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GATE 2020 CH – Question 52

Heat Transfer · Conduction: steady and unsteady, equation of energy · 2 marks · Numerical answer

An infinitely long rectangular fin loses heat to fluid at Tₐ = 27°C. Its excess temperature θ = T − Tₐ obeys $d^2\theta/dx^2=m^2\theta$, with m = 0.04 cm⁻¹ and base T₀ = 227°C. Find T at x = 25 cm in °C, to one decimal place.

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Correct answer: 100.0 to 101.5

Explanation

The bounded infinite-fin solution is $\theta(x)=\theta(0)e^{-mx}$; the growing exponential is excluded by the far-field condition T→Tₐ. Here θ(0) = 227 − 27 = 200°C and mx = 0.04(25) = 1. Therefore $T(25)=27+200e^{-1}=100.5759$°C, rounding to 100.6°C.

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