Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A cylinder of radius $R$ made of a material of thermal conductivity $K_{1}$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $K_{2}$ . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is-

NTA AbhyasNTA Abhyas 2022

Solution:

Parallel combination of cross - section area $\pi R^{2}$ and $\pi 2 R^{2}-R^{2}=3 \pi R^{2}$
$\frac{1}{R_{ eq }}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$ with $R=\frac{L}{K A}$
$\frac{K_{ eq } \cdot 4 \pi R^{2}}{L}=\frac{K_{1} \pi R^{2}}{L}+\frac{K_{2} 3 \pi R^{2}}{L}$
$\Rightarrow K_{ eq }=\frac{K_{1}+3 K_{2}}{4}$