1. Graph Paper (a) Two different potatoes are baked in an oven at a temperature of 200C with air containing 20% steam circulating around them. You can assume that the potatoes can be modelled as spheres of diameters 4 cm and 8 cm suspended in the air. The heat transfer coefficient between air and the small potato is 18 W m K-1 and between air and the large potato is 12.5 W m K-1 (i) Name the mechanisms of heat transfer to, and inside the potatoes and for each of these mechanisms write the equation relating the heat flux to the temperature, name the proportionality coefficients in these equations and give their units. (ii) Calculate the time necessary to heat the potatoes from 20C to 100C and the amount of energy supplied to each potato. [10%] [15%] (b) Water is cooled as it flows through a pipe surrounded by air. It is suggested to increase the intensity of cooling by using fins. (i) Where would you attach the fins to achieve this: on the water side or on the air side? Justify your answer. (ii) What parameters should you consider when designing those fins? (iii) Explain why fins should be tightly attached to the surface. [10%] (c) It is proposed to cool oil in a counter-current, concentric tube heat exchanger composed of a thin-walled inner tube of 0.02 m diameter carrying oil and thin-walled, perfectly insulated outer tube of 0.05 m diameter carrying water. The oil flow rate is 50.0 kg min1 and it has to be cooled from 90C to 40C using 60 kg min 1 water at 20C. (i) Calculate the heat load and the outlet water temperature. [10%] (ii) Can the method of main resistance be used to determine the length of this heat exchanger? Heat transfer coefficients can be calculated from appropriate correlations shown below in the data section for this question. [10%]