The extent to which the tip condition affects the thermal

Chapter , Problem 3.131

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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 of length L 10 mm, thickness t 1 mm, and width w t. The base temperature of the fin is Tb l00 C, and the fin is exposed to a fluid of 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 f , effectiveness f , 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).