182 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
Solution
For conduction through the lagging:
QD 4 $k
T 1 T 2 /
1 /r 1 1 /r 2 (equation 9.25)whereT 1 will be taken as the temperature of boiling oxygenD90 K and the tank radius,
r 1 D 1 .0m.
In this way, the resistance to heat transfer in the inside film and the walls is neglected.
r 2 is the outer radius of the lagging.
∴ QD 4 $ð 0. 07
90 T 2 /
1 / 1. 0 1 /r 2 W(i)
For heat transfer from the outside of the lagging to the surroundings,QDhA
T 2 Ta
wherehD 4 .5W/m^2 K,AD 4 $r 22 andTa, ambient temperatureD288 K.
∴ QD 4. 5 ð 4 $r^22
T 2 288 D 18 $r^22
T 2 288 W (ii)
The volume of the tankD 4 $r 13 / 3 D
4 $ð 1. 03 / 3 D 4 .189 m^3.∴ volume of oxygenD
4. 189 ð 80 / 100 D 3 .351 m^3
and mass of oxygenD
3. 351 ð 1140 D3820 kg∴ mass of oxygen which evaporatesD
3820 ð 1 / 100 D 38 .2kg
or: 38. 2 /
10 ð 103 D 0 .00382 kg/s
∴heat flow into vessel: QD
215 ð 103 ð 0. 00382 D821 W
∴In (ii) 821 D 18 $r 22
T 2 288 andT 2 D 288
14. 52 /r^22
Substituting in (i):
821 D 4 $ð 0 .07[90 288 C
14. 52 /r^22 ]/
1 1 /r 2 or: r 22 1. 27 r 2 C 0. 0198 D0andr 2 D 1 .25 m
Thus the thickness of laggingD
r 2 r 1 D 0 .25 m.
PROBLEM 9.52
Benzene is to be condensed at the rate of 1.25 kg/s in a vertical shell and tube type of
heat exchanger fitted with tubes of 25 mm outside diameter and 2.5 m long. The vapour
condenses on the outside of the tubes and the cooling water enters at 295 K and passes
through the tubes at 1.05 m/s. Calculate the number of tubes required if the heat exchanger
is arranged for a single pass of the cooling water. The tube wall thickness is 1.6 mm.