CHEMICAL ENGINEERING

168 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

whereTis the water outlet temperature.

Thus:
T 285 D
GoCp/GwCp 
420  350 D
0. 5 ð 70

and: TD320 K

∴  1 D
420  285 D135 deg K, 2 D
350  320 D30 deg K, again for co-current
flow,

and from equation 9.9:mD
135  30 /ln
135 / 30 D 69 .8deg K

In equation 9.1:Goso
420  350 DUal 69. 8

∴ lD
GoCp/Uað 1. 003 D

1. 85 ð 1. 003 D 1 .86 m

PROBLEM 9.37

In a countercurrent-flow heat exchanger, 1.25 kg/s of benzene (specific heat 1.9 kJ/kg K
and density 880 kg/m^3 ) is to be cooled from 350 K to 300 K with water which is available
at 290 K. In the heat exchanger, tubes of 25 mm external and 22 mm internal diameter
are employed and the water passes through the tubes. If the film coefficients for the water
and benzene are 0.85 and 1.70 kW/m^2 K respectively and the scale resistance can be
neglected, what total length of tube will be required if the minimum quantity of water is
to be used and its temperature is not to be allowed to rise above 320 K?

Solution

Heat load:

For the benzene:QD 1. 25 ð 1. 9
350  300 D 118 .75 kW.
In order to use the minimum amount, water must leave the unit at the maximum
temperature, 320 K. Thus forGkg/s water:

118. 75 DGð 4. 18

320  290 orGD 0 .947 kg/s

Temperature driving force

 1 D 

350  320 D30 deg K, 2 D 

300  290 D10 deg K

and in equation 9.9:mD
30  10 /ln
30 / 10 D 18 .2 deg K. In the absence of further
data, it will be assumed that the correction factor is unity.

Overall coefficient

Inside: hiD 0 .85 kW/m^2 K or based on the tube o.d., hioD
0. 85 ð 22 / 25
D 0 .748 kW/m^2 K.