CHEMICAL ENGINEERING

HEAT TRANSFER 185

D

√

0. 0328

 80 tanh 1. 3011

D 14. 49

 e^1.^301 e^1.^301 /

e^1.^301 Ce^1.^301

D 14. 49

3. 673  0. 272 /

 3. 673 C 0. 272 D 12 .5W

PROBLEM 9.54

A shell-and-tube heat exchanger consists of 120 tubes of internal diameter 22 mm and
length 2.5 m. It is operated as a single-pass condenser with benzene condensing at a
temperature of 350 K on the outside of the tubes and water of inlet temperature 290 K
passing through the tubes. Initially there is no scale on the walls, and a rate of conden-
sation of 4 kg/s is obtained with a water velocity of 0.7 m/s through the tubes. After
prolonged operation, a scale of resistance 0.0002 m^2 K/W is formed on the inner surface
of the tubes. To what value must the water velocity be increased in order to maintain the
same rate of condensation on the assumption that the transfer coefficient on the water
side is proportional to the velocity raised to the 0.8 power, and that the coefficient for
the condensing vapour is 2.25 kW/m^2 K, based on the inside area? The latent heat of
vaporisation of benzene is 400 kJ/kg.

Solution

Area for heat transfer, based on the tube i.d.D
$ð 0. 022 ð 1. 0 D 0 .0691 m^2 /m or:

120 ð 2. 5 ð 0. 0691 D 20 .74 m^2.

With no scale

Heat load:QD
4 ð 400 D1600 W.
Cross-sectional area of one tubeD
$/ 40. 0222 D 0 .00038 m^2
and hence area for flow per passD
120 ð 0. 00038 D 0 .0456 m^2.

∴ volume of flow of waterD
0. 0456 ð 0. 7 D 0 .0319 m^3 /s

and: mass flow of waterD
0. 0319 ð 1000 D 31 .93 kg/s

The water outlet temperature is given by, 1600D 31. 93 ð 4. 18
T 290 orTD302 K

 1 D 

350  290 D60 deg K, 2 D 

350  302 D48 deg K

and in equation 9.9, mD
60  48 /ln
60 / 48 D 53 .8degK.

In equation 9.1, UDQ/AmD 1600 /
20. 74 ð 53. 8 D 1 .435 kW/m^2 K

Neglecting the wall resistance, 1/UD 1 /hiC 1 /h 0 i

1 / 1. 435 D 1 /hiC 

1 / 2. 25 andhiD 3 .958 kW/m^2 K

hiis proportional tou^0.^8 or 3. 958 Dk

 0. 70.^8 andkD 5. 265