Chapter 12, Problem 12.127P

Consider a thin opaque, horizontal plate with an electrical heater on its backside. The front side is exposed to ambient air that is at ${20}^{\circ }C$ and provides a convection heat transfer coefficient of ${\text{10 W/m}}^2\cdot \text{K}$ , solar irradiation of ${\text{600 W/m}}^2$ , and an effective sky temperature of $-{40}^{\circ }C$ .

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