In this paper, the authors investigate the laminar mixed convection flow of Cu-water nanofluid near density maximum of water in a lid-driven enclosure. The governing equations based on the Boussinesq and non-Boussinesq homogenous models are solved using a pressure-based finite volume method. Four different lid-driven cases are simulated when volume fractions of nanoparticles range from 0.0, 0.03 and 0.05 and the Richardson (Ri) number varies from 0.01, 0.1, 1, 10 and 100 under both the Boussinesq and non-Boussinesq approximations. Streamlines, isotherms, mid-plane velocities, mid-plane temperature and the average Nusselt (Nu) number in various boundary conditions have been analyzed. Results show that the flow pattern and thermal behavior of the nanofluid strongly depend on the density inversion of water and the presence of nanoparticles. Further, the findings indicate that the density inversion phenomenon leads to a lower average Nu number under the non-Boussinesq approximation compared to the Boussinesq approximation, suggesting that studies with the Boussinesq approximation may overestimate heat transfer performance. In addition, the average Nu number increases as the volume fractions of nanoparticles increase. Finally, the maximum value of the average Nu number can be achieved under the Boussinesq approximation when the shear-driven force is aligned with the buoyancy force. (C) 2016 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.