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For the three-dimensional object shown in the figure below, five faces are insulated. The sixth face (PQRS), which is not insulated, interacts thermally with the ambient with a convective heat transfer coefficient of 10 W/m²·K. The ambient temperature is 30°C. Heat is uniformly generated inside the object at the rate of 100 W/m³. Assuming the face PQRS to be at uniform temperature, its steady-state temperature is

1. 10°C
2. 20°C
3. 30°C
4. 40°C

Correct answer: 40°C

Solution

Since five faces are insulated, all the heat generated inside the body must be removed by convection from face PQRS. Equating internal heat generation to convective heat loss gives the surface temperature. The result is 40°C.

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