Consider a horizontal pin fin of 6-mm diameter and 60-mm length fabricated from plain carbon steel (k = 57 W/m · K, s = 0.5). The base of the fin is main- tained at 150°C, while the quiescent ambient air and the surroundings are at 25°C. Assume the fin tip is adiabatic.
(a) Estimate the fin heat rate, qf. Use an average fin surface temperature of 125°C in estimating the free convection coefficient and the linearized radiation coefficient. How sensitive is this esti- mate to your choice of the average fin surface temperature?
(b) Use the finite-difference method of solution to obtain qf when the convection and radiation coefficients are based on local, rather than average, tem- peratures for the fin. How does your result compare with the analytical solution of part (a)?