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
.

Answer

`[(K_(1)+3K_(2))/(4)]`

Explanation

At steady state,
`(dQ)/(dt)=(dQ)/(dt)+(dQ_(2))/(dt)`
or `(K pi(2R)^(2)(T_(1)-T_(2)))/(l)=(K_(1)pi R^(2)(T_(1)-T_(2)))/(l)+(K_(2)pi(2R)^(2)-pi R^(2)(T_(1)-T_(2)))/(l)`
or `4 K=K_(1)+3 K_(2)` or `K+((K_(1)+3K_(2))/(4))`