Chapter 1, Problem 1.85P

A solar flux of $700{\text{W/m}}^{\text{2}}$ is incident on a flat-plate solar collector used to heat water. The area of the collector is $3{\text{m}}^{\text{2}},$ 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 To. The cover glass, operating at a temperature of $30°\text{C,}$ has an emissivity of 0.94 and experiences radiation exchange with the sky at $-10°\text{C}\text{.}$ The convection coefficient between the cover glass and the ambient air at $25°\text{C}$ is $10{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$

1. 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 $q_u^{"}.$ 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 $4179\text{J/kg}\cdot \text{K}\text{.}$ The collector efficiency 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 $\eta ?$