Consider a pin fin as shown in Figure 2-10d. Assume that the fin is exposed to an evacuated space such that convection is negligible and that the radiation loss per unit surface area is given by

where ε is a surface emissivity constant, σ is the Stefan-Boltzmann constant, and the temperatures are expressed in degrees Kelvin. Derive a differential equation for the temperature in the pin fin as a function of x, the distance from the base. Let T0 be the base temperature, and write the appropriate boundary conditions for the differential equation.

9rad/A = ea(T - T)