Standard tests on a commercially available flat-plate collector gave a thermal efficiency of

\[ \begin{gathered} \eta=0.7512-\frac{0.138\left(T_{f, i n}-T_{\alpha}\right)}{I_{c}} \\ K_{\tau \alpha}=1-0.15\left[\frac{1}{\cos (i)}-1\right] \end{gathered} \]

where \(\left(T_{\text {fin }}-T_{a}\right) / I_{c}\) is in \(\mathrm{K} \mathrm{m}^{2} / \mathrm{W}\)

Find the useful energy collected from this collector each hour and for the whole day in your city on September 15.

Assume that all the energy collected is transferred to water storage with no losses. Calculate the temperature of the storage for each hour of the day. Assume a reasonable ambient temperature profile for your city. Given Collector area \(=6 \mathrm{~m}^{2}\)

Collector tilt \(=30^{\circ}\) (south facing in northern hemisphere, north facing in southern hemisphere)

Storage volume \(=0.3 \mathrm{~m}^{3}\) (water)

Initial storage temperature \(=30^{\circ} \mathrm{C}\)