Project ForgeHeat Transfer
Conduction
GATE 2015
Hard
A solid block (unit thickness), thermal conductivity decreasing with temperature, has T(x=0)>T(x=1), steady 1-D conduction, no source/sink. Four candidate temperature profiles (I-IV, bowing progressively lower from the T(x=0) line toward T(x=1)) are shown. Which is the correct profile?
- AI
- BII
- III
- DIV
Explanation
Steady conduction requires constant flux q0=k(T)|dT/dx|. Since k is lower at the hot end (x=0) and higher at the cold end (x=1), the temperature gradient must be correspondingly steeper near x=0 and shallower near x=1 — matching profile III's moderate bow toward the cold-side temperature.
Source: GATE CH 2015 (2015)
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