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Hot oil circulates inside an insulated container topped by a wooden lid of conductivity K = 0.149 J/(m s deg C), thickness t = 5 mm and emissivity e = 0.6. In steady state the top surface of the lid is at T = 127 deg C while the ambient temperature is Tₐ = 27 deg C. Taking sigma = (17/3) x 10⁻⁸ W/(m² K⁴), find (a) the rate of heat loss per unit area by radiation from the lid, and (b) the temperature of the oil.

1. (a) 595 W/m², (b) 167 deg C
2. (a) 460 W/m², (b) 150 deg C
3. (a) 595 W/m², (b) 147 deg C
4. (a) 680 W/m², (b) 187 deg C

Correct answer: (a) 595 W/m², (b) 147 deg C

Solution

Radiation loss = e*sigma*(400⁴ - 300⁴) = 595 W/m²; equating to conduction K(T_oil - 400)/t gives T_oil approx 420 K = 147 deg C.

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