temperature distribution expression of rod and heat transfer from rod

Question

1. A thin rod of length l has its two ends connected to two reservoirs at temperatures t₁ and t₂ respectively. The rod has the perimeter P and its cross-sectional area A. The rod loses heat to the environment at temperatures, t_s. The convection coefficient of heat transfer between the rod and the environment in h. Assuming the thermal conductivity of the material of the rod to be constant k, derive an expression for (i) the temperature distribution in the rod and (ii) the heat transfer from the rod to the environment.                                                              15

C = 0.38(1-263/T)

Obtain an expression for the absorptivity of solar radiation as a function of surface temperature.

The intensity of solar radiation at earth’s surface may be calculated from the following data:

Diameter of sun = 1.39 ´ 10⁶ km

Surface temperature of sun = 600 K.

Distance between sun and earth = 149 ´ 10⁶ km

Assume sun to behave as a black body.