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/mK) rectangular fin of length L = 10 mm, thickness t = 1mm w>>t, The base temperature of the fin is Tb = l00°C, and the fin is exposed to a fluid of temperature T[infinity] = 25°C.
a) Assuming a uniform convection coefficient of h =50 W/m2 ⋅ K over the entire fin surface, determine the fin heat transfer rate per unit width q′f, efficiency ηf , effectiveness ε f, thermal resistance per unit width R′t, 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 = 11.7 W/m ⋅ K). (Use h=100 W.m2 K)