GATE 2016 ME (ME1) – Question 53
An infinitely long furnace has 0.5 m × 0.4 m cross section. All surfaces are black. Top and bottom are at $T_1=T_3=927^\circ$C; sides are at $T_2=T_4=527^\circ$C. Given $F_{1-2}=0.26$ and $\sigma=5.67\times10^{-8}$ W/m²K⁴, the net radiation heat loss or gain on side 1 is ______ W/m.
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Correct answer: 24528 to 24532
Explanation
Side3 has the same temperature as side1 and contributes no net exchange. Symmetry gives F12=F14=0.26, so the total factor to cooler walls is0.52. For one metre length A1=0.5m², and temperatures are1200K and800K using the paper’s rounded Celsius conversion. Loss is0.5·0.52·5.67e−8(1200⁴−800⁴)=**24530.688W/m**.