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GATE 2023 ME – Question 28

Heat Transfer · Modes of heat transfer, one-dimensional conduction, resistance concept · 1 mark · Multiple select

Consider a laterally insulated rod of length L 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?

four temperature profiles against $x$ from 0 to L. (A) A straight line rising from left to right. (B) A straight line falling from left to right. (C) A curve that rises and then falls, concave downward (an arch). (D) A wavy curve that goes up, down and up again.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (A) Option A in the figure; (B) Option B in the figure

Explanation

For steady one-dimensional conduction with constant conductivity and no heat generation, the equation is $\frac{d^2T}{dx^2} = 0$, so the temperature profile is a straight line. Only (A) and (B) are straight lines. The arch in (C) would need a heat source, and the wavy curve in (D) would need alternating sources and sinks.