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GATE 2017 ME (ME1) – Question 47

Heat Transfer · Radiative heat transfer: laws, view factors, radiation network · 2 marks · MTA

Black surfaces AB and BC have lengths 5 m and 6 m, respectively, and extend infinitely in the third dimension. Their orientation and surface labels are shown. Given $F_{12}=0.5$, $T_1=800$ K, $T_2=600$ K, surroundings at 300 K and $\sigma=5.67\times10^{-8}$ W/(m² K⁴), find the heat-transfer rate from surface 2 to the surroundings in kW.

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Correct answer: MTA

Explanation

The diagram labels BC as surface 1 and AB as surface 2. Use unit depth, so $A_1=6$ m² and $A_2=5$ m². Reciprocity gives $A_2F_{21}=A_1F_{12}=3$ m². Since surface 2 is flat, its self-view factor is zero, leaving $A_2F_{2,s}=5-3=2$ m². Net exchange with the surroundings is $2\sigma(600^4-300^4)=13778.1$ W = 13.78 kW per metre depth. The stated infinite depth makes a finite total rate undefined. The earlier numerical key used a per-unit-depth result; the final key awards marks to all, which is preserved here.

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