# Numerical and Parametric Analysis for Enhancing Performances of Water Photovoltaic/Thermal System
## 2 Methodology  
### Numerical Model  
A numerical model was developed to evaluate the thermal and electrical behavior of a PV/T system, operating in dynamic conditions. The parametric analysis was performed by varying some PV/T key flow parameters, such as the water velocity from 0.01 m/s to 0.035 m/s, water film thickness from 3 mm to 10 mm, and water inlet temperature from 20 \({}^{\circ}\)C to 30 \({}^{\circ}\)C.  
The PV/T system investigated in this work consists mainly of four solid components and cooling liquid (water). According to the PV/T system design shown in cross section in Figure 1a, six sub-numerical models were established as follows:  
* Sub-numerical model for the glass cover;
* Sub-numerical model for the PV module;
* Sub-numerical model for the Tedlar layer;
* Sub-numerical model for the upper aluminum layer;
* Sub-numerical model for the water film in channel;
* Sub-numerical model for the lower aluminum layer.  
For the six PV/T system sub-models, a heat balance equation was done separately, based on the internal energy variation equation [25] and the heat transfer between layers as shown in Figure 1b. Moreover, the Runge-Kutta numerical method (RK4) was used for resolving the (ODE) governing equations in MATLAB Software. The main advantage of the developed numerical model is allowing the determination of the mean temperature of each PV/T layer (glass cover, PV cells, Tedlar, absorbers, and fluid), based on the different heat exchanges between these ones.  
The main PV technical characteristics (applied to Standard Test Conditions of solar irradiance of 1000 W/m\({}^{2}\) and ambient temperature of 25 \({}^{\circ}\)C) and the selected PV/T system properties are reported in Tables 1 and 2. Moreover, the assumptions considered in developing the PV/T model due to its different components were [22,23,26]:  
* A (1D) numerical model is built since the layers thickness are very thin relative to the other dimensions. As a result, heat losses are considered to be neglected at the PV/T sides and average uniform temperature is determined for each layer;
* The amount of absorbed solar irradiation that is not converted into electricity is transferred from the PV cells back to the rest of system;
* The material properties remain constant in the PV/T system, for a temperature limited range;
* The heat flux between PV cells and EVA is supposed to be negligible;
* A perfect contact between PV/T components is supposed;
* The effects of dust and partial shading were neglected.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline PV Type & \begin{tabular}{c} **Pmax** \\ **(W)** \\ \end{tabular} & \begin{tabular}{c} **Vmp** \\ **(V)** \\ \end{tabular} & \begin{tabular}{c} **Imp** \\ **(A)** \\ \end{tabular} & \begin{tabular}{c} **Voc** \\ **(V)** \\ \end{tabular} & \begin{tabular}{c} **Isc** \\ **(A)** \\ \end{tabular} & \
\begin{tabular}{c} **\(\eta_{\text{e}}\)** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **NOCT** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} \\ \hline AE320 HM-60 & 320 & 33.40 & 9.59 & 40.90 & 10.15 & 19.30 & \(45\pm 2\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: PV module technical characteristics applied to STC.  
Figure 1: Components (**a**) and heat exchange mechanism in the PV/T system (**b**).