Question

An infinitely long pin fin, attached to an isothermal hot surface, transfers heat at a steady rate of π‘ΈΜ‡πŸ to the ambient air. If the thermal conductivity of the fin material is doubled, while keeping everything else constant, the rate of steadystate heat transfer from the fin becomes π‘ΈΜ‡πŸ. The ratio π‘ΈΜ‡πŸ/π‘ΈΜ‡πŸ is

Options :

  1. √2

  2. 2

  3. 1/√2

  4. 1/2

Show Answer

Answer :

√2

Solution :

Let the amount of heat loss be Q̇1 when thermal conductivity is (k1) = k

Let the amount of heat loss be Q̇2 when thermal conductivity is (k2) = 2k

Q 2 Q 1 = k 2 k 1

Q 2 Q 1 = 2 k k

Q 2 Q 1 = 2

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