# Computational Modeling of Passive and Active Cooling Methods to Improve PV Panels Efficiency
## 2 Modeling and Computational Details
### Modeling of the PV Panel  
Figure 1 shows the geometric diagrams of the PV panels modeled for the investigation. The standard PV panel, PV panel with perforations (passive), PV panel with water (active), and hybrid PV panel (passive and active) are presented. The models were implemented with the 3D figure design method of the COMSOL Multiphysics software, for which a geometric figure is defined--in this case a parallelepiped--with the required dimensions.  
Thus, the geometry of the PV panel is a rectangle with dimensions of 82 cm \(\times\) 80.8 cm and a thickness of 0.6 cm. The thickness is divided into a 0.4 cm silicon layer and a 0.2 cm glass layer. Table 1 shows the technical specifications of the 100 W panel used. Table 2 shows the physical properties of the materials used in the simulation.  
In the case of the perforated panel, the same structure as for the standard panel was modeled but perforating several parts of its area with a matrix built based on cylinders, which were defined with a circumference and a separation distance between holes of 6.5 cm in width and 13 cm in length. The diameter implemented for the cylinders is 1 cm. For the active method, water was sprayed on the surface of the solar panel, to act as a heat sink. For the simulation of the hybrid panel, an additional geometry of equal dimension to the standard panel was considered, but using water as a material, and then superimposing the two geometries to study the dissipation effect that water could cause. After that, usinga simple Boolean operation, that matrix was subtracted from the geometry of the PV panel (parallelepiped).  
A physics-controlled meshing adjustment tool was used to define the geometry of the PV panels. Thus, the COMSOL software chooses the most pertinent mesh depending on the study to be carried out. Thus, we implement a mesh with a tetrahedral meshing algorithm, and a minimum element size of 0.06 m and a maximum of 0.48 m (Table 3). After choosing a fine mesh resolution, the results shown in Figure 2 were obtained. The panel is enclosed in a computational domain with dimensions of 4 m \(\times\) 4 m \(\times\) 2 m, which allows observing the behavior of the wind around the PV panel and graphing the flow only in the contours where it collides with the panel. Both the PV panel and the computational domain are meshed (Figure 2), and the specifications obtained are shown in Table 4.  
\begin{table}
\begin{tabular}{c c} \hline
**Specifications** & **Value** \\ \hline Type & Monocrystalline \\ Maximum power & 100 W \\ Maximum power voltage & 18.75 V \\ Maximum power current & 5.34 A \\ Open-circuit voltage & 22.53 V \\ Short-circuit current & 5.70 A \\ Temperature power coefficient & \(-\)0.45\(\%\)/\({}^{\circ}\)C \\ Dimensions & 820 \(\times\) 808 \(\times\) 35 mm \\ \hline \end{tabular}
\end{table}
Table 1: Specifications of the panel used in the simulations (SC Origin, SPM100-M).  
Figure 1: Schematic of the modeled PV panels. (**a**) Standard PV panel; (**b**) PV panel with perforations (passive); (**c**) PV panel with water (active); (**d**) hybrid PV panel (passive and active).  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Properties** & **Silicon** & **Water** & **Air** & **Units** \\ \hline Density & 2329 & 1000 & 1.28 & kg/m\({}^{3}\) \\ Thermal conductivity & 130 & 0.58 & 0.02 & W/(m \(\times\) K) \\ Surface emissivity & 0.9 & 0.95 & 1.012 & - \\ Constant pressure heat capacity & 700 & 4180 & - & J/(kg \(\times\) K) \\ Thermal expansion coefficient & 2.6 \(\times\) 10\({}^{-6}\) & - & - & 1/K \\ Relative permittivity & 11.7 & - & - & - \\ Dynamic viscosity & - & 0.001 & 0.0000174 & Pa \(\times\) s \\ \hline \end{tabular}
\end{table}
Table 2: Physical properties of materials used in the simulation.  
Finally, meteorological data used in the simulation were taken from the station located at the Ernesto Cortizzos airport in Colombia (Figure 3). For this, we used the ambient thermal properties interface, which allows modifying parameters such as temperature and simulation date.