In this work, numerical simulation of natural convection of nanofluids within a square enclosure are conducted by using the non-dimensional lattice Boltzmann method (NDLBM). The effects of key governing parameters Knudsen number (10^-6 \leqslant Kn_\rmf,\rms \leqslant 10^4), Rayleigh number (10^3 \leqslant Ra_\rmf,\rmL \leqslant 10^6), and nanoparticle volume fraction (10^-2 \leqslant \phi_\rms \leqslant 10^-1) on the heat and mass transfer of nanofluids are discussed. The results show that in the low Ra_\rmf,\rmL conduction dominated regime, the nanoparticle size has little effect on heat transfer, whereas in the high Ra_\rmf,\rmL convection dominated regime, larger nanoparticle size significantly enhances flow intensity and heat transfer efficiency. For fixed Ra_\rmf,\rmL and \phi_\rms, the heat transfer patterns change from conduction to convection dominated regime with Kn_\rmf,\rms increasing. The influence of nanoparticle volume fraction is also investigated, and in the convection-dominated regime, the maximum heat transfer efficiency is achieved when \phi_\rms = 8 \text%, balancing thermal conduction and drag fore of nanofluid. Additionally, by analyzing the full maps of mean Nusselt number (\overline Nu_\rmf,\rmL) and the enhancement ratio related to the base fluid (Re_\rmn,\rmf), the maximum value of \overline Nu_\rmf,\rmL and Re_\rmn,\rmf occur when the nanoparticle size is Kn_\rmf,\rms = 10^-1 for both conductive and convection dominated regime. To ascertain the effects of all key governing parameters on \overline Nu_\rmf,\rmL, a new empirical correlation is derived from the numerical results, providing a more in-depth insight into how these parameters influence on heat transfer performance.