The GATE Grind

GATE 2021 AG – Question 19

Dairy and Food Engineering · Heat and Mass Transfer · 1 mark · Multiple choice

For one-dimensional radial conduction,$r^{-n}\partial_r(kr^n\partial_rT)+E=\rho C_p\partial_tT$. What is n for a sphere?

  1. 1
  2. 2
  3. 3
  4. 4

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Correct answer: (B) 2

Explanation

Spherical radial area scales as r². Conservation of heat therefore gives $r^{-2}\partial_r(kr^2\partial_rT)$,so **n=2,B**. The corresponding cylindrical and planar forms have n=1 and 0 respectively.

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