Consider a horizontal 5-mm-thick, 100-mm-long straight fin fabricated from plain carbon steel \((k=57\) \(\mathrm{W} / \mathrm{m} \cdot \mathrm{K}, \varepsilon=0.5)\). The base of the fin is maintained at \(100^{\circ} \mathrm{C}\), while the quiescent ambient air and the surroundings are at \(25^{\circ} \mathrm{C}\). Assume the fin tip is adiabatic, and estimate the fin heat rate per unit width, \(q_{f}^{\prime}\). Use an average fin surface temperature of \(80^{\circ} \mathrm{C}\) to estimate the free convection coefficient and the linearized radiation coefficient. How sensitive is your estimate to the choice of the average fin surface temperature?