The GATE Grind

GATE 2026 ME – Question 43

Heat Transfer · Heat transfer through fins · 2 marks · Multiple choice

A very long fin of a uniform square cross-section is replaced by another very long fin of a uniform circular cross-section of the same material. Assume uniform and identical heat transfer coefficient for both the fins. If the diameter of the circular fin is equal to the side length of the square fin, then the ratio of heat transfer rates before and after the replacement is

  1. $4/\pi$
  2. $16/\pi^2$
  3. $1/\pi$
  4. $1/\pi^2$

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Show answer and explanation

Correct answer: (A) $4/\pi$

Explanation

For a very long fin the heat transfer rate is $q = \sqrt{hPkA_c}\,\theta_b$. For a square fin of side $a$, $PA_c = 4a \times a^2 = 4a^3$. For a circular fin of diameter $a$, $PA_c = \pi a \times \frac{\pi a^2}{4} = \frac{\pi^2a^3}{4}$. The ratio before to after is $\sqrt{\frac{4a^3}{\pi^2a^3/4}} = \frac{4}{\pi}$.