

&

& &

&

( )

( )cb ca

ha ca

T T

T T

−∈=

−

1 1 exp 1c pc c pchb cb o o

ha ca h ph c pc h ph

m c m cT T U A

T T m c m c m c

− −= − + ∈= + ÷ ÷ ÷ ÷−

& &

& & &


8/18

5/12/16 | Slide :



or co%nter flo& Heat Exchanger; f hot fl%id is fl%id then term and are

interchanged s a conse,%ence) the effectiveness is %s%all$ &ritten

1 exp 1

1

c pco o

c pc h ph

c pc

h ph

m cU A

m c m c

m cm c

−− + ÷ ÷ ∈=

+ ÷ ÷

&

& &

&&

1 1 exp 1c pc c pco o

h ph c pc h ph

m c m cU A

m c m c m c

−− + ∈= + ÷ ÷

÷ ÷

& &

& & &

min

min max

min

max

1 exp 1

1

o oU A C C C

C

C

−− + ÷ ∈=

+ ÷


9/18

5/12/16 | Slide <


or co%nter flo& Heat Exchanger

Term is called as n%m*er of transfer

%nits =NTU> since it is indicative of thesi.e of the heat exchanger

3a#acit$ ?atio

min

min max

min min

max min max

1 exp 1

1 exp 1

o o

o o

U A C

C C

U AC C C C C

−− − ÷

∈=

−− − ÷


10/18

5/12/16 | Slide 1@

or 8oling and condensation

n *oiling or condensation #rocess the

fl%id tem#erat%re sta$s essentiall$

constant) or the fl%id acts as if it had

infinite s#ecific heat(

n these cases C min /C maxA@ and all the

heat-exchanger effectiveness relationsa##roach a single sim#le e,%ation)

Barallel flo& Heat Exchanger

min

min max

min

max

min

1 exp 1

1

1 exp

o o

o o

U A C

C C

C C

U A

C

−− + ÷

∈=

+ ÷

−= −

1 e

NTU −∈= −


11/18

5/12/16 | Slide 11

Heat-exchanger effectiveness relations


12/18

5/12/16 | Slide 12

Effectiveness Cs Heat-Transfer ?ates

High effectiveness at a certain flo&

config%ration does not mean that it &ill

have a higher heat-transfer rate than at

some lo& effectiveness condition(

High val%es of ε corres#ond to small

tem#erat%re differences *et&een the hotand cold fl%id) &hile higher heat-transfer

rates res%lt from larger tem#erat%re

differences that leads to higher driving

#otential


13/18

5/12/16 | Slide 1

Berformance nal$sis and Si.ing anal$sis

Performance nal!"i"

3alc%late the ca#acit$ ratio 3r 0 3min/3max and NTU 0 U/3min from in#%t data

"etermine the effectiveness from the a##ro#riate charts or e-NTU e,%ations for the

given heat exchanger and s#ecified flo& arrangement(

+hen ∈ is 'no&n) calc%late the total heat transfer rate 3alc%late the o%tlet tem#erat%re(

Si#ing nal!"i"

+hen the o%tlet and inlet tem#erat%res are 'no&n) calc%late ∈( 3alc%late the ca#acit$ ratio 3r 0 3min/3max

3alc%late the overall heat transfer coefficient) U

+hen ∈ and 3 and the flo& arrangement are 'no&n) determine NTU from the e-NTU e,%ations(

+hen NTU is 'no&n) calc%late the total heat transfer s%rface area(

NTU method


14/18

5/12/16 | Slide 17

m#ortant factors to *e considered

Heat-transfer re,%irements

3ost

Bh$sical si.e

Bress%re-dro# characteristics

"esign of heat exchanger


15/18

5/12/16 | Slide 15

Bress%re "ro# in Heat Exchangers3orrelation for t%*e side #ress%re dro#

&here)

DBt)f 0 total #ress%re dro# in the *%ndle of t%*e

f 0 friction factor =can *e fo%nd o%t from !ood$s chart>

gf 0 mass velocit$ of the fl%id in the t%*e

0 t%*e length

n 0 no of t%*e #asses

g 0 gravitational acceleration

Ft 0 densit$ of the t%*e fl%id

dt 0 inside diameter of the t%*e

m 0@(17 for ?e G 21@@

@(25 for ?e 21@@

Due to frictional losses


16/18

5/12/16 | Slide 16

Bress%re "ro# in Heat Exchangers

Bress%re losses d%e to the change in direction is called

ret%rn-loss

&here n 0 no of t%*e #ass

vt 0 velocit$ of the t%*e fl%id

Ft 0 densit$ of the t%*e fl%id

Therefore, the total tube side pressure drop will be,

Δpt = ΔPt,f + ΔPt,r

3orrelation for t%*e side #ress%re dro#


17/18

5/12/16 | Slide 19

Bress%re "ro# in Heat Exchangers

or an %n*affled shell)

or a *affled shell)

&here

0 shell length

ns 0 no of shell #ass

n* 0 no of *affles

Fs 0 shell side fl%id densit$

gs 0 shell side mass velocit$

"h 0 h$dra%lic diameter of the shell

"si 0 inside diameter of shell

f s 0 shell side friction factor

nt 0 n%m*er of t%*es in the shelldo 0 o%ter diameter of the t%*e

3orrelation for shell side #ress%re dro#


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Lect - 20 Heat Exchanger Lecture 4 of 4.pptx