Project ForgeA 0.2 m thick infinite black plate having a thermal conductivity of 3.96 W/m-K is exposed (across vacuum gaps) to two infinite black surfaces at 300 K and 400 K. At steady state, the surface temperature of the plate facing the cold (300 K) side is 350 K. Stefan-Boltzmann constant σ=5.67×10⁻⁸ W/m²K⁴. Assuming 1-D heat transfer, the magnitude of heat flux through the plate (in W/m²) is __________ (correct to two decimal places).
Explanation
At steady state, the flux is the same across every section, including the radiative exchange between the plate's cold face (350 K, black) and the 300 K black surface: q = σ(Tcold-face⁴ − T300⁴) = 5.67×10⁻⁸×(350⁴−300⁴) = 5.67×10⁻⁸×(1.500625×10¹⁰ − 0.81×10¹⁰) ≈ 5.67×10⁻⁸×6.906×10⁹ ≈ 391.6 W/m².
Source: GATE ME 2018 Session 2 (Set 2) (2018)
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