GATE 2018 ME (ME2) – Question 51
A 0.2 m thick infinite black plate of conductivity 3.96 W/(m·K) is exposed to infinite black surfaces at 300 K and 400 K across vacuum gaps as shown. At steady state its cold-side face is 350 K. Take $\sigma=5.67\times10^{-8}\ \mathrm{W/(m^2K^4)}$ and one-dimensional conduction. Find heat flux through the plate (W/m²), to two decimal places.
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Correct answer: 385.00 to 395.00
Explanation
At steady state conduction through the plate equals radiation from the cold face to the 300 K black surface. Therefore $$q^{\prime\prime}=\sigma(350^4-300^4)=5.67\times10^{-8}(350^4-300^4)=391.58\ \mathrm{W/m^2}.$$ The given cold-face temperature fixes the flux directly.