Chapter 4 HXs

8/16/2019 Chapter 4 HXs

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Chapter 4: Heat Exchangers

Devices that facilitate the exchange of heat between

two fluids that are at different temperatures whilekeeping them from mixing with each other.

Used in practice in a wide range of applications, from

heating and air-conditioning systems in a household, to

chemical processing (Cooling and heating of acids and

caustic solutions and power production in large plants.


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!eat transfer in a heat exchanger usually involves

convection in each fluid and conduction throughthe wall separating the two fluids.

"n the analysis of heat exchangers, it is

convenient to work with an overall heat transfer

coefficient U that accounts for the contribution of

all these effects on heat transfer.

#he rate of heat transfer between the two fluids at

a location in a heat exchanger depends on the

magnitude of the temperature difference at that

location, which varies along the heat exchanger.


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"n the analysis of heat exchangers, it is usuallyconvenient to work with the logarithmic mean

temperature difference LMTD, which is an

e$uivalent mean temperature difference between

the two fluids for the entire heat exchanger.


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Double Pipe Heat Exchangers

#wo types of flow arrangement%

&arallel flow% !ot and cold fluids enter the heat

exchanger at the same end and move in thesame direction.

Counter flow: #he hot and cold fluids enter the

heat exchanger at opposite ends and flow inopposite directions


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Double Pipe Heat Exchangers


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Heat Exchangers: Types


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Compact Heat Exchangers

'pecifically designed to realie a large heat transfersurface area per unit volume

#he ratio of the heat transfer surface area of a heat

exchanger to its volume is called the area density .

) heat exchanger with ! *++ mm is classified as

being compact.


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Compact Heat Exchangers (Examples)

Car radiators ( " /+++ m

m

Compact heat exchangers enable us to achieve high

heat transfer rates between two fluids in a small volume,and they are commonly used in applications with strict

limitations on the weight and volume of heat exchangers


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Car 0adiator


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Compact Heat Exchangers

#he large surface area in compact heat

exchangers is obtained by attaching closely spaced

thin plate or corrugated fins to the walls separating

the two fluids.

Compact heat exchangers are commonly used in

gas-to-gas and gas-to-li$uid (or li$uid-to-gas heat

exchangers to counteract the low heat transfer

coefficient associated with gas flow with increasedsurface area.

Car radiator, is a water-to-air compact heat

exchanger.


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Cross Flow Heat Exchangers

Different flow configurations in cross-flow heat

exchangers

1hen fluids move perpendicular to each other, and

such flow configuration is called cross!low


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"hellan#Tube Heat Exchangers

#he schematic of a shell-and-tube heat exchanger

(one-shell pass and one-tube pass


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"hellan#Tube Heat Exchangers


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Plate an# Frame Heat Exchangers


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Heat Exchangers

) condenser is a heat exchanger in which one of thefluids is cooled and condenses as it flows through the

heat exchanger.

) #oiler is another heat exchanger in which one of thefluids absorbs heat and vapories.

) space radiator is a heat exchanger that transfers

heat from the hot fluid to the surrounding space byradiation.


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The o$erall heat trans!er coe!!icient:

!lat wall

!eat transfer% 2rom the hot fluid to the wall by convection,

through the wall by conduction, and then from the wall to the cold

fluid #y convection.


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U is the overall heat transfer coefficient



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1hen the wall thickness is small and the thermal

conductivity of the tube material is high,

#hen we can use a simplify e$uation%



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%pproximate $alues o! o$erall heat

trans!er coe!!icient


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%pproximate $alues o! o$erall heat

trans!er coe!!icient


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Fouling Factors

% &ouling factor for inner

surface

% &ouling factor for inner

surface


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0epresentative fouling factors

'ource:

Tu#ular (xchange

Manufacturers )ssociation


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Fouling Factors

&recipitation fouling of ash particles on superheater

tubes (from 'team, *ts +eneration, and Use,

6abcock and 1ilcox Co., /7*8


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E!!ect o! Fouling on the &$erall Heat

Trans!er Coe!!icient

) double-pipe (shell-and-tube heat exchanger isconstructed of a stainless steel ( % /9./ 1m : ;C inner

tube of inner diameter Di % /.9 cm and outer diameter

Do % /.7 cm and an outer shell of inner diameter . cm.

#he convection heat transfer coefficient is given to be hi


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Trans!er Coe!!icient"&'T&*

#he heat transfer coefficientsand the fouling factors on the

tube and shell sides of a heat

exchanger are given. #he

thermal resistance and the

overall heat transfer

coefficients based on the inner

and outer areas are to bedetermined.

Assumptions

#he heat transfer coefficients and the fouling factors are

constant and uniform.


