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GATE 2018 ME (ME1) – Question 57

Heat Transfer · Modes of heat transfer, one-dimensional conduction, resistance concept · 2 marks · Numerical answer

A slab is 20 cm thick with conductivity 2.5 W/m K. Side Q is maintained at 25°C; side P is exposed to fluid at 45°C with h = 10 W/m² K, as shown. Steady surface temperature TP, to two decimals, is ______ °C.

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Correct answer: 33.50 to 34.30

Explanation

Convection and conduction heat fluxes are equal: $10(45-T_P)=(2.5/0.2)(T_P-25)$. Thus $22.5T_P=762.5$ and $T_P=33.89$ °C.