The Oberbeck-Boussinesq (OB) form of the Navier-Stokes equations can provide reliable solutions only for problems where the density differences are relatively small and all other material properties can be considered constant. For heat transfer problems at large temperature differences, the dependence of the material properties on temperature is the main source of non-Oberbeck-Boussinesq (NOB) effects. When a numerical solution is attempted for this category of problems, due to the density variations of the heated medium, a variable coefficient Poisson equation for the pressure emerges which is difficult to solve in a computationally efficient manner. In the present study, an efficient methodology to treat incompressible flows with variable properties outside the range of validity of the OB approximation is proposed. In the context of this methodology, the variable coefficient Poisson equation for the pressure is transformed into a constant coefficient Poisson equation using a pressure-correction scheme. In addition, all thermophysical properties are considered to be temperature dependent for all terms of the conservation equations. The proposed methodology is validated against results provided by previous studies on the natural convection flow of air, water and glycerol. Moreover, the potential of this methodology is demonstrated with the direct numerical simulation (DNS) of the NOB Rayleigh-Benard convection of water inside a three-dimensional (3D) cavity. The comparison between two-dimensional (2D) and 3D results reveals significant differences, highlighting the need for efficient methodologies capable to accurately simulate NOB problems in 3D. (C) 2018 Elsevier Ltd. All rights reserved.