A two-phase model based on the double-diffusive approach is used to perform a numerical study on natural convection of water-based nanofluids in square cavities differentially heated at two opposite walls, and inclined with respect to gravity so that the heated wall faces upwards. It is assumed that Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase. The system of the governing equations of continuity, momentum and energy for the nanofluid, and continuity for the nanoparticles, is solved through an inhouse developed computational code which incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity, and the thermophoretic diffusion coefficient, all based on literature experimental data. The pressure-velocity coupling is handled by way of the SIMPLE-C algorithm. Numerical simulations are executed for three different nanofluids, using the diameter and the average volume fraction of the suspended nanoparticles, as well as the tilting angle of the enclosure, the enclosure width, the average temperature of the nanofluid, and the temperature difference imposed across the cavity, as independent variables, whose effects are thoroughly analyzed and discussed. The existence of an optimal tilting angle of the enclosure and an optimal particle loading for maximum heat transfer is detected. In addition, a thermophoresis-induced periodic flow at tilting angles larger than 50 is found to occur for low to moderate values of both the nanofluid average temperature and the volume fraction of the suspended solid phase. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.