## 3 Theoretical Study
The shortwave radiation received by the panels is given in Equation (5), as follows:  
\[q_{sw}=\alpha\times\;I_{t}\times A \tag{5}\]  
where \(I_{t}\) is the incident solar radiation, and \(\alpha\) is the absorptivity of the panel, taken as \(0.7\), after considering a glass reflectivity of \(10\%\)[29]. The convection heat loss \(q_{c}\) is given in Equation (6), which consists of two terms: forced convection \(h_{c,\;forced}\) due to wind blowing and natural convection \(h_{c,\;free}\). \[q_{c}=-(h_{c,\;free}+h_{c,\;forced})\times A\times\left(T_{p}-T_{a}\right) \tag{6}\]  
where \(h_{c,\;free}\) and \(h_{c,\;forced}\) are given in Equation (7) [29] and Equation (8) [30], respectively:  
\[h_{c,\;free}=1.31\left(T_{p}-T_{a}\right)^{1/3} \tag{7}\]  
\[h_{c,\;forced}=3.0w+2.8 \tag{8}\]  
where w is the wind speed. The power output of the PV panel \(P_{o}\) is determined based on the electrical efficiency of the panel, as shown in Equation (9)  
Figure 2:0  
The electrical efficiency \(\eta_{el}\) is, again, a function of the cell temperature [31]. Figure 2:1where \(\eta_{\rm ref}\) is the nominal efficiency of the panel at a reference temperature T\({}_{\rm ref}\) of 298 K, T\({}_{\rm c}\)  is the cell temperature (K), and \(\beta_{\rm c}\) is the cells temperature coefficient, which indicates the drop of efficiency with temperature. The temperature coefficient used in this panel is \(-0.4\%/^{\circ}\)C (as per the manufacturer's specifications). When the HPT is attached to the PV panel, the overall rate of temperature change with time for the PV module will be the same as Equation (1), with an additional term that includes the impact of HP. Hence, Equation (1) will be modified as follows:  
Figure 2:2  
The longwave radiation \(q_{hw}\) includes the heat loss from the top of the panel and the bottom of the panel, excluding the area occupied by the heat pipe. Figure 2:3  
The longwave heat \(q_{\rm hwp}\) is transferred from the HP to the ground. Initially, when the panel is at temperature below the phase change temperature, Equation (13) is used for calculating \(q_{\rm hwp}\), and when the panel temperature reaches phase change temperature, Equation (14) is used. Figure 2:4  
Figure 2:5  
where T\({}_{p}\) is panel temperature and T\({}_{pc}\) is the phase change temperature of WF. The term \(q_{\rm hp}\) represents the amount of latent heat absorbed by the HPT during the phase change process of the acetone inside the HP. It is calculated using Equations (15) and (16):  
Figure 2:6  
Figure 2:7  
where \(\Delta x_{t}\) is the thickness of Tedlar, \(k_{t}\) is the thermal conductivity of the Tedlar, \(\Delta x_{\rm hp}\) is the thickness of the HPT material, \(k_{\rm hp}\) is the thermal conductivity of the HPT material, and \(\Delta T\) is the difference between the temperature of the panel and the temperature of the phase change material. [PERSON]'s method was used to find the temperature of the temperature of the PV panels numerically. At any time, the temperature of the PV panel can be computed numerically, as follows:  
Figure 2:8  
where T\({}_{module}\)(n) is the temperature of the PV module at time n, T\({}_{module}\)(n + 1) is the temperature of the module at time n + 1, h is the time interval constant (60 s), and dT\({}_{cell}\) = is the change in temperature of a module with change of time dt. Since [PERSON]'s method is an initial value problem, the initial value of this is taken as equal to T\({}_{a}\) in the first step, with T\({}_{module}\)(n) = T\({}_{module}\)(n), the experimental value.