Chapter 9, Problem 9.38P

Consider a horizontal 6-mm-thick, 100-mm-long straight fin fabricated from plain carbon steel $\left(k=57\text{W/m}\cdot \text{K,}\epsilon =0.5\right)$ . The base of the fin is maintained 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 per unit width $q_f^{\text{'}}$ . Use an average fin surface temperature of 125°C to estimate the free convection coefficient and the linearized radiation coefficient. How sensitive is your estimate to the choice of the average fin surface temperature?
Generate a plot of $q_f^{\text{'}}$ as a function of the fin emissivity for $0.05\le \epsilon \le 0.95$ . On the same coordinates, show the fraction of the total heat rate due to radiation exchange.