GATE ME 2023 Set 1 — Question 47
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Heat Transfer → Conduction → Biot & Fourier Numbers
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Question
A very large metal plate of thickness and thermal conductivity is cooled by a stream of air at temperature with a heat transfer coefficient , as shown in the figure. The centerline temperature of the plate is . In which of the following case(s) can the lumped parameter model be used to study the heat transfer in the metal plate?

Correct answer
(A) h = 10 Wm⁻²K⁻¹, k = 100 Wm⁻¹K⁻¹, d = 1 mm, T_P = 350 K; (C) h = 100 Wm⁻²K⁻¹, k = 1000 Wm⁻¹K⁻¹, d = 1 mm, T_P = 325 K
Solution
The lumped parameter model is valid when the Biot number . For a large plate of thickness cooled from both sides, the characteristic length is .
.
.
- Case (A): . (Valid)
- Case (B): . (Invalid)
- Case (C): . (Valid)
- Case (D): . (Invalid)
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