A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2 R . The…

Let $q_1$ and $q_2$ be the rate of flow of heat through inner part from outer part respecting net flow of heat


$q=q_1+q_2$

$=\frac{K_1\pi R^2}{l}.\mathrm{\Delta }T+\frac{K_2.\pi \left[{\left(2R\right)}^2-R^2\right]}{l}.\mathrm{\Delta }T$

$=\frac{\pi R^2}{l}\mathrm{\Delta }T\left(K_1+3K_2\right)$

If the cylinder is replaced by a single material of thermal conductivity $K$ then

$q=\frac{K.{\left(2R\right)}^2}{l}.\mathrm{\Delta }T$

On comparison,

$K=\frac{K_1+3K_2}{4}$.