CHEMICAL ENGINEERING

HEAT TRANSFER 181

Solution

The terms “black body” and “grey body” are discussed in Sections 9.5.2 and 9.5.3.
For two large parallel plates with grey surfaces, the heat transfer by radiation between
them is given by puttingA 1 DA 2 in equation 150 to give:

qD[e 1 e 2 9/

e 1 Ce 2 e 1 e 2 ]

T^41 T^42 W/m^2

In this case: qD[
0. 8 ð 0. 4 ð 5. 67 ð 10 ^8 /
0. 8 C 0. 4  0. 8 ð 0. 4 ]
3504  3004

D 

0. 367 ð 5. 67 ð 10 ^8 ð 6. 906 ð 109 D 143 .7W/m^2

PROBLEM 9.50

A longitudinal fin on the outside of a circular pipe is 75 mm deep and 3 mm thick. If the
pipe surface is at 400 K, calculate the heat dissipated per metre length from the fin to the
atmosphere at 290 K if the coefficient of heat transfer from its surface may be assumed
constant at 5 W/m^2 K. The thermal conductivity of the material of the fin is 50 W/m K
and the heat loss from the extreme edge of the fin may be neglected. It should be assumed
that the temperature is uniformly 400 K at the base of the fin.

Solution

The heat lost from the fin is given by equation 9.254:

QfD

√

hbkA 1 tanhmL

wherehis the coefficient of heat transfer to the surroundingsD5W/m^2 K,bis the
fin perimeterD
2 ð 0. 075 C 0. 003 D 0 .153 m, k is the thermal conductivity of the
finD50 W/mK,A is the cross-sectional area of the finD
0. 003 ð 1. 0 D 0 .003 m^2 ,
 1 is the temperature difference at the rootD
T 1 TG D
400  290 D100 deg K,
mD

p



hb/kAD

p

5 ð 0. 153 /
50 ð 0. 003 D 2 .258 andLis the length of the finD
0 .075 m.

∴ QfD

√

5 ð 0. 153 ð 50 ð 0. 003 [110 tanh 

2. 258  0. 075 ]

D 

0. 339 ð100 tanh 0. 169 D 6 .23 W/m

PROBLEM 9.51

Liquid oxygen is distributed by road in large spherical insulated vessels, 2 m internal
diameter, well lagged on the outside. What thickness of magnesia lagging, of thermal
conductivity 0.07 W/m K, must be used so that not more than 1% of the liquid oxygen
evaporates during a journey of 10 ks (2.78 h) if the vessel is initially 80% full? Latent
heat of vaporisation of oxygenD215 kJ/kg. Boiling point of oxygenD90 K. Density of
liquid oxygenD1140 kg/m^3. Atmospheric temperatureD288 K. Heat transfer coefficient
from the outside surface of the lagging surface to atmosphereD 4 .5W/m^2 K.