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GATE 2019 ME (ME1) – Question 21

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

Two slender rods each of length L and diameter d, with L ≫ d, have conductivities $k_1,k_2$. They are joined end to end into a 2L composite. Neglect radial heat transfer and contact resistance. Find effective conductivity.

  1. $k_1+k_2$
  2. $\sqrt{k_1k_2}$
  3. $k_1k_2/(k_1+k_2)$
  4. $2k_1k_2/(k_1+k_2)$

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Correct answer: (D) $2k_1k_2/(k_1+k_2)$

Explanation

Series resistance is $L/(k_1A)+L/(k_2A)$. Set this equal to the equivalent resistance $2L/(k_{eff}A)$ and rearrange: **$k_{eff}=2k_1k_2/(k_1+k_2)$, D**. This is the harmonic mean, appropriate to heat flowing successively through both rods.