Because the temperature gradient (corresponding to the temperature difference driving force) is small and the temperature is high in the lower left corner, the density of water in the lower left corner is thus low. For a high Rayleigh number (Ra = 1 × 105), the temperature gradient and the corresponding driving force become larger, then the lower-density water, including

that in the lower left corner, rises to the top CB-839 right corner. The denser water is cooled by the top wall and flows downward to the lower right corner, and the area where the denser water in the lower right corner becomes larger. Figure 6 Density KPT-330 supplier distribution of water phase at Ra = 1 × 10 3 (a) φ = 0.01 (b) φ = 0.03 (c) φ = 0.05. Figure 7 Density distribution of water phase at Ra = 1 × 10 5 (a) φ = 0.01 (b) φ = 0.03 (c) φ = 0.05. Figures 8 and 9 respectively present the nanoparticle distribution of nanofluid with volume fractions at Ra = 1 × 103 and Ra = 1 × 105. For a low Rayleigh number (Ra = 1 × 103), the driving force along the left wall is upward, and many nanoparticles are driven to the top right corner, which contributes to the high nanoparticle volume fraction in the top right corner. However, the temperature gradient

in the lower left corner is small and causes a correspondingly small temperature difference driving force. Thus, many nanoparticles are left in the lower left corner, which contributes to the high nanoparticle volume fraction in the lower left corner. There is a large temperature gradient in the lower right corner, and the large driving force displaces the nanoparticles off the lower right corner, which QNZ purchase contributes to the low nanoparticle volume fraction in the lower right corner. For a high Rayleigh number (Ra = 1 × 105), the convection heat transfer is enhanced and the velocity of the nanofluid becomes larger, and the temperature gradient and the corresponding driving force become bigger. Thus, many nanoparticles from the bottom are driven to the top by the driving force, which contributes to the low nanoparticle volume fraction enough at the bottom and a high nanoparticle

volume fraction at the top. In addition, we can see that the nanoparticle volume fraction distribution is opposite to that of the water-phase density distribution. From Table 4, we can see that the temperature difference driving force is the biggest one, and the changes of the water-phase density and the inhomogeneous nanoparticle distribution are mainly due to the driving force. Through the above analysis, it is found that the nanoparticles migrate to locations where the water density is small, and thus, the conclusion that the nanoparticle volume fraction distribution is opposite to that of the water-phase density distribution is obtained. Figure 8 Nanoparticle volume fraction distribution at Ra = 1 × 10 3 . (a) φ = 0.01, (b) φ = 0.03, and (c) φ = 0.05.