## 2 Materials and Methods
### Energy Model  
The energy absorbed by the solar collector is given in Equation (1). This equation calculates the energy \(Q_{a}\) absorbed by the thermal collector, it is measured in units of energy (joules or kilojoules). The effect of reflector is considered proportional to the gap between tubes; therefore, the total area of absorption was estimated as the area of thermal collector box. The magnitude of \(Q_{a}\) is determined by the product of the water mass flow rate \(m\), the specific heat capacity of water \(c_{p}\) and the temperature difference between the outlet temperature \(T_{o}\) and the inlet temperature \(T_{i}\). The mass flow rate, measured in kilograms per second (kg\(\cdot\)s\({}^{-1}\)), determines the rate at which heat is transferred from the collector to the water. Higher flow rates can increase the efficiency of heat transfer but may require more energy to pump the water. Whereas the specific heat capacity, measured in joules per kilogram-degree Celsius (J\(\cdot\)kg\({}^{-1}\)\(\cdot\)\({}^{\circ}\)C\({}^{-1}\)), determines how much heat energy is required to raise the temperature of the water in the collector. The temperature difference, \(T_{o}-T_{i}\), measured in degrees Celsius (\({}^{\circ}\)C), indicates the amount of heat absorbed by the water as it flows through the collector. A larger temperature difference implies more heat absorption. This formula represents the basic principle of energy transfer in the collector, where the water absorbs heat as it passes through the collector, ultimately contributing to the overall thermal efficiency of the system.  
The photothermal conversion efficiency, \(\eta_{th}\), is derived from Equation (2). It is calculated based on the heat absorbed by the collector (\(Q_{a}\)) and the solar energy received by the collector is calculated by multiplying the solar irradiance (\(Is\)) with thermal collector  
Figure 5: Solar irradiance and ambient air temperature plotted against time.  
surface area (\(A\c\)). Efficiency is dependent on several factors; \(F_{R}\) is the heat removal factor, representing the fraction of absorbed heat that is effectively transferred to the working fluid. It is influenced by factors such as the collector design and operating conditions. \(\tau\) is the emissivity of the glazing material, which affects the amount of heat retained by the collector (1 in the case of an unglazed system). A lower emissivity means that the material retains more heat, increasing the efficiency of the collector. \(\alpha\) is the absorptivity of the thermal collector tube, indicating the fraction of incident solar radiation absorbed by the collector. A higher absorptivity means that the collector absorbs more solar radiation, increasing its efficiency. \(U_{L}\) is the overall heat loss coefficient, representing the efficiency of heat transfer from the absorber surface to the working fluid. It depends on the collector's design and fluid properties. Ultimately, the equation shows how the efficiency of the system is influenced by factors related to the collector's design, operating conditions and environmental factors.  
\[Q_{a}=\dot{m}c_{p}(T_{o}-T_{l}) \tag{1}\]  
\[\eta_{th}=F_{R}\tau\alpha-F_{R}U_{L}\bigg{(}\frac{T_{l}-T_{a}}{l_{s}}\bigg{)}= \frac{Q_{a}}{l_{s}A_{c}} \tag{2}\]