In this research, the effect of different models of thermal conductivity and dynamic viscosity has been investigated by considering the effect of Brownian motion of nanoparticles on the flow field and heat transfer of nanofluids. This study was performed numerically in a square cavity with water/aluminum-oxide nanofluid in three modes of natural, mixed and forced convection by changing the independent variable such as nanoparticle volume fraction, Rayleigh number, Richardson number, and Reynolds number. The governing equations with certain boundary conditions are solved using the finite volume method. Also, according to the obtained numerical results, Nusselt number has been investigated for different conditions with and without consid-ering Brownian motion. The results showed that for all the studied models, in all three modes of natural, mixed and forced convection, the average Nusselt number when the effect of Brownian motion is considered, is more than the case that the effect of this motion is not considered. In all cases, the Koo & Kleinstreuer and Li & Kleinstreuer models show approximately the same values for the maximum mean Nusselt number. The similar results are obtained employing the Wajjha & Das and Xiao et al. models. For mixed convection, the highest and lowest increases of Nusselt number, considering Brownian motion are 17.68% and 14.84%, respectively. While referred val-ues for forced convection are 30.46% and 17.94 %, respectively.