GATE ME 2023 Set 1 — Question 28
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Heat Transfer → Conduction → 1D Steady Conduction
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Question
Consider a laterally insulated rod of length and constant thermal conductivity. Assuming one-dimensional heat conduction in the rod, which of the following steady-state temperature profile(s) can occur without internal heat generation?
Correct answer
(A) [figure]; (B) [figure]
Solution
For steady-state 1D heat conduction in a rod with constant thermal conductivity and no internal heat generation, the governing equation is:Since is constant:Integrating twice with respect to :This represents a linear temperature profile. Both options (A) and (B) show linear variations of temperature with distance , which are possible steady-state profiles. Option (C) is parabolic, which would require uniform internal heat generation. Option (D) is non-linear and non-parabolic, which is not possible under these conditions.
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