Condensing steam is used to maintain a room at 20 oC. The steam flows through pipes that keep the pipe surface at 100 oC. To increase heat transfer from the pipes, stainless steel fins (k = 15 W/m-oC), 20 cm long and 0.5 cm in diameter, are welded to the pipe surface as shown in Figure P13-11. A fan forces the room air over the pipe and fins, resulting in a heat transfer coefficient of 50 W/m2 -oC at the base surface of the fin where it is welded to the pipe. However, the air flow distribution increases the heat transfer coefficient to 80 W/m2 -oC at the fin tip. Assume the variation in heat transfer coefficient to then vary linearly from left end to right end of the fin surface. Determine the temperature distribution at L/4 locations along the fin. Also determine the rate of heat loss from each fin.
Figure P13-11

Fin diameter= h = 50 W/m2-C d; T = 20C h = 80 W/m2.C 100C Fin tip -20 cm Pipe wall