A 40-mm-Iong, 2-mm-diameter pin fin is fabricated of an aluminum alloy (k = 140 W/m2 ∙ K).

(a) Determine the fin heat transfer rate for Th = 50°C, T∞. = 25°C, h = 1000 W/m2 ∙ K. and an adiabatic tip condition.

(b) An engineer suggests that by holding the fin tip at a low temperature, the fin heat transfer rate can be increased. For T(x = L) = O°C, determine the new fin heat transfer rate. Other conditions are as in part (a).

(c) Plot the temperature distribution, T(x), over the range 0 < x < L for the adiabatic tip case and the prescribed tip temperature case. Also show the ambient temperature in your graph. Discuss relevant features of the temperature distribution.

(d) Plot the fin heat transfer rate over the range 0 S h < 1000 W/m2 ∙ K for the adiabatic tip case and the prescribed tip temperature case. For the prescribed tip temperature case, what would the calculated fin heat transfer rate be if Equation 3.73 were used to determine qf rather than Equation 3.71?