In this research, effect of nanoparticles dimeter on free convection of aluminum oxide-water was investigated in a cavity by single phase and two phase models. The range of Rayleigh number is considered 105-107 in volume fractions of 0.01 to 0.03 for nanoparticles with various diameters (25, 33, 50 and 100 nm). Given that the two phase nature of nanofluids, necessity of modeling by this method is increasing. Single phase approach (in contrary of two phase) for nanofluids is based on that the behaviors of each two solid phase (nanoparticles) and liquid phase (base fluid) are completely similar. In this study, Eulerian-Eulerian approach and mixture model was used given that Brownian motion and thermophoresis effects. Brownian motion and thermophoresis creates under influences of volume fraction gradient and temperature gradient, respectively that cause to creating slip between nanoparticles and base fluid; thus, kind of non-uniformity creates on behavior between nanoparticles and base fluid. This non-uniformity leads to significant effects on results of two phase modeling that creates better agreement to single phase modeling with experimental results. Results indicate that heat transfer decreases with increasing diameter and volume fraction of nanoparticles. Also, effect of nanoparticle diameter on flow and heat transfer is tangible. پرونده مقاله