Abstract: In the present simulations, the first three moments of the particle size distribution of nanoparticles in a two dimensional Rayleigh-Bénard convection system are calculated with the combination of SIMPLE algorithm and the Tayler-series expansion method of moments (TEMOM) to probe into Brownian coagulation and mixing of nanoparticles. Driven by Brownian coagulation, diffusion and thermal convection, the number concentration of nanoparticles decreases, while the average volume increase generally as time goes on. The temporal evolution of nanoparticles can be divided into three stages, named the diffusion stage, the mixing stage and the fully mixing stage respectively. The correlation coefficients between moments of nanoparticles and the temperature, and relative standard deviation of moments experience distinct characteristics in three stages. The long-time behavior for moments of nanoparticles is obtained and is in good agreement with the asymptotic solution. Finally, the time to attain such an asymptotic solution is investigated and its dependence on Ra, Sc_M and Da is also determined numerically. The results show that the time decreases logarithmically when Ra and Sc_M increase, while it increases linearly when Da increases.