3.107 The extent to which the tip condition affects the ther- mal performance of a fin depends on the fin geometry in and thermal conductivity, as well as the convection X00 coefficient. Consider an alloyed aluminum (k180 xem W/m K) rectangular fin of length L = 10 mm, thick- ness t = 1 mm, and width w»t. The base temperature of the fin is T, = 100°C, and the fin is exposed to a fluid of temperature T.. = 25°C. on t . (a) Assuming a uniform convection coefficient of h=100 W/m². K over the entire fin surface, deter- mine the fin heat transfer rate per unit width q efficiency n, effectiveness &, thermal resistance per unit width R', and the tip temperature T(L) for 201 ib 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/mK).