Question

A cylinder of radius R, made of a material of thermal conductivity k₁, is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The shell is made of a material of thermal conductivity k₂. 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 –

• A. k₁+ k₂
• B. $\frac{k_{1}k_{2}}{k_{1} + k_{2}}$
• C. $\frac{k_{1} + 3k_{2}}{4}$
• D. $\frac{3k_{1} + k_{2}}{4}$

Answer 1

Answer: (C)

$\frac{k_{1} + 3k_{2}}{4}$

Answer 2

Resistance of inner cylinder R₁ = $\frac{\mathcal{l}}{k_{1}\pi R^{2}}$

Resistance of outer cylinder

R₂ = $\frac{\mathcal{l}}{k_{2}(4\pi R^{2}–\pi R^{2})}$

As inner & outer cylinder in parallel

R_eq = $\frac{R_{1}R_{2}}{R_{1} + R_{2}}$