Question

A cylinder of radius R made of material of thermal conductivity K₁ is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity K₂. The two ends of the combined system are maintained at two different temperatures. What is the effective thermal conductivity of the system?

Options

• K₁ + K₂

• `(K_1 + 8K_2)/9`

• `(K_1K_2)/(K_1 + K_2)`

• `(8K_1 +  K_2)/9`

Answer 1

`underlinebb((K_1 + 8K_2)/9)`

Explanation:

`1/R_{eq} = 1/R_1 + 1/R_2`

`(K_{eq}(9piR^2))/L = (K_1piR^2)/L + (K_2 8piR^2)/L`

`K_{eq} = (K_1 + 8K_2)/9`