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Question 4 A house is to be retrofitted with a heat pump, supplying hot water to radiators at a surface temperature of 40°C. Each radiator delivers heat through one large vertical surface, which is 1.3 m high. Heat must be supplied from each radiator at a rate of 400 W to air at 20°C. Walls and other surfaces in the room can be assumed to be at 20°C also. The emissivity of the radiator surface is 0.9. (a) [8] (i) Calculate the convection coefficient for heat transfer from the radiator to the air. (ii) Neglecting radiation, how wide should each radiator be? (iii) Accounting for radiation, how wide should each radiator be? [3] (b) The water for the radiators is heated by a vapour-compression heat pump with a shell-and- tube heat exchanger as its condenser. The heat transfer coefficient U in the condenser is 250 W m-K- and the tube diameter is 12 mm. Water enters the tubes of the condenser at a temperature of 30°C, exits at 45°C, and flows at 0.074 kg/s. Refrigerant R134a enters the shell as saturated vapour at 52°C, and exits as saturated liquid. (i) Calculate the required mass flow rate of refrigerant. 141 (ii) Calculate the required UA value of the heat exchanger. [7] (iii) Calculate the total tube length required in the heat exchanger. [2]