The extent 10 which the tip condition affects the thermal performance of a fin depends on the fin geometry and thermal conductivity, as well as the convection coefficient. Consider an alloyed aluminum (k = 180 W/m ∙ K) rectangular fin of length L = 10 mm, thickness t = 1 mm, and width w t. The base temperature of the fin is Tb = 100°C, and the fin is exposed to a fluid M temperature T∞ = 25°C.

(a) Assuming a uniform convection coefficient of h = 100 W/m2 ∙ K over the entire fin surface, determine the fin heat transfer rate per unit width qf, efficiency ηf' effectiveness εf' thermal resistance per unit width Rt,f' and the tip temperature T(L) for Cases A and B of Table 3.4. Contrast your results with those based on an infinite fin approximation.

(b) Explore the effect of variations in the convection coefficient on the heat rate for 10 < h < 1000 W/m2 ∙ K. Also consider the effect of such variations for a stainless steel fin (k = 15 W/m ∙ K).