A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K₁ and that of the outer cylinder is K₂. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:
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Question

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K₁ and that of the outer cylinder is K₂. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:

Options

G1 Physics · Accepted Answer

Heat flows along the cylinder length, so the inner cylinder and the annular shell conduct in parallel. Their areas are A₁=πR² and A₂=π[(2R)²−R²]=3πR². Thus Keff=(K₁A₁+K₂A₂)/(A₁+A₂)=(K₁+3K₂)/4. Option D.