This work examines the enhancement of heat transfer caused by a ternary hybrid nanofluid in a lid-driven cavity that is filled with saturated porous media. The flow through a porous media is thought to be described by the Darcy-Brinkmann-Forchheimer (DBF) model. We assume thermal equilibrium between the fluid and porous media properties. The two different sets of ternary hybrid nanofluids such as Water − Cu − Ag − Cuo and Water−Graphene