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Heat Exchanger AnalysisLMTD

NTU Method


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'og mean temperature #i!!erence

'+TD)

'teady-flow devices >ass flow rate of each fluid remains constant 2luid properties remain the constant inetic and potential energy changes are negligible#here is no heat loss to the surrounding medium


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('+TD)

and

"f / is the total rate of heat transfer #etween the hot andcold fluids application of the steady flow

energy e$uation ( /st ?aw of thermodynamics, reduces

to%

p h h in h out Q mc T T = -, , ,( )&

&

p c c out c inQ mc T T = -

, , ,( )& &


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('+TD)'o we can write

and

where

,e can #e!ine heat capacity

rates:

p c c out c in

p h h in h out

Q mc T T

Q mc T T

= -

= -

, , ,

, , ,

( )

( )

& &

& &


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Con#enser an# -oiler

1e can see here that @# is ero for condensing fluid in condenser and

for boiling fluid in boiler


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('+TD)

"t is appropriate to use some mean or average @#for heat exchanger analysis and we can write as%

where U is the overall heat transfer coefficient, )s is the heat transfer area,

and @#m is an appropriate average temperature difference #etween the

two fluids.

"t is observed the appropriate form of the mean

temperature difference between the two fluids is

logarithmic in nature


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'+TD

Consider a parallel flow double pipe !34

Auter surface of the heat exchanger to be well

insulated and heat transfer occurs between the

two fluids only

inetic and potential energy changes are

negligible.

3nergy balance on each fluid can be written%


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'+TD



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'+TD

#he rate of heat transfer in the differential section of the

heat exchanger can also be expressed as

"ntegrating this e$uation from inlet to outlet


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'+TD


heat exchanger can also be expressed asrating this e$uation from inlet to outlet

p c c out c in

p h h in h out

Q mc T T

Q mc T T

= -

= -

, , ,

, , ,

( )

( )

& &

& &

p c

c out c in

p h

h in h out

Qmc

T T

Q

mcT T

=-

=-

,

, ,

,

, ,

( )

( )

&&

&

&

2

1

h out c out

h in c in

T T T

T T T

D = -

D = -

, ,

, ,

1 1 2

2

s

T T T UA

T Q

é ù é ùD D - Dê ú ê ú=ê ú ê úD ë ûë û

ln&


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'+TD

2

1

h out c out

h in c in

T T T

T T T D = -

D = -

, ,

, ,

1 1 2

2

1 2

1

2

s

s

T T T UAT Q

T T

Q UA T

T

é ù é ùD D - Dê ú ê ú=

ê ú ê úD ë ûë û

é ùê úê úD - Dê ú

= ê úé ùDê úê úê úê úDê úë ûë û

ln

ln

&

&


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'+TD

1e may like to consider using arithmetic average instead of

?>#D but%

#he temperature difference between the two fluids

decreases from @T0 at the inlet to @T1 at the outlet. 'o

arithmetic mean temperature @T am %2 @T 03 @T 1 4 51 is not truerepresentation.

6hereas the logarithmic mean temperature difference T lm is

o#tained #y tracing the actual temperature profile of the

fluids along the heat exchanger and is an exact

representation of the average temperature difference.

@T am will overestimate the rate of heat

transfer in a heat exchanger


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CounterFlow Heat

Exchangers

#he relation of log mean temperature difference is developed

using a parallel-flow heat exchanger, but we can show by

repeating the analysis for a counter-flow heat exchanger by

redefining @#/ and @T1 as shown in figure a#ove


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'+TD


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>ulti pass and Cross 2low !eat

3xchangers

Beneralised expression is limited to only parallel and

counter flow !4s. 6ut when these are transformed to

cross flow and multipass !xs, too complicatedexpressions are developed.

) convenient approach is to introduce a correction

factor 2 which depend upon the geometry of !x andtemperatures of hot and cold streams.


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2 is found from figures


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#he correction factor & for common cross-flow and

shell-and-tu#e heat exchanger configurations arecalculated from two different temperature ratios 7

and $ defined as :

where the subscripts / and represent the inlet and outlet,

respectively. 8ote that for a shell-and-tube heat exchanger, T and t

represent the shell- and tu#e-side temperatures respectively


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#he value of 7 ranges from 9 to 0.

The value of $, on the other hand, ranges from + to infinity,

$ % 9 corresponding to the phase-change (condensation or

boiling on the shell-side

$ to phase-change on the tube side.

#he correction factor is & % 0 for #oth of these limiting cases.

#herefore, the correction factor for a condenser or #oiler is

& % 0, regardless of the configuration of the heat exchanger.


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Correction Factor Charts


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Con#ensation o! "team in a Con#enser

'team in the condenser of a

power plant is to be condensed

at a temperature of +;C withcooling water from a nearby

lake, which enters the tubes of

the condenser at /=;C and

leaves at ;C. #he surface areaof the tubes is =9 m, and the

overall heat transfer coefficient is

/++ 1m ;C. Determine the

mass flowrate of the cooling

water needed and the rate of

condensation of the steam in the

condenser.


