A theoretical model based on the integral formalism approach for laminar external natural convection in the vicinity of a vertical wall is used to be extended to nanofluids. Two kinds of thermal boundary conditions including uniform wall temperature (UWT) and uniform heat flux (UHF) are used for this modeling. Two different nanofluids are tested, namely, Cu/water and CuO/water nanofluids for which both viscosity and thermal conductivity were determined using Brownian motion-based models. A close attention is focused on the influence due to increasing the volume fraction of nanoparticles on both the heat transfer and dynamic parameters. Results are presented only for particle volume fractions up to 4% to ensure a Newtonian behavior of the mixture. It has been found that natural convection heat transfer increases with the volume fraction for a fixed Grashof number, whatever the nanofluid is. Nevertheless, the enhancement of heat transfer is more pronounced in the case of Cu/water than for the CuO/water nanofluid. Moreover, this trend is also confirmed regarding the dynamical parameters such as the maximum velocity value within the dynamical boundary layer and the corresponding boundary layer thickness.