## 5 Numerical Simulation
The nanofluid streamlines presents two elliptical core vortices globally symmetric for an inclination angle \(\gamma=0^{\circ}\). As the Rayleigh number increased from Ra = \(10^{3}\) to Ra = \(10^{5}\), the nanofluid buoyancy increased. As the enclosure inclination angle increases, the maximum buoyancy was pushed towards the right area of the enclosure (nanofluid streamlines gradually loses its symmetry), while the nanofluid flow in the left area of the enclosure became more laminar. Figure 8: Nanofluid temperature and \(Nu/\kappa\) evolutions at the levels: \(Y=0.5\) (**right**) and \(Y=1\) (**left**) respectively. Figure 10 shows the combined effect of Rayleigh number and enclosure inclination angle on nanofluid velocity magnitude distribution, when there are no fins below the absorber plate (\(\delta=0\)). As the Rayleigh number increased from \(\text{Ra}=10^{3}\) to \(\text{Ra}=10^{5}\), the nanofluid velocity magnitude distribution became more homogenous, and its maximum value drastically increased from 0.5 to 19, 0.6 to 30, 0.7 to 36, and 0.8 to 45 for an inclination angle of \(\gamma=0^{\circ}\), \(\gamma=15^{\circ}\), \(\gamma=30^{\circ}\) and \(\gamma=45^{\circ}\), respectively. It is to note that the maximum nanofluid velocity magnitude was pushed towards the right area of the enclosure (nanofluid magnitude distribution gradually loses its symmetry) as the inclination angle increased. Figure 11 shows the combined effect of Rayleigh number and enclosure inclination angle on nanofluid isotherms, when there are no fins below the absorber plate (\(\delta=0\)). As the Rayleigh number increased from \(\text{Ra}=10^{3}\) to \(\text{Ra}=10^{5}\), the nanofluid temperature distribution became globally more homogenous, especially in the central area of the enclosure, away from walls where the cold and hot temperatures were imposed. It is to note that the most homogenous nanofluid temperature was pushed towards the right area of the enclosure as the inclination angle increased. Figure 9: Effects of Rayleigh number and enclosure inclination angle on nanofluid streamlines. Figure 11: Effects of Rayleigh number and enclosure inclination angle on nanofluid isotherms. Figure 10: Effects of Rayleigh number and enclosure inclination angle on nanofluid velocity magnitude. Figure 12 shows the combined effect of fins height and enclosure inclination angle on nanofluid streamlines for a Rayleigh number \(\text{Ra}=10^{5}\). The nanofluid streamlines present two elliptical core vortices globally symmetric for an inclination angle \(\gamma=0^{\circ}\), whatever the fins' height. As the inclination angle increased, buoyancy was pushed towards the right area of the enclosure (nanofluid streamlines gradually lose their symmetry), while the nanofluid flow in the left area of the enclosure became more laminar. This phenomenon was more pronounced for relatively low fin height. As the fin height increased from \(\delta=\frac{h}{8}\) to \(\delta=\frac{h}{2}\), the nanofluid buoyancy increased. Figure 13 shows the combined effect of fin height and enclosure inclination angle on nanofluid isotherms for a Rayleigh number \(\text{Ra}=10^{5}\). As the fin height increased from \(\delta=\frac{h}{8}\) to \(\delta=\frac{h}{2}\), the nanofluid temperature distribution became globally more homogenous, especially in the central area of the enclosure, away from walls where the cold and hot temperatures were imposed. It is to note that the most homogenous nanofluid temperature was pushed towards the right area of the enclosure as the inclination angle increased. Figure 12: Effects of fin height and enclosure inclination angle on nanofluid streamlines.