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GATE Civil Engineering (CE) 2023 Shift 2 Solved Paper

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Question : 52

Total: 65

A 5 cm long metal rod AB was initially at a uniform temperature of T0°C. Thereafter, temperature at both the ends are maintained at 0°C. Neglecting the heat transfer from the lateral surface of the rod, the heat transfer in the rod is governed by the one-dimensional diffusion equation ‌

, where D is the thermal diffusivity of the metal, given as 1.0 cm2/s.
The temperature distribution in the rod is obtained as
T(x,t)=Σn=1,3,5...∞Cnsin‌⁡‌

e−βn2t,
where x is in cm measured from A to B with 𝑥 = 0 at A, t is in s, 𝐶𝑛 are constants in °C, T is in °C, and β is in s−1 .
The value of β (in 𝑠−1 , rounded off to three decimal places) is ________.

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