Chapter 1, Problem 1.85P

A solar flux of $\text{700}{\text{W/m}}^{\text{2}}\cdot \text{K}$ 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 $-10°\text{C}$ . The convection coefficient between the cover glass and the ambient air at 25°C is $\text{10}{\text{W/m}}^{\text{2}}\cdot \text{K}$ .

(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, ${q^{″}}_{te}$ . Determine the value of ${q^{″}}_{te}$ .
(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 $4179\text{J/kg}\cdot \text{K}$ .
(c) The collector efficiency $\eta$ 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 $\eta$ ?