Two equal-diameter solid spheres X and Y have thermal diffusivities 10010-6 and 2510-6\ m2/s. Both are heated in a furnace at 1000 K. X reaches 800 K at its centre in 1 h. How long does Y take?

GATE 2020 MT – Question 21

Transport Phenomena and Rate Processes · Heat transfer · 1 mark · Multiple choice

Two equal-diameter solid spheres X and Y have thermal diffusivities $100\times10^{-6}$ and $25\times10^{-6}\ \mathrm{m^2/s}$. Both are heated in a furnace at 1000 K. X reaches 800 K at its centre in 1 h. How long does Y take?

1 h
2 h
4 h
16 h

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Correct answer: (C) 4 h

Explanation

For identical geometry and comparable initial/surface conditions, reaching the same nondimensional centre temperature requires the same Fourier number $Fo=\alpha t/R^2$. Hence $t_Y/t_X=\alpha_X/\alpha_Y=100/25=4$, giving 4 h, C. This keyed diffusion-time scaling presumes matching thermal boundary conditions; diffusivity alone would not fix the time if the Biot numbers and surface histories differed arbitrarily.

GATE 2020 MT – Question 21

Explanation

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