A cylindrical hot water storage tank, 1.7 m in diameter and 2.1 m high, is made from a steel plate ( = 7800 kg/m3, Cp = 0.46 kJ/kgK) 6 mm thick. Apart from the mass of the steel required for making the surface, an additional 200 kg of steel is required in the form of angles, etc. for strengthening the tank, which is insulated all around with the glass wool insulation 20 cm thick (k = 0.040 W/mK). The initial temperature of the water in the tank is 50°C at 0700 h in the morning on a particular day and the variation of qu and Ta up to 2000 h is as shown in the below table: Time 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19- 20 18660 37496 5489060070698907012062205 55490 4107019195 0 0 0 9น (kJ/h) Ta (°C) 17.8 21.9 25.1 27.4 29.1 30.2 30.9 31.2 31.3 30.8 28.9 26.0 24.0 The load requirement is such that energy is continuously withdrawn from the tank at a constant rate of 27,000 kJ/h for 18 hours a day starting at 0500 h. Assuming that the water in the tank is always well-mixed, calculate the variation of its temperature.
