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One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is

1. Linear
2. Quadratic
3. Logarithmic
4. Exponential

Correct answer: Logarithmic

Solution

In one-dimensional steady state heat conduction with a varying cross-sectional area, the temperature distribution is logarithmic due to the relationship between heat flow and area. As the area changes, the heat flux must adjust accordingly, leading to a logarithmic profile rather than a linear or polynomial one.

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