The preliminary design of a fast-response hot-water heater has been completed in Design Problem 2.4. In the

Question:

The preliminary design of a fast-response hot-water heater has been completed in Design Problem 2.4. In the sketch, a cross section of the heater is shown. An extruded heating element is located inside the pipe carrying water to be heated. (The cross-sectional shape of the heater element provides more surface area than a square or round cross-sectional heating element.) The heating element dissipates 4800 watts per meter length, has a thermal conductivity of 20 W/m K, and has a maximum operating temperature of 110°C. Water is to be heated up to 65°C by the device. The surface of the heating element should not

exceed 100°C to avoid boiling. Determine the required convective heat transfer coefficient, assuming it to be uniform over the surface of the heating element.

Data from in Problem 2.4

A circumferential fin of rectangular cross section, 3.7-cm OD and 0.3 cm thick, surrounds a 2.5-cmdiameter tube as shown below. The fin is constructed of mild steel. Air blowing over the fin produces a heat transfer coefficient of 28.4 W/m² K. If the temperatures of the base of the fin and the air are 260ºC and 38ºC, respectively, calculate the heat transfer rate from the fin.