An air heater consists of a shell-and-tube heat exchanger with 24 longitudinal fins on the outside of the tubes. The tubes are 1.5-in, 14 BWG, and the fins are 0.75 mm thick and are 15 mm long. A total of 8 fins are spaced uniformly around the circumference of each tube. The tubes are made from carbon steel, and their length is 3 m. Air at 0.8 kg/s is being heated from 30°C to 200°C in the shell, and the heat transfer coefficient may be taken as h_o = 25 W/m²/K (without fins). Steam is condensing at 254°C in the tubes, and at that temperature l = 1700 kJ/kg. The tube-side heat transfer coefficient may be taken as h_i = 6000 W/m²/K, and no fouling occurs for this service.

Calculate the overall heat transfer coefficient with and without fins.

Calculate the heat transfer area and the number of tubes needed with and without fins.