exampleh-x.pdf

8/11/2019 ExampleH-X.pdf

1/13

Example

In the counterflow heat exchanger shown in Fig. 5-4, a flowrate of 0.5 kg/s of water enters one circuit of the heatexchanger at a temperature of 30C, and the same flow rateof water enters the other circuit at a temperature of 65C.The UA of the heat exchanger is 4 kW/K.

What is the mean temperature difference between the twostreams?


2/13

( )12 cccp TTcmQ = &

mTUAQ =

( )2121

/ln TT

TTT

m

=

122

211

ch

ch

TTT

TTT

=

=

( )21 hhhp TTcmQ = &


3/13

( ) ( )

( )( )( ) ( )

( )( ) ( )

( ) ( )

( ) ( )

( ) ( )1221

1221

1221

1221

12

1212

21

2121

:

kW/K2.095kW/K2.095kW/K2.095

K)]kJ/(kg.[4.19kg/s)(0.5kW/K2.095

K)]kJ/(kg.[4.19kg/s)(0.5

chchm

chch

cchh

cchh

cc

cccccp

hh

hhhhhp

TTTTT

TTTT

rearrange

TTTT

TTTTTT

TTTTcmQTT

TTTTcmQ

==

=

=

=

=

===

==

&

&


4/13

( )( ) ( )

( ) ( )

( ) ( )( ) ( ) ( )

( ) ( )( ) ( )

( ) ( ) ( ) 12300305.42

0305.42

2792.1229093.2652792.579093.1

65kW/K2.095304

kW/K2.0954

kW/K2.095

9530653065

kW/K2.095

kW/2.095

1221

2

2

22

22

2112

211221

1221

22222

1221

12

21

====

=

==

==

===

==

=+==

=

=

=

chchm

h

h

hh

hh

hhch

hhchch

chchm

cchch

cchh

cc

hh

TTTTT

T

TTT

TT

TTTT

TTTTUATTUAQ

TTTTT

TTTTT

TTTT

TTQ

TTQ


5/13

Example EVAPORATORS AND CONDENSERS A special set of equations is possible-and indeed necessary-when one of

the fluids flowing through a heat exchanger changes phase.

In an evaporator or condenser, as shown in Fig. 5-5, assume that there isno superheating or subcooling of the fluid that changes phase. That fluidwill then remain at a constant temperature, provided that its pressure does

not change.


6/13

For a heat exchanger of known characteristics Eq. (5.10) can

be used to compute the outlet temperature of the fluid that doesnot change phase when its entering temperature and the

temperature of the boiling or condensing fluid tc are known.

The characteristic shape of the temperature curves of the two

fluids is shown in Fig. 5-6, applicable to a condenser.

( ) ( )

( ) ( )[ ] ( )

( ) ( )[ ] ( ) ( )[ ]

( ) ( )

( )( )p

p

cmUA

icio

ic

iiococic

cmUA

icococic

p

iopocic

ocic

etttt

tt

tttttttte

ttttttttcm

UA

ttcmtttt

ttttUAq

&

&

&

&

/

/

1

Then

/

givesantilogthetaking

/ln/ln

formtheintoconvertedbecan5.9Equation

/ln

+=

+==

==

=

=

The log-mean temperature difference still applies and in combination with a heatbalance gives


7/13


8/13

Example 5.2.

Water is continuously heated from 25 to 50C by steamcondensing at 110C. If the water flow rate remains

constant but its inlet temperature drops to 15C, what will

its new outlet temperature be?

Solution. The terms U, A, m, cp, and tc all remain constant.

9.42

15110

15

25110

2550

1/

=

=

==

o

o

ic

iocmUA

ic

io

t

t

tt

tte

tt

tt p&


9/13

Example What is the maximum rate of heat transfer possible in a

counterflow heat exchanger shown in Fig. 5-7 if water

enters at 30C and cools oil entering at 60C?

=

=

water)/(19.4

oil)/(2.2heatSpecific

water/5.1oil/6.2rateFlow

KkgkJ

KkgkJ

skgskg


10/13

Solution: The break in the heat exchanger

indicates that to achieve the maximum rate ofheat transfer the area must be made infinite.

The next question, then, is: What are the

outlet temperatures? Does the oil leave at30C, or does the water leave at 60C?

From energy balances those two options give

the following consequences:

1. Oil leaves at 30C

3.57)]/(19.4)[/5.1(

6.17130

6.171)3060)](/(2.2)[/6.2(

=+

==

kgKkJskg

kW

avesandwaterle

kWkgKkJskgq


11/13

2 water leaves at 60

The second case is clearly impossible because

the oil temperature would drop below that of theentering water, which would violate the second

law of thermodynamics. Thus, qmax = 171.6 kW.

272.26.2

6.18860

6.188)3060(19.45.1

=

== kWq


12/13

( )( ) fluidstwotheofsmallertheiswhere

)(

min

,,min

pp

incoldinhotp

actual

wccm

ttcm

q

&

& =


13/13

Example Compute the effectiveness of a counterflow heat

exchanger having a U value of 1.1 kW/(m2. K) and an

area of 16 m2 when one fluid has a flow rate of 6 kg/s

and a specific heat of 4.1 kJ/(kg .K) and the other fluid a

flow rate of 3.8 kg/s and a specific heat of 3.3 kJ/(kg .K).

( )

668.51.

1

5.13Eq.Formand

686..51-11.4D5.14Eq.From

67.5.9Fig.From

4.154.12

161.1

Wdesignate54.123.38.3

6.241.46

686.

686.

min

min

=

=

==

=

=

==

==

==

e

e

C

UANTU

C

C

b

a

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