A microprocessor has an aluminum heat sink attached that consists of a series of parallel, rectangular fins. Each fin is \(2 \mathrm{~mm}\) thick, \(25 \mathrm{~mm}\) long, \(25 \mathrm{~mm}\) high, and spaced on \(6 \mathrm{~mm}\) centers. When the microprocessor is turned on it begins producing heat at a rate of \(1 \mathrm{~mW} /\) \(\mathrm{cm}^{2}\) of surface area. A fan within the computer circulates air at \(T_{\infty}=25^{\circ} \mathrm{C}\) through the machine providing a heat transfer coefficient of \(150 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\). The fin tip can be assumed to be exposed to the convecting fluid.

a. Determine the steady-state temperature profile in the fin.

b. What is the temperature of the base?