Consider a thin, opaque, horizontal plate with an electrical heater on its back side. The front side is exposed to ambient air that is at \(20^{\circ} \mathrm{C}\) and provides a convection heat transfer coefficient of \(20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), solar irradiation of \(800 \mathrm{~W} / \mathrm{m}^{2}\), and an effective sky temperature of \(-40^{\circ} \mathrm{C}\).

What is the electrical power \(\left(\mathrm{W} / \mathrm{m}^{2}\right)\) required to maintain the plate surface temperature at \(T_{s}=60^{\circ} \mathrm{C}\) if the plate is diffuse and has the designated spectral, hemispherical reflectivity?

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Ty Th T sky 1.0 0.7 Plate 0.2 0 0 2 Insulation Electrical heater ()