Project ForgeHeat Transfer
Conduction
GATE 2018
Medium
A plane slab of thickness L=20 cm and thermal conductivity k=2.5 W/mK is heated by a fluid at 45°C (surface heat transfer coefficient h=10 W/m²K) on one side (P), while the other side (Q) is held at a constant TQ=25°C. The steady state temperature, TP (in °C), of the side exposed to the fluid is _______ (correct to two decimal places).
33.9 °C(± 0.4 accepted)
Explanation
At steady state, the convective heat flux into the slab equals the conductive flux through it: h(T∞−TP) = k(TP−TQ)/L. 10(45−TP) = 2.5(TP−25)/0.2 = 12.5(TP−25). 450−10TP = 12.5TP−312.5 → 762.5=22.5TP → TP≈33.89°C.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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