Chapter 12, Problem 12.132P

A spherical satellite in near-earth orbit is exposed to solar irradiation of $1368{\text{ W/m}}^2$ . To maintain a desired operating temperature, the thermal control engineer intends to use a checker pattern for which a fraction F of the satellite surface is coated with an evaporated aluminum $\left(\epsilon =0.03,{\alpha }_s=0.09\right)$ , and the fraction $\left(1-F\right)$ is coated with a white, zinc-oxide paint $\left(\epsilon =0.85,{\alpha }_s=0.22\right)$ .Assume the satellite is isothermal and has no internal power dissipation. Determine the fraction F of the checker pattern required to maintain the satellite at 300 K.