The GATE Grind

GATE 2021 ME (ME1) – Question 24

Heat Transfer · Heat transfer through fins · 1 mark · Multiple choice

An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of $Q_1$ to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steady-state heat transfer from the fin becomes $Q_2$. The ratio $Q_2/Q_1$ is

  1. $\sqrt2$
  2. 2
  3. $1/\sqrt2$
  4. $1/2$

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Show answer and explanation

Correct answer: (A) $\sqrt2$

Explanation

For an infinite fin, $Q=\sqrt{hPkA_c}(T_b-T_\infty)$. All factors except k remain unchanged, so Q is proportional to √k.

Doubling k gives **Q₂/Q₁=√2 (A)**, rather than a factor of two.