Question

A cylinder of radius R made of material of thermal conductivity K₁ is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity K₂. The two ends of the combined system are maintained at two different temperature. What is the effective thermal conductivity of the system?

• A. K₁ + K₂
• B. $\frac{K_{1} + 8K_{2}}{9}$
• C. $\frac{K_{1}K_{2}}{K_{1} + K_{2}}$
• D. $\frac{8K_{1} + K_{2}}{9}$

Answer 1

Answer: (B)

$\frac{K_{1} + 8K_{2}}{9}$

Answer 2

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

$\frac{K_{eq}(9\pi R^{2})}{L}$= $\frac{K_{1}\pi R^{2}}{L}$+ $\frac{K_{2}8\pi R^{2}}{L}$

K_eq = $\frac{K_{1} + 8K_{2}}{9}$