An evacuated thick walled cylindrical tube 2 cm inside diameter by 5 cm outside diameter surrounds a concentrically located high temperature radiant heater which produces a 105 W/m2 heat flux at the inner surface. The temperature of the outer surface of the tube which is cooled by a flowing fluid at 300 K, is 633 K. The thermal conductivity of the tube material is 2.2 W/mºc. Determine:
(a) The rate of heat transfer per unit length of cylindrical tube.
(b) The heat transfer coefficient at the outer surface of the tube.
(c) The temperature of the inner surface of the cylindical tube.
Prove that the temperature of the inner surface of the cylindrical tube would decrease if 1 cm of material with thermal conductivity k = 5 W/m°c were applied at the outer surface of the tube.