GATE 2017 ME (ME1) – Question 48
A long solid cylindrical rod of diameter 10 mm generates heat uniformly at $4\times10^7$ W/m³. Thermal conductivity is 25 W/(m K). At steady state, find the centre-to-surface temperature difference in °C.
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Correct answer: 10 to 10
Explanation
For steady radial conduction with uniform volumetric generation in a solid cylinder, $T(r)-T_s=q\prime\prime\prime(R^2-r^2)/(4k)$. At the centre, $\Delta T=q\prime\prime\prime R^2/(4k)$. The radius is 0.005 m, so $\Delta T=4\times10^7(0.005)^2/[4(25)]=10$ K, numerically 10°C as a temperature difference.