# Natural Convection of Dusty Hybrid Nanofluids in an Enclosure Including Two Oriented Heated Fins
## 4 Results and Discussion
### Local and Average Nusselt Number  
Figure 14 shows the local Nusselt number along \(X\)-axis under the effects of (a) an inclination angle, (b) fins lengths with two values of an inclination angle, (c) nanoparticle volume fraction for hybrid nanofluid, and (d) mixture densities ratio with two values of dusty parameter, at \(Ra=10^{5}\) and \(\gamma=0.1\). It is observed that, the inclination angle affects the local Nusselt number along the \(X\)-axis without uniform tendency. Also, there are maximum values of the local Nusselt number that occurred at different locations along \(X\)-axis particulary, at the range \(0.5\leq X\leq 2.5\). As the fins lengths increase from 0.1 to 0.6, the local Nusselt number increases with three different peaks near to the location of the heated fins. The third results showed that the local Nusselt number is enhanced with a small rate as the nanoparticles volume fraction of hybrid nanofluid increase from 1% to 4%. Finally, in case of the low dusty parameter \((\alpha_{s}=0.001)\), effects of the mixture densities ratio on the local Nusselt number appear only when the mixture densities ratio \(D_{s}\) equals 1000 and then the local Nusselt number decreases clearly as \(D_{s}\) increases from 100 to 1000. While in case of the higher dusty parameter \((\alpha_{s}=0.01)\), the effects of \(D_{s}\) on the local Nusselt number appear soon from \(D_{s}=10\) to 100 and lowest values of local the Nusselt number at \(\alpha_{s}=0.01\) with \(D_{s}=1000\). The physical explanation of this behavior is due to the fact that the carrier fluid loses kinetic energy by loading the dust particles and this factor leads to a reduced rate of the heat transfer. Figure 15 depicts the average Nusselt number under the effects of (a) an inclination angle, (b) fins lengths with two values of an inclination angle, (c) solid volume fraction for hybrid nanofluid, and (d) mixture densities ratio with two values of dusty parameter. As the inclination angle increases from \(0^{\circ}\) to \(180^{\circ}\), the average Nusselt number is fluctuating between increasing or decreasing. The average Nusselt number is increasing between \(0^{\circ}\) to \(45^{\circ}\), decreasing between \(45^{\circ}\) to \(100^{\circ}\) and increasing between \(100^{\circ}\) to \(180^{\circ}\). As the heated fins lengths increase from \(L_{1}=L_{2}=0.1\) to 0.9 this enhances the average Nusselt number. The average Nusselt number is higher at an inclination angle \(45^{\circ}\) compared to \(0^{\circ}\) when fins lengths vary from 0.1 to 0.6 only. The third results exposed that the average Nusselt is enhanced as the nanoparticles volume fraction increases due to the increase in the thermal conductivity of the nanofluid. At the end, the average Nusselt number is decreasing as the mixture densities ratio increases especially at a higher dusty parameter \((\alpha_{s}=0.01)\) and a slight decrease on the average Nusselt number occurs at a lower dusty parameter \((\alpha_{s}=0.001)\)Figure 16 presents the time-dependent of isothermal contours for three values of heated-fin lengths \(L_{1}=L_{2}=0.3,\ 0.5\) and \(0.9\) at an inclination angle \(\gamma_{1}=45^{\lx@math@degree}\), \(\phi_{Al_{2}O_{3}}=\ \phi_{Cu}=0.02\), \(D_{\rm s}=10\), \(\alpha_{\rm s}=0.01\), \(Ra=10^{5}\) and \(\gamma=0.1\). In this figure, the transition of the isothermal distributions across the cavity from the initial to the final was introduced for three values of heated-fin lengths \(L_{1}=L_{2}=0.3,\ 0.5\) and \(0.9\). In this figure, the formation of hot layers around the heated fins are increase as the times increase. In addition, an increase of the fin lengths enhances the heated area inside the enclosure and consequently the thermal boundary layers are supported.