During an experiment to determine the thermal conductivity of a material used in a thick cylindrical shell (inner radius 10 cm and outer radius, 20 cm) two thermocouples were inserted, one at a radius...

During an experiment to determine the thermal conductivity of a material used in a thick cylindrical shell (inner radius 10 cm and outer radius, 20 cm) two thermocouples were inserted, one at a radius equal to 12 cm and the other at a radius equal to 18 cm. The temperatures reacorded were 100°C and 50°C respectively. If the heat transfer per metre length of the shell was 600 W, calculate the thermal conductivity of the material and the temperatures at the inner and outer surfaces of the shell. Hints: From Eq. (1.20),

Substitute Q = 600 W, r₂
= 18 cm, r₁
= 12 cm, L = 1 m, T₁
= 100°C and T₂
= 50°C, find k. Temperature at the inner radius = T₁
+ Q ln (12/10)/2kL and temperature at the outer radius = T₂
– Q ln (20/18)/2 kL.