The extent to 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 whose base temperature is Tb = 100°C. The fin is exposed to a fluid of temperature T[infinity] = 25°C, and a uniform convection coefficient of h = 100 W/m2 ∙ K may be assumed for the fin surface. (a) For a fin of length L = 10 mm, thickness t = 1 mm, and width w >> t, determine the fin heat transfer rate per unit width q;, efficiency ηf effectiveness εf' thermal resistance per unit width Rt. f, and 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 L on the heat rate for 3 < L < 50 mm. Also consider the effect of such variations for a stainless steel fin (k = 15 W/m' K)