## 3 Theoretical Study  
The panel was considered a lumped system composed of materials with different physical properties. The panel temperature is a function of the intensity of solar irradiation, tilt angle of the panel to the ground, ambient temperature, wind temperature, and properties of the atmosphere and the nature of the ground. The objective of this analysis is to find the temperature of the panels analytically and compare it to the experimental results under similar input conditions. The solar energy is the input energy that is absorbed by the PV panel. Heat is lost to the environment from the front side and back side of the panel by convection and radiation. The HPT helps in heat loss by three mechanisms: latent heat when the acetone phase changes from liquid to vapor, sensible heat convection, and finally, heat radiation when there is no phase change. The following assumptions were assumed during the analysis of the PV panel:  
* The temperature distribution is uniform all over the panel. * The average panel temperature is a linear average of the temperatures at different panel layers and at different points on the surface. * Heat loss through the supporting structure is negligible. * The heat pipe has no loses and all the heat received from the panel is used to evaporate the phase change fluid used inside the heat pipe. * No dry out of the evaporator region occurs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Boiling Point** & **Volume** & **Density (Liquid)** & **Density (Vapor at 330 K)** \\ \hline Acetone & 56 \({}^{\circ}\)C & 0.3925 L/tube & 784 kg/m\({}^{3}\) & 2.325 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The specification of the WF. Figure 2: The distribution of the thermocouples that were used to measure the temperature of the cooled and reference PV panels. (**a**) Reference panel without heat pipe (**b**) panel with heat pipe. The overall rate of energy transfer for PV module without HPT is given by the energy balance of all the incoming and outgoing energy over the panel. Using this energy balance, the change in panel temperature with time is given by Equation (1):  
\[C_{t}\times\frac{dT_{module}}{dt}=q_{sw}-q_{hw}-q_{c}-P_{o} \tag{1}\]  
where \(q_{sw}\) is the solar radiations received from the sun, \(q_{hw}\) is the heat dissipated as the longwave radiation from the top of the panel to the sky and from the bottom of the panel to the ground, \(P_{o}\) represents the electrical power output, \(q_{c}\) represents the convection losses from both sides due to wind, and \(C_{t}\) is the total specific heat capacity of the panel, which is the sum of the specific heat capacity of each layer of the panel, and it is given by Equation (2):  
\[C_{t}=\sum_{m}A_{m}\;t_{m}C_{m}\rho_{m} \tag{2}\]  
where \(A_{m},t_{m},C_{m},\rho_{m}\) are the area, thickness, specific heat capacity, and density of each layer m. Using the values in Table 1, \(C_{t}=2717.69\;J/kg\cdot K\). The longwave radiation loss is shown in Equation (3) and comprises three parts, namely the radiation exchange to the sky, to the ground, and from the panel. \[q_{hw}=A\times\sigma\times\left[\frac{(1+\cos\beta)}{2}\times\varepsilon_{s} \times T_{s}^{4}+\frac{(1-\cos\beta)}{2}\times\varepsilon_{g}\times T_{g}^{4} -\left(\varepsilon_{p}\times T_{p}^{4}\right)\right] \tag{3}\]  
where \(\sigma\) is the Boltzmann's constant (\(5.669\times 10^{-8}\) (\(W/m^{2}\) K\({}^{4}\))), \(\varepsilon_{g}\) is the emissivity of the ground (\(0.95\)), and \(\varepsilon_{p}\) is emissivity of the panel (\(0.9\)). The two factors, (\(1-\cos\beta\))/2 and (\(1+\cos\beta\))/2, represent the shape factors for radiation loss to the top and bottom of the panel. The sky temperature \(T_{s}\) is given by Equations (4) and (4b) for clear and overcast sky conditions, respectively. The sky temperature \(T_{a}\) is equal to ambient temperature \(T_{a}\). \[T_{sky}=T_{a}-\Delta t \tag{4}\]  
where \(\Delta t=20\) and \(T_{a}\) is the ambient temperature [28].