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A hollow cylinder has length L, inner radius r1, outer radius r2, and thermal conductivity k. The thermal resistance of the cylinder for radial conduction is

1. ln(r2 / r1) / 2 kL
2. ln(r1 / r2) / 2 kL
3. 2 kL / ln(r2 / r1)
4. 2 kL / ln(r1 / r2)

Correct answer: ln(r2 / r1) / 2 kL

Solution

The correct option is based on the formula for thermal resistance in cylindrical coordinates, which accounts for the logarithmic relationship between the inner and outer radii. This formula reflects how heat flows radially through the material, with the resistance being proportional to the natural logarithm of the ratio of the outer radius to the inner radius, divided by the product of thermal conductivity and length.

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