A demonstrative numerical study on natural convection of water-based nanofluids in square enclosures with different boundary conditions imposed at the walls, and different orientations with respect to the gravity vector, is performed using both the single-phase and the two-phase approaches, with the main scope to evaluate in what measure the single-phase approach fails in describing the basic heat and fluid flow features, as well as in determining the thermal performance of nanofluids. The system of the mass, momentum and energy transfer governing equations is solved by way of a computational code based on the SIMPLE-C algorithm. Empirical correlations are used for the calculation of the effective thermal conductivity, the effective dynamic viscosity, and the thermophoretic diffusion coefficient. The following configurations are investigated: a tilted cavity differentially-heated at two opposite walls; a vertical cavity partially-heated at the bottom wall and cooled at both sides; and a vertical cavity differentially-heated at the vertical and horizontal walls. It is found that the non-uniform distribution of the suspended solid phase throughout the enclosure gives rise to a solutal buoyancy force, whose competition with the thermal buoyancy force results in a periodic flow detectable only if the two-phase approach is applied. Moreover, the impact of the dispersion of the nanoparticles into the base liquid, which turns out to be notably higher at higher average temperatures, is found to be systematically underestimated by the single-phase approach.