HEAT TRANSFER 149
PROBLEM 9.17
An organic liquid is boiling at 340 K on the inside of a metal surface of thermal conduc-
tivity 42 W/m K and thickness 3 mm. The outside of the surface is heated by condensing
steam. Assuming that the heat transfer coefficient from steam to the outer metal surface
is constant at 11 kW/m^2 K, irrespective of the steam temperature, find the value of the
steam temperature would give a maximum rate of evaporation.
The coefficients of heat transfer from the inner metal surface to the boiling liquid which
depend upon the temperature difference are:
Temperature difference between metal
surface and boiling liquid (deg K)Heat transfer coefficient metal surface
to boiling liquid kW/m^2 K
22. 24. 43
27. 85. 91
33. 37. 38
36. 17. 30
38. 96. 81
41. 76. 36
44. 45. 73
50. 04. 54Solution
For a steam temperatureTsK, the heat conducted through the film of condensing steam,
QDhcA
TsT 1 ,or:
QD
11 ð 1. 0
TsT 1 D 11. 0
TsT 1 kW/m^2 (i)whereT 1 is the temperature at the outer surface of the metal.
For conduction through the metal,
QDkA
T 1 T 2 /x
D
42 ð 10 ^3 ð 1. 0
T 1 T 2 / 0. 003
D 14. 0
T 1 T 2 kW/m^2 (ii)whereT 2 is the temperature at the inner surface of the metal.
For conduction through the boiling film:
QDhb
T 2 340 Dhb
T 2 340 kW/m^2 (iii)wherehbkW/m^2 K is the film coefficient to the boiling liquid.
Thus for an assumed value ofT 2 the temperature difference
T 2 340 is obtained
andhbfrom the table of data.Qis then obtained from (iii),T 1 from (ii), and henceTs
from (i) as follows: