Consider a horizontal 6-mm-thick, 100-mm-Iong straight fin fabricated from plain carbon steel (k = 57 W/m ∙ K, ε = 0.5). The base of the fin is maintained at 150°C, while the quiescent ambient air and the surroundings are at 25°C. Assume the fin tip is adiabatic.

(a) Estimate the fin heat rate per unit width, q'f. Use an average fin surface temperature of 125°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?

(b) Generate a plot of q; as a function of the fin emissivity for 0.05 < B < 0.95. On the same coordinates, show the fraction of the total heat rate due to radiation exchange.