GATE ME 2024 Set 1 — Question 17
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Heat Transfer → Conduction → 1D Steady Conduction
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Question
A plane, solid slab of thickness , shown in the figure, has thermal conductivity that varies with the spatial coordinate as , where and are positive constants (). The slab walls are maintained at fixed temperatures of and . The slab has no internal heat sources. Considering one-dimensional heat transfer, which one of the following plots qualitatively depicts the steady-state temperature distribution within the slab?
Correct answer
(B) [figure]
Solution
For steady-state, one-dimensional heat conduction without internal heat generation, the heat flux is constant:Given , we have:Since and , the temperature increases with , so . This implies must be negative. Let where .To find the curvature, we take the second derivative:Since and , for all . A negative second derivative indicates that the temperature profile is concave down. Plot (B) qualitatively depicts this distribution.
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