Consider two very long, straight fins of uniform cross section, as shown in Figure 3.17. The rectangular fin has dimensions t = 1 mm and w = 20 mm. The circular pin fin has the same cross-sectional area as the rectangular fin. Both fins are constructed of aluminum with k = 237 W/m · K. In both cases, the base temperature is Tb = 85°C. Airflow is directed as shown in the figure, with T∞ = 20°C and u∞ = 5 m/s.
(a) Calculate the heat loss from each fin. Assume that the heat transfer coefficient on the edges of the rectangular fin is equal to the average value on the upper and lower surfaces.
(b) What diameter cylindrical fin would be needed to provide the same fin heat transfer rate as the rectangular cross-section fin?