$10\mathrm{.}8$ A liquid heating system with a one$-$cover selective collector with emittance of $0\mathrm{.}2$ is set up to preheat water from the mains and supply it at $T_s$ to a boiler, as shown in the accompanying diagram. The characteristics of the system are as follows:

$F_R({)}_n=0\mathrm{.}73$

$F_R{U}_L=5\mathrm{.}10\frac{W}{m^2}C$

Heat exchanger effectiveness $0\mathrm{.}60$

Capacitance rate on collector side $1020\frac{W}{}C$

Capacitance rate on tank side $1120\frac{W}{}C$

Collector area $20m^2$

Tank capacity $1000$ liters

Tank $UA6\mathrm{.}0\frac{W}{}C$

Supply water temperature $11C$

Initial tank temperature $35C$

The meteorological data and load flow rate for a $4-$h period are shown in the following table:

$\backslash$table$[[$Hour$,I_T,M\frac{J}{m^2},T_a,C,$Load Flow, $kg$