Calculate the efficiency of the collector described in Problem 7.1 on March 1 at a latitude of \(40^{\circ} \mathrm{N}\) between 11 and 12 a.m. Assume that the total horizontal insolation is \(450 \mathrm{~W} / \mathrm{m}^{2}\), the ambient temperature is \(280 \mathrm{~K}\), and the collector is facing south.

Problem 7.1

Calculate the heat-removal factor for a collector having an overall heat loss coefficient of \(6 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\) and constructed of aluminum fins and tubes. Tube-to-tube centered distance is \(15 \mathrm{~cm}\), fin thickness is \(0.05 \mathrm{~cm}\), tube diameter is \(1.2 \mathrm{~cm}\), and fluid tube heat-transfer coefficient is \(1200 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\). The cover transmittance to solar radiation is 0.9 and is independent of direction. The solar absorptance of the absorber plate is 0.9, the collector is \(1 \mathrm{~m}\) wide and \(3 \mathrm{~m}\) long, and the water flow rate is \(0.02 \mathrm{~kg} / \mathrm{s}\). The water temperature is \(330 \mathrm{~K}\).