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Heat is conducted through the gap between two spheres (an inner sphere and a surrounding outer shell) maintained at fixed temperatures. If the two spheres are made non-concentric (their centres displaced) while the same surface temperatures are maintained, the rate of heat transfer through the medium between them:

1. Increases
2. Decreases
3. Remains the same
4. Cannot be predicted

Correct answer: Increases

Solution

For concentric spheres the gap is uniform, giving a fixed thermal resistance. When the spheres become non-concentric, the inner sphere moves closer to the shell on one side; the gap there shrinks, and since thermal resistance of a layer is inversely related to how short the conduction path is, that thinner region conducts disproportionately more heat. The increased conduction on the close side outweighs the reduced conduction on the far side, so the net thermal resistance falls and the overall rate of heat transfer increases.

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