## 2 Materials and Methods
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Melting Point**} & \multirow{2}{*}{
\begin{tabular}{c} **Heat** \\ **Storage** \\ **Capacity** \\ \(\pm\)7.5\%** \\ \end{tabular} } & **Specific** & **Density** & **Density** & **Heat** & & & & & \\  & & **Heat** & **Solid at** & **Liquid at** & **Conductivity** & **Volume** & **Expansion** & **Flash Point** & **Operating** \\  & & **Capacity** & **15 \({}^{\circ}\)C** & **80 \({}^{\circ}\)C** & **Phases** & & & & **Temp.** \\ \hline
41–48 \({}^{\circ}\)C & 160 kJ/kg & 2 kJ/kg K & 0.88 kg/L & 0.77 kg/L & 0.2 W/m k & 12\% & \(>\)180 \({}^{\circ}\)C & 65 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table} 
Table 2: The specifications of the RT-47 PCM used in the present work [32]. \[a=n\frac{r}{sin\theta_{acc}} \tag{1}\]  
\[L=(a+r)\ cot\theta^{\prime}_{acc} \tag{2}\]  
\[f=\frac{r(sin\theta_{out}+sin\theta_{acc})}{n} \tag{3}\]  
\[\theta^{\prime}_{acc}=2 across\frac{1}{n}-\theta^{\prime}_{out} \tag{4}\]  
where \(a\) is the input radius; \(r\) is the exit radius; \(L\) is the LCPV length; \(\theta_{out}\) and \(\theta^{\prime}_{out}\) are the external and internal output angle, respectively; and \(\theta_{acc}\) and \(\theta^{\prime}_{acc}\) are the external and internal acceptance angle, respectively. Reference PV (PV1): For PV1, the PV panel obtained from the market was used without modifications as a reference PV panel, and three BST-TP01 K-type thermocouples were fixed at the middle line of the PV panel's back and used to measure the back surface temperature. Similarly, three thermocouples were fixed at the same position on the back of each of the other three panels. The average of the readings of the three thermocouples was considered to represent the PV temperature. Figure 3: LCPV cross-sectional view. PV-PCM (PV2): In this case, after fixing the thermocouples, the back side of the PV2 panel was filled with 12.5 kg of Rubitherm RT-47 PCM, as shown in Figure 4a. Then, it was completely sealed from the back with an acrylic sheet of 5 mm thickness. PV/T-PCM (PV3): Here, after fixing the thermocouples, a copper tube coil in rectangular shape was fixed to the back surface of the panel, assuring a good contact to eliminate the thermal contact resistance as shown in Figure 4b. Then, 11 kg of Rubitherm RT-47 was used to fill the back of the panel. After that, an acrylic sheet of 10 mm was used to cover the opening. LCPV/T-PCM (PV4): The panel is identical to the PV3 panel as shown in Figure 4c, but a low-concentration frame was designed for this case and fixed in the frame structure of the system, as shown in Figure 4d. The performance of the PV panels in this study are expressed by the instant electrical power and the daily average electrical and overall efficiencies. The maximum electrical power output that could be generated from each PV panel was traced by the PV analyzer and recorded every 10 min. The PV analyzer applied a load on the PV panels for a few seconds to record the maximum power, while the solar batteries were connected to the PV panels to ensure continuous loading on the panels over the day. The typical equation used to calculate the daily average electrical efficiency can be written as follows:  
\[\eta_{electrical}=\frac{P_{electrical}}{I\ A} \tag{5}\]  
where \(P_{electrical}\) and \(I\) are the daily average electrical power and solar irradiance over the investigated period, respectively, while \(A\) is the panel area. The PV3 and PV4 panels also provide thermal power output that can be used to drive an external system. Therefore, the daily average thermal and overall efficiencies of the PV3 and PV4 panels can be written as follows [34; 35]:  
\[\eta_{thermal}=\frac{\dot{m}_{w}\ c_{pw}\ (T_{e}-T_{i})}{I\ A} \tag{6}\]  
\[\eta_{overall}=\eta_{electrical}+\eta_{thermal} \tag{7}\]  
where \(\dot{m}_{w}\) is the thermal fluid mass flow rate; \(c_{pw}\) is the specific heat capacity of the thermal fluid; and \(T_{i}\) and \(T_{e}\) are the inlet and exit temperatures of the thermal fluid.