Rayleigh–Benard (R-B) convection in water-based alumina (Al2O3) nanofluid is analyzed based on a single-component non-homogeneous volume fraction model (SCNHM) using the lattice Boltzmann method (LBM). The present model accounts for the slip mechanisms such as Brownian and thermophoresis between the nanoparticle and the base fluid. The average Nusselt number at the bottom wall for pure water is compared to the previous numerical data for natural convection in a cavity and a good agreement is obtained. The parameters considered in this study include the Rayleigh number of the nanofluid, the volume fraction of alumina nanoparticle and the aspect ratio of the cavity. For the Al2O3/water nanofluid, it is found that heat transfer rate decreases with an increase of the volume fraction of the nanoparticle. The results are demonstrated and explained with average Nusselt number, isotherms, streamlines, heat lines, and nanoparticle distribution. The effect of nanoparticles on the onset of instability in R-B convection is also analyzed. © 2017 Taylor & Francis.