The effects of two kinds of base fluid (H2O and Ga) and three different nanoparticle radiuses (20 nm, 40 nm and 80 nm) on the natural convection heat transfer of a rectangular enclosure filled with Al2O3 H2O and Al2O3-Ga nanofluid at different Rayleigh numbers (Ra =10(3) and Ra =10(5)) are discussed based on a two-phase lattice Boltzmann method in this paper. It is found that Al2O3-Ga nanofluid shows a better heat transfer enhancement than Al2O3-H2O nanofluid. Al2O3-Ga and Al2O3-H2O nanofluid with the same smallest radius (r = 20 nm) can enhance the heat transfer by 86.0% and 24.5% compared with water respectively. It is also found that Al2O3-Ga nanofluid at low Rayleigh number (Ra =103) shows the biggest heat transfer enhancement (shows a 4.4% increase for every nanoparticle radius decreasing 20 nm) compared with Al2O3-H2O nanofluid. The enhancement ratio at low Rayleigh number is about 3-10.8% and 23.5-28.8% more than that at high Rayleigh number for Al2O3-water and Al2O3-Ga nanofluid respectively. In addition, the nanoparticle fraction distributions in the enclosure are also investigated. (C) 2016 Elsevier Ltd. All rights reserved.