To investigate effects of particle sizes on natural convection of nanofluids, nanoparticle sizes together with mean free paths in solid and fluid phases are used to define two Knudsen numbers Kn and Kn, respectively. These two Knudsen numbers are further applied to build the new effective conductivity and viscosity models, which include non-linear effects of both Knudsen numbers and volume fractions. A sub-continuous non-dimensional lattice Boltzmann model is built to compute the velocity and temperature fields. Effective thermal conductivity and base fluid conductivity based Nusselt numbers are compared. Heat flux enhancement ratios relative to pure base fluid are calculated. Nusselt numbers and enhancement ratios in wide ranges of key governing parameters over 10≤Kn≤10, 10≤Ra≤10, and 10≤ϕ≤10 are plotted. The optimal governing parameters and corresponding nanoparticle sizes are obtained from the full maps. The changes of heat transfer patterns with varying Knudsen numbers are also illustrated by temperature and streamline fields. Results agree with various experimental and simulation results. Also, the present sub-continuous models and simulation results provide a correlation with all parameters for practical engineering applications of nanofluids with effects of particle sizes.