## 3 Results and Discussion  
Effects of nanoparticle addition to the water in the channel of a PV-thermal module on the thermal and PV-efficiency was numerically investigated. SiO\({}_{2}\) nanoparticles different shapes and solid particle volume fractions were used. Figure 3 shows the velocity and temperature distribution in the PV-module. In the channel, a laminar velocity profile is developed and its maximum value is seen in the mid of the channel which has a value of 0.025 m/s for the fixed value of (q = 1000 W / m\({}^{2}\), h = 5 W / m\({}^{2}\) K, \(\phi=0.02\) with cylindrical shape particles). For this flow velocity, Reynolds number remains less than 2100 in the channel. Thermal gradients are seen in the layers of the PV module, which is due to the different thicknesses and thermal conductivities of these layers. Figure 4 shows the effects of nanoparticle volume fraction (\(\phi\)) and particle type on the variation of thermal and total efficiency of the PV-thermal module. Both efficiencies enhance with higher \(\phi\) values. Among different particle shapes, cylindrical ones perform best. Discrepancy between cylindrical shape and other shapes increases for higher particle volume fractions. Total efficiency increases by about 7.39% at the highest volume fraction (\(\phi=0.05\)) with cylindrical shape particles. As compared to spherical shape particle, cylindrical ones gives 3.95% more enhancement in the total efficiency for the highest particle volume fraction. As the inlet temperature of water-SiO\({}_{2}\) nanofluid increases, thermal and total efficiency deteriorate as shown in Figure 5. The rate of deterioration is higher for the thermal efficiency and up to 40% in the reduction of the efficiency is seen when nanofluid temperature is increased from 10 \({}^{\circ}\)C to 50 \({}^{\circ}\)C.  
Figure 6 demonstrates the effects of solar irradiation and solid nanoparticles volume faction on the variation of efficiencies (h = 5 W / m\({}^{2}\) K, T\({}_{in}\) = 30 \({}^{\circ}\)C with cylindrical shape particles). Thermal efficiency increases with higher values of solar irradiation while the PV-efficiency decreases and higher \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Grid Name** & **Number of Elements** & **Thermal Efficiency (\%)** & **PV Efficiency (\%)** \\ \hline G1 & 10,816 & 50.32 & 12.52 \\ G2 & 19,457 & 48.25 & 12.50 \\ G3 & 66,056 & 47.20 & 12.49 \\ G4 & 144,934 & 47.13 & 12.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Grid independence test (q = 1000 W/m\({}^{2}\), h = 5 W/m\({}^{2}\)K, \(\phi=0.05\), \(T_{i}n=30\)\({}^{\circ}\)C). Figure 2: Code validation study. efficiency values are achieved for higher \(\phi\) values. Higher surface temperature is obtained for higher values of solar irradiation and PV-efficiency decreases, which are defined in Equation (5). Thermal efficiency increases by about 9.17% and 9.82% for water and for nanofluid with highest volume fraction. There is a negligible effect of the particle addition on the PV-efficiency enhancements. Convective loss is characterized by the convective heat transfer coefficient dependent upon the wind speed \(v\). As the value of heat transfer coefficient enhances, thermal efficiency decreases as it is shown in Figures 7 and 8. However, PV-efficiency enhances with higher \(h\) values since the PV-layer surface temperature decreases, but the rate of enhancement is not significant.The discrepancy between thermal efficiency for heat transfer coefficient of h = 5  
Figure 4: Effects of the particle shape and solid volume fraction on the variation of efficiencies (q = 1000 W/m\({}^{2}\), h = 5 W/m\({}^{2}\)K, \(T_{i}n=30\)\({}^{\circ}\)C)  
Figure 5: _Cont._  
Figure 5: Effects of the inlet temperature on the variation of efficiencies (q = 1000 W/m\({}^{2}\), h = 5 W/m\({}^{2}\)K, \(\phi=0.02\), cylindrical shape). Figure 6: _Cont._  
Figure 6: Effects of the solar radiation on the variation of efficiencies for various solid particle volume fraction (h = 5 W/m\({}^{2}\)K, \(T_{i}n\) = 30 \({}^{\circ}\)C, cylindrical shape ).