A cylinder of radius `R` made of a material of thermal conductivity `K_(1)` is surrounded by cylindrical shell of inner radius `R` and outer radius `2R` made of a material of thermal con-ductivity `K_(2)` The two ends of the combined system are maintained at two differnet tem-peratures There is no loss of heat across the cylindrical surface and system is in steady state What is the effective thermal conductivity of the system
.

Options

A. `K_(1)+K_(2)`
B. `(K_(1)K_(2))/(K_(1)+K_(2))`
C. `(K_(1)+3K_(2))/(4)`
D. `(K_(1)+8K_(2))/(9)`

Answer

D

Explanation

Two rods are in parallel
`K_(eff) (A_(1)+A_(2))=K_(1)A_(1)+K_(2)A_(2)`
`A_(1)=piR^(2)` and `A_(2)= pi (9R^(2)-R^(2))` .