Calculate the plate temperature in Example 7.3 at 10 a.m., if the insolation during the first \(3 \mathrm{~h}\) is 0,150 , and \(270 \mathrm{~W} / \mathrm{m}^{2}\), respectively, and the air temperature is \(285 \mathrm{~K}\).

Example 7.3

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Calculate the temperature rise between 8 and 10 a.m. of a 1 x 2 m single-glazed water collector with a 0.3 cm thick glass cover if the heat capacities of the plate, water, and back insulation are 5, 3, and 2 kJ/K, respectively. Assume that the unit surface conductance from the cover to ambient air is 18 W/m K, and the unit surface conductance between the collector and the ambient air is U = 6 W/m. K. Assume that the collector is initially at the ambient temperature. The absorbed insolation a,I, during the first hour averages 90 W/m and that between 9 and 10 a.m. is 180 W/m. The air temperature between 8 and 9 a.m. is 273 K and that between 9 and 10 a.m. is 278 K.