Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
A constant heat flux of 500 W m⁻² is supplied to one face of a food material having a plate like structure with a thickness of 10 mm. The thermal conductivity of the food material is 1.5 W m⁻¹ °C⁻¹. From the other face of the food material, heat is dissipated by convection into a fluid of 40 °C temperature. The heat transfer coefficient of the fluid is 100 W m⁻² °C⁻¹. The temperature in °C of the surface to which the heat flux is supplied will be
Options:
(A) 43.3
(B) 45.3
(C) 48.3
(D) 54.3
Official Answer Key:
C
Step-by-Step Solution & Explanation
In steady state, the same heat flux (500 W/m²) passes through conduction across the plate and then by convection into the fluid. Convective face temperature: q = h(T_s2 − T_fluid) ⇒ T_s2 = 40 + 500/100 = 45 °C. Conduction across the plate: q = k(T_s1 − T_s2)/L ⇒ T_s1 = T_s2 + qL/k = 45 + (500×0.010)/1.5 = 45 + 3.33 = 48.33 ≈ 48.3 °C, matching option (C) — this is the temperature of the face to which the flux is supplied.
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