A rectangular plate of thickness t, length L, and width W is proposed for use as a radiator in a spacecraft application. The plate material has a thermal conductivity of 300 W/m. K, a solar absorptivity of 0.45, and an emissivity of 0.9. The radiator is exposed to solar radiation only on its top surface, while both surfaces are exposed to deep space at a temperature of 4K.

  (a) If the base of the radiator is maintained at T_b = 80°C, what is its tip temperature and the rate of heat rejection? Use a computer-based, finite-difference method with a space increment of 0.1 m to obtain your solution.

  (b) Repeat the calculation of part (a) for the case when the space ship is on the dark side of the earth and is not exposed to the sun.

  (c) Use your computer code to calculate the heat rate and tip temperature for G_s = 0 and an extremely large value of the thermal conductivity. Compare your results to those obtained from a hand calcula. tion that assumes the radiator to be at a uniform temperature T_b. What other approach might you use to validate your code?