Summary: In this study, a numerical investigation for magneto-free convective flow in square cavity with internal heat generation is performed. The cavity is filled with nanofluids \(Cu\)-water embedded in an isotropic porous medium and is under an oblique uniform magnetic field. All sides of the cavity have heated portions near the corners (heated corners) while the remaining parts of the upper and lower walls are thermally insulated and the remaining portions in the left and right sides are cold. The governing equations are converted to dimensionless form and then solved numerically using the finite difference method. The problem is controlled by various parameters such as the heat sink length, the Hartmann number, the Rayleigh number, and the heat generation. The outcomes are given in forms of the isotherms, streamlines, local and average Nusselt numbers. The obtained results show perfect agreement compared with the previous published studies. It is found that the global entropy generation decreases when increases the nanoparticle volume fraction in the Rayleigh number. The average Nusselt number decreases as the volume fraction increases in the Hartmann number. Increasing the Darcy numbers enhances the nanoparticle volume fraction, although its rate of increase is steeper for the thermal performance rate. The total entropy generation is increasing via enhancing the volume fraction of the nanoparticles. As the strength of the magnetic field increases average Nusselt number decreases.