GATE ME 2022 Set 1 — Question 45
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Heat Transfer → Conduction → 1D Steady Conduction
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Question
Consider a rod of uniform thermal conductivity whose one end () is insulated and the other end () is exposed to flow of air at temperature with convective heat transfer coefficient . The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given as . The steady state temperature at the mid-location of the rod is given as . What will be the temperature at the same location, if the convective heat transfer coefficient increases to ?
Correct answer
(C) T_A
Solution
The total heat generated in the rod is .
Since the total heat generation is zero and one end is insulated, the heat flux at the other end () must also be zero for steady state.
.
This boundary condition is independent of the value of (as long as ).
The temperature distribution relative to depends only on the heat generation profile and thermal conductivity. Since remains constant at regardless of , the temperature at any point (including the mid-location ) will remain unchanged. Thus, the temperature remains .
Since the total heat generation is zero and one end is insulated, the heat flux at the other end () must also be zero for steady state.
.
This boundary condition is independent of the value of (as long as ).
The temperature distribution relative to depends only on the heat generation profile and thermal conductivity. Since remains constant at regardless of , the temperature at any point (including the mid-location ) will remain unchanged. Thus, the temperature remains .
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