The free convective hybrid nanofluid (Fe3O4+MWCNT/H2O) magnetized non-Darcy flow over a porous cylinder is examined by considering the effects constant heat source and uniform ambient magnetic field. The developed coupled PDEs (partial differential equations) are numerically solved using the innovative computational technique of control volume finite element method (CVFEM). The impact of increasing strength of medium porousness and Lorentz forces on the hybrid nanofluid flow are presented through contour plots. The variation of the average Nusselt number (Nuave) with the growing medium porosity, buoyancy forces, radiation parameter, and the magnetic field strength is presented through 3-D plots. It is concluded that the enhancing medium porosity, buoyancy forces and radiation parameter augmented the free convective thermal energy flow. The rising magnetic field rises the temperature of the inner wall more drastically at a smaller Darcy number. An analytical expression for Nusselt number (Nuave) is obtained which shows its functional dependence on the pertinent physical parameters. The augmenting Lorentz forces due to the higher estimations of Hartmann retard the hybrid nanoliquid flow and hence enhance the conduction.