A water heating system consists of a heat exchanger made from a 12m long copper pipe. The inside diameter of the copper pipe is d = 50mm and the outside diameter is do = 70mm. Annular aluminium fins 10mm in length are attached to the pipe. The fins are 1 mm thick and are spaced 1 mm apart from each other (total number of fins = 6000). Water flows inside the pipe at a rate of = 0.2 kg/s, entering the heat exchanger at a mean temperature of 20 C. Hot air at 120C flows around the outer surface of the heat exchanger at a velocity of 3 m/s. The heat exchanger is shown in the following figure (not to scale). The properties of the various materials and fluids are given as follows: Water: Pw = 1000 kg/m Hw = 1080 106 Ns/m Prw = 7.86 Kw = 598 10 W/mK Cpw = 4184 J/kgK Air: P = 1.1614 kg/m H= 184.6 107 Ns/m Pra = 0.707 K= 26.3 10- W/mK Copper: Kcopper = 401 W/mK Aluminum: KAluminium = 237 W/mK Air U-3 m Tw=120C Aluminum Fins. Copper Pipe Water m-0.2kg/s T-20C Hot-Tub Water Heater a) Using a thermal resistance diagram, illustrate how heat is transferred from the hot air to the water inside the copper pipe. (5 marks) b) Determine the convection coefficient inside the copper pipe. (5 marks) c) Determine the convection coefficient on the outside of the pipe. Note: assume the flow outside the pipe is similar to that over the surface of a plain cylinder with the same outer diameter as the copper pipe (i.e. neglect aerodynamic effects of the fins). (5 marks) d) Calculate the mean temperature of the water at the outlet of the water heater. Note: assume that the convection coefficient around the fins is the same as the one around the pipe (calculated in part c)). (17 marks) e) Evaluate the heat transfer rate for the water. (3 marks)