Chapter 12, Problem 12.137P

Consider the spherical satellite of Problem 12.130. Instead of the entire satellite being coated with a material that is spectrally selective, half of the satellite is covered with a diffuse gray coating characterized by ${\alpha }_1=0.6$ . The other half of the satellite is coated with a diffuse gray material with ${\alpha }_2=0.3$ .

(a) Determine the steady-state satellite temperature when the satellite is on the bright side of the earth with the high-absorptivity coating facing the sun. Determine the steady-state satellite temperature when the low-absorptivity coating faces the sun. Hint: Assume one hemisphere of the satellite is irradiated by the sun and the opposite hemisphere is irradiated by the earth.

(b) Determine the steady-state satellite temperature when the satellite is on the dark side of the earth with the high-absorptivity coating facing the earth. Determine the steady-state satellite temperature when the low-absorptivity coating faces the earth.

(c) Identify a scheme to minimize the temperature variations of the satellite as it travels between the bright and dark sides of the earth.