Project ForgeHeat Transfer
Conduction
GATE 2014
Medium
The bottom face of a horizontal slab of thickness 6 mm is maintained at 300°C. The top face is exposed to a flowing gas at 30°C. The thermal conductivity of the slab is 1.5 W m⁻¹ K⁻¹ and the convective heat transfer coefficient is 30 W m⁻² K⁻¹. At steady state, the temperature (in °C) of the top face is _____
271 °C(± 3 accepted)
Explanation
At steady state, the conductive flux through the slab equals the convective flux from the top face: (k/L)(Tbottom−Ttop)=h(Ttop−Tgas). (1.5/0.006)(300−Ttop)=30(Ttop−30). 250(300−Ttop)=30Ttop−900. 75,000−250Ttop=30Ttop−900. 75,900=280Ttop. Ttop≈271.1°C.
Source: GATE CH 2014 (2014)
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