Spacecraft must be cooled via radiative mechanisms and one means of doing this is radiation fins. In many instances, these fins are heated rods that protrude from the spacecraft. Assume that the rod is of length, \(L\), cross-sectional area, \(A_{c}\), and perimeter, \(P_{d}\). Its base temperature is \(T_{b}\), and the rod has a thermal conductivity and emissivity, \(k\) and \(\varepsilon\) respectively. Set up the differential equation describing the temperature profile within the rod assuming that space is a blackbody at \(3 \mathrm{~K}\).