The GATE Grind

GATE 2019 ME (ME2) – Question 21

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

One-dimensional steady heat conduction occurs through a solid whose area varies linearly in the heat-flow direction. There is no heat generation and conductivity is constant and independent of temperature. What is the temperature distribution?

  1. Linear
  2. Quadratic
  3. Logarithmic
  4. Exponential

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Show answer and explanation

Correct answer: (C) Logarithmic

Explanation

With no generation, steady heat rate Q is constant. For $A=A_0+bx$, Fourier’s law gives $dT/dx=-Q/[k(A_0+bx)]$. Integration yields a logarithmic temperature distribution. **C**.