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 T_b = 100°C. The fin is exposed to a fluid of temperature T_∞ = 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  effectiveness ε_f, thermal resistance per unit width  and tip temperature T(L) for Cases A and B of Table 3.4. Contrast your results with those based on an infinite f approximation.

(b) Explore the effect of variations in L on the heat rate for 3 ∙ K).