GATE 2023 MT – Question 58
Two circular surfaces A and B have emissivities, temperatures, and view factors as shown. Consider radiation only between A and B. Given $\sigma=5.67\times10^{-8}$ W m$^{-2}$ K$^{-4}$, the net radiative heat flow from A is ______ kW (one decimal place).
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Correct answer: 9.2 to 9.7
Explanation
For two diffuse-gray surfaces, $Q=\sigma(T_A^4-T_B^4)/[(1-\epsilon_A)/(A_A\epsilon_A)+1/(A_AF_{AB})+(1-\epsilon_B)/(A_B\epsilon_B)]$. Both areas are $\pi$ m$^2$ (radius 1 m). Substitute $\epsilon_A=0.7,\epsilon_B=0.8,F_{AB}=0.172,T_A=800$ K, $T_B=500$ K. The resistance denominator is about 2.0667 m$^{-2}$ and the numerator 19680.57 W m$^{-2}$, giving **9.5 kW**.