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A solid cylinder of radius R is surrounded by a coaxial cylindrical shell of inner radius R and outer radius 2R. The inner cylinder has thermal conductivity K1 and the shell has thermal conductivity K2. With no heat loss, find the effective thermal conductivity of the combination for heat flow along the axis (length) of the cylinder.

1. K1 + K2
2. (K1 + K2) / 2
3. (2*K1 + 3*K2) / 5
4. (K1 + 3*K2) / 4

Correct answer: (K1 + 3*K2) / 4

Solution

For heat flow along the length the regions act in parallel, so K_eff = (K1*A1 + K2*A2)/(A1 + A2) = (K1 + 3*K2)/4.

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