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Purpose This paper aims to traitted the combined effects of ferromagnetic particles and magnetic field on mixed convection in the Falkner Skan equation using analytical solution by the Duan–Rach method. Design/methodology/approach Visualization and grouping of effects of various physical parameters such as electrical conductivity of ferro-particles (electrical conductivity calculated using Maxwell model), ferro fluid volume fraction for Magnetite-Fe3O4-water and magnetic field represented by the Hartmann number in a set of third- and second-order nonlinear coupled ordinary differential equations. This set of equations is analytically processed using the Duan–Rach Approach (DRA). Findings Obtained DRA results are validated using a numerical solution (Runge–Kutta–Fehlberg-based shooting method). The main objective of this research is to analyze the influence of physical parameters, in particular electrical conductivity, Ferrofluid volume fraction in the case of Magnetite-Fe3O4-water, in addition to the types of solid nanoparticles and Hartmann number on dynamic and thermal distributions (velocity/temperature). Results of the comparison between the numerical solution (Runge–Kutta–Fehlberg-based shooting method) and the analytical solution (DRA) show that the DRA data are in good agreement with numerical data and available literature. Originality/value The study uses Runge–Kutta–Fehlberg-based shooting method) and the analytical solution (DRA) to investigate the effect of mixed convection, in the presence of Ferro particles (Magnetite-Fe3O4) in a basic fluid (water for example) and subjected to an external magnetic field on the Falkner–Skan system.