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In the field of heat transfer enhancement, there is a very new growing strategy to use hybrid nanofluid consisting of two or more nanoparticles dispersed in a base fluid. The current perusal introduces a numerical analysis to investigate the importance of hybrid nanofluid in the free convection inside a partially heated square cavity, and subjected to inclined magnetic field with heat generation/absorption. The horizontal walls are kept adiabatic. Numerical solution of mathematical model which describes the problem is achieved by finite difference method. The Conventional models of Brinkman and Maxwell were applied to assess the viscosity and thermal conductivity of the Cu-Al2O3-Water hybrid nanofluid. The considered problem was studied by varying some parameters such as the size and position of the heat source/sink, heat generation parameter, Hartmann number, and three combinations of nanoparticles volume fractions. The results show that the Nusselt number of hybrid nanofluid is higher than the Alumina-water nanofluid and less than the Copper-water nanofluid.