# Enhancement of PV Panel Power Production by Passive Cooling Using Heat Sinks with Perforated Fins
## 3 Materials and Methods
### Numerical Simulation  
The numerical simulation was performed using the ANSYS-Fluent 2021-R1 software. The geometry and discretization of the computing domain was performed within the platform using the Fluent-Meshing and SpaceClaim programs. For simulation the control volume method, SIMPLE pressure-velocity coupling and second-order accuracy for equation solving were used, taking into account that the flow was not aligned with the mesh [45]. This method used a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field. A fully implicit numerical scheme was employed, in which upwind differences were used for the convective terms and central differences for the diffusion terms [11]. The calculation was iterative, with a convergence criteria of \(10^{-6}\) for the energy equation and \(10^{-3}\) for the pressure, velocities, \(k\), \(\varepsilon\) and continuity equations. The simulation of solar radiation was realized using the Solar Ray Tracing model of the Fluent program. The absorption of solar radiation by the front of the PV panel was imposed as a global coefficient \(\alpha\) = 0.7, taking into account all the layers of the PV panel [11; 46]. Figure 1: Overview of the components of the heat sink attached to the PV panel for cooling (case with perforated fins). The heat transfer balance was set in order to include the convection and radiation with the surroundings [46]. The numerical simulation was realized using the \(k\)-\(\varepsilon\) realizable model [45]. For all studied configurations, the distance between fins was set to 150 mm. The fins were perpendicular to the heat sink plate--Figure 1. For the case of perforated fins, they had circular holes of 30 mm or 60 mm diameter, which were placed at a distance of 100 mm to one to another [34]. Their role was to improve the air circulation near the heat sink and to extract more heat from the PV panel. The accuracy and the solution time were both highly depend on the characteristic of the mesh. Computational fluid dynamics (CFDs) solvers depended on the highly orthogonal mesh that could be difficult to achieve on different types of geometries. For the present study, a polyhedral mesh was used for the surfaces and a poly-hex core for one of the volumes. The choice of these types of cells was made due to an increase in speed of simulation from 20 to 50% while maintaining the high level of accuracy. In addition, this approach in the simulation opened up the possibility of improving the solver speed and accuracy compared with the tetrahedral cells. The mesh was realized with different refinements for the heat sink and air volume. The mesh quality achieved for the numerical analysis was as follows:  
- Aspect ratio was in the range 5-60;  
- Skewness was in the range 0.4-0.7;  
- Orthogonal quality was in the range 0.1-0.3. A mesh independence study was carried out, taking into account the large number of elements that resulted due to modeling the air volume that flowed over the PV panel and heat sinks. Figure 2 presents the mesh independence study, which was achieved for approximately 3 million cells in the base case and over 5.5 million cells for cases with heat sinks and perforated fins. The numerical analysis was conducted on a workstation that had 48 cores, 256 GB of RAM and a graphical computing video card Nvidia Quadro P6000. Typical approaches from the literature considered the position of the PV panel as either horizontal [31] or vertical [11; 34], with a channel simulating the wind behind the PV panel. There were only a few studies on cooling tilted PV panels [16; 40]. During this study the modelling was realized by taking into account the air circulation in the vicinity of a tilted PV panel cooled with heat sinks. In this way, by using an optimized resource consumer mesh, the airflow and the heat transfer were more realistic and easier to visualize and understand.