A tapered aluminum fin (k = 200W/ m-° C), shown in Figure P13–12, has a circular cross s...

A tapered aluminum fin (k = 200W/ m-° C), shown in Figure P13–12, has a circular cross section with base diameter of 1 cm and tip diameter of 0.5 cm. The base is maintained at 200 ° C and looses heat by convection to the surroundings at T_∞ = 10 ° C, h = 150W/m²-° C. The tip of the fin is insulated. Assume one-dimensional heat flow and determine the temperatures at the quarter points along the fin. What is the rate of heat loss in Watts through each element? Use four elements with an average cross-sectional area for each element.