In this work, numerical simulation of natural convection of nanofluids within a square enclosure were investigated by using the non-dimensional lattice Boltzmann method (NDLBM). The effects of key governing parameters Knudsen number ($10^{-6} \le Kn_{f,s} \le 10^4$), Rayleigh number ($10^3 \le Ra_{f,L} \le 10^6$), and nanoparticle volume fraction ($10^{-2} \le \phi_s \le 10^{-1}$) on the heat and mass transfer of nanofluids were discussed. The results show that in the low $Ra_{f,L}$ conductive domited regime, the nanoparticle size has little effect on heat transfer, whereas in the high $Ra_{f,L}$ convective dominated regime, larger nanoparticle sizes significantly enhance flow intensity and heat transfer efficiency. As fixed $Ra_{f,L}$ and $\phi_s$, the heat transfer patterns change from conduction to convection dominated regimes with increasing $Kn_{f,s}$. The influence of nanoparticle volume fraction was also investigated, and in convection dominated regime, the maximum heat transfer efficiency was achieved when $\phi_s = 8 \%$, balancing both thermal conduction and drag fore of nanofluids. Additionally, by analyzing the full maps of mean Nusselt number ($\overline {Nu}_{f,L}$) and the enhancement ratio related to the base fluid ($Re_{n,f}$), the maximum values of $\overline {Nu}_{f,L}$ and $Re_{n,f}$ occur when the nanoparticle size is $Kn_{f,s} = 10^{-1}$ for both conductive and convective dominated regimes. To capture the effects of all key governing parameters on $\overline {Nu}_{f,L}$, a new empirical correlation has been derived from the numerical results, providing deeper insights into how these parameters influence heat transfer performance.