GATE ME 2019 Set 2 — Question 21
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Heat Transfer → Conduction → 1D Steady Conduction
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Question
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
Correct answer
(C) Logarithmic
Solution
For 1D steady state heat conduction without heat generation, the heat transfer rate is constant:Given that the area varies linearly: .
Substituting this into the Fourier's law equation:Integrating with respect to :Thus, the temperature distribution is logarithmic.
Substituting this into the Fourier's law equation:Integrating with respect to :Thus, the temperature distribution is logarithmic.
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