Rosie is an engineer working in the laundry factory of Fragrance Airlines to wash and clean fabrics. She is in charged of hot water supply for washing machine 24 hours a day. The hot water supply system is shown in Figure Q2 below with a rectangular tank of cross-sectional area 2 m x 1 m. At steady state, the inlet water supply has temperature 25 C and outlet temperature of 90 C at water level 2 m to meet the demand of 5 liters hot water for every kilogram of fabric being washed. The hot water temperature variation should be kept at range 87-93 C to ensure efficient washing while do not harm fabrics. In common operation, the factory is able to wash 300 kg of fabrics per hour with the cleaning services capacity can be increased when flight frequency is peak. This morning, Rosie received instruction from manager that the factory needs to increase the cleaning capacity to 500 kg per hour at 2.00 pm. However, coincident there is routine maintenance for the heater which cause the shutdown of the heater for 45 minutes starting at 2.15 pm. Rosie would like to keep the hot water supply on-going while the heater shutdown. (Heat capacity, Cwater = 4200 J/kg.C; Density water, pw = 1000 kg/m) Inlet water supply Wi T = 25 C Hot water W T= 90 C Heat supply. Q Figure Q2 (a) Derive the model and transfer function for the temperature dynamics of the heating tank system temperature (16 marks)