A solar flux of 700 W/m² is incident on a flat-plate solar collector used to heat water. The area of the collector is 3 m², and 90% of the solar radiation passes through the cover glass and is absorbed by the absorber plate. The remaining 10% is reflected away from the collector. Water flows through the tube passages on the back side of the absorber plate and is heated from an inlet temperature T_i; to an outlet temperature T_o. The cover glass, operating at a temperature of 30°c' has an emissivity of 0.94 and experiences radiation exchange with the sky at - 10°C. The convection coefficient between the cover glass and the ambient air at 25°C is l0 W/m² ∙ K.

(a) Perform an overall energy balance on the collector to obtain an expression for the rate at which useful heat is collected per unit area of the collector, q''_u. Determine the value of q''_u.

(b) Calculate the temperature rise of the water, T_o - T_i, if the flow rate is 0.01 kg/s. Assume the specific heat of the water to be 4179 J/kg ∙ K.

(c) The collector efficiency η is defined as the ratio of the useful heat collected to the rate at which solar energy is incident on the collector. What is the value of η?

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Cover glass Air space Absorber plate Water tubing Insulation