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"&'T&*

'team is condensed by cooling water in the condenserof a power plant. #he mass flow rate of the cooling water

and the rate of condensation are to be determined.

Assumptions

. 'teady operating conditions exist./ #he heat exchanger is well insulated.

0 Changes in the kinetic and potential energies of fluid

streams are negligible.

4 #here is no fouling.1 2luid properties are constant.

Properties #he heat of vaporiation of water at +;C is

hfg % =/ kkg and the specific heat of cold water at

the avera e tem erature of /8;C is C % =/8= k : ;C

C # i ! " i C #


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#he temperature difference between the steam and the

cooling water at the two ends of the condenser is

!eat transfer rate in the condenser is determined from

>ass flow rate of the cooling water and the rate of the

condensation of the steam are determined from

C # ti ! "t i C #


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1hen there is fouling on one of the surfaces, the overall heattransfer coefficient U is :

E!! ti *T th #


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E!!ecti$eness*T metho#

5 #he ?>#D approach to !34 analysis works well when

the inlet and outlet temperatures are known or easilyobtained

5 1hen either inlet or outlet temperatures are to be

determined, iterative procedures should be used with the?>#D

5 'uch analysis can be facilitated using the method

based on the effectiveness of !34 in transferring agiven amount of heat

E!! ti *T th #


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5 #he heat transfer effectiveness is defined as

#he actual heat transfer rate in a heat exchanger can be

determined from an energy balance on the hot or coldfluids.

E!! ti *T th #


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"n that case the fluid with the smaller heat capacity ratewill experience a larger temperature change

( )max min , ,

h in c in

Q C T T = -&

min

ifor

if

h h c

c c h

C C C

C

C C C

ì


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( )max min , , h in c inQ C T T = -&

min

ifor

if

h h c

c c h

C C C

C

C C C

ì


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Auter surface of the heat exchanger to be well

insulated and heat transfer occurs between the

two fluids only

inetic and potential energy changes are

negligible

) xial heat conduction along the tube is negligible

3nergy balance on each fluid can be written%


E!!ecti$eness *T metho#


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Consider a parallel floe double pipe !34




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heat exchanger can also be expressed as

"ntegrating this e$uation from inlet to outlet


0earranging



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0earranging

therefore



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6ut

therefore

#aking either C c or C h to be C min



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3ffectiveness relations of the heat exchangers typically

involve the dimensionless group U)s

5C min.

This ;uantity is

called the number of transfer units *T an# is expresse#

as

'o for parallel flow we can write

[ ]1 1

1

c

c

e

- - +=

+

exp NTU( )




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[ ]1 1

1

c

c

e- - +=

+

ln ( )NTU

[ ]1 11

cc

e - - +=+

exp NTU( )




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2ollowing observations from the effectiveness relations

and charts already given%

/. #he value of the effectiveness ranges from + to /. "tincreases rapidly with E#U for small values (up to about

E#U < /.9 but rather slowly for larger values. #herefore,

the use of a heat exchanger with a large E#U (usually

larger than and thus a large sie cannot be Fustifiedeconomically, since a large increase in E#U in this case

corresponds to a small increase in effectiveness. #hus, a

heat exchanger with a very high effectiveness may be

highly desirable from a heat transfer point of view but

rather undesirable from an economical point of view.


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#he case c < CminCmax G + corresponds to


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#he case c < CminCmax G + corresponds to

Cmax G H, which is realied during a phase-

change process in a condenser or boiler. )ll

effectiveness relations in this case reduce to



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-oilers an# Con#ensers


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Cooling Hot &il by ,ater in a +ultipass Heat Exchanger


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!ot oil is to be cooled by water

in a /-shell-pass and 8-tube-passes heat exchanger. #he

tubes are thin-walled and are

made of copper with an internal

diameter of /.= cm. #he lengthof each tube pass in the heat

exchanger is 9 m, and the

overall heat transfer coefficient

is /+ 1m : ;C. 1ater flows through the tubes at a rate

of +. kgs, and the oil through the shell at a rate of +.

kgs. #he water and the oil enter at temperatures of

+;C and /9+;C, respectively.



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Determine the rate of heat transfer in the heat

exchanger and the outlet temperatures of the water and

the oil.

"&'T&* !ot oil is to be cooled by water in a heat

exchanger. #he mass flow rates and the inlet

temperatures are given. #he rate of heat transfer andthe outlet temperatures are to be determined.

Assumptions

. 'teady operating conditions exist.

/ #he heat exchanger is well insulated.0 #he thickness of the tube is negligible.

4 Changes in the I3 and &3 are negligible.

1 #he overall heat transfer coefficient is constant and

uniform.



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Chapter 4 HXs

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