Project ForgeA spherical steel ball of 12 mm diameter is initially at 1000 K. It is slowly cooled in a surrounding of 300 K. The heat transfer coefficient between the steel ball and the surrounding is 5 W/m²K. The thermal conductivity of steel is 20 W/mK. The temperature difference between the centre and the surface of the steel ball is
- Alarge because conduction resistance is far higher than the convective resistance
- Blarge because conduction resistance is far less than the convective resistance
- Csmall because conduction resistance is far higher than the convective resistance
- small because conduction resistance is far less than the convective resistance
Explanation
Biot number Bi=hLc/k, with Lc=r/3=0.006/3=0.002m for a sphere: Bi=5×0.002/20=0.0005, a very small value. A small Biot number means conduction resistance is far LESS than convective resistance, so the temperature gradient within the ball is negligible — the centre-to-surface temperature difference is small.
Source: GATE ME 2011 (2011)
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