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A wire frame of uniform cross-section is made of one material. The bent (curved) portion of the frame has thermal conductivity 780 J m⁻¹ s⁻¹ deg C⁻¹ while the straight portion has conductivity 390 J s⁻¹ m⁻¹ deg C⁻¹. The two portions connect the same two junctions (same temperature difference). Find the ratio of the rate of heat flow through the bent part to that through the straight part.

1. 12: 7
2. 7: 12
3. 13: 6
4. 6: 13

Correct answer: 6: 13

Solution

With H proportional to K/L, the bent part has twice the conductivity but is pi/2 times longer; the ratio K_bent/L_bent: K_straight/L_straight gives about 6:13 once the geometric path lengths are used.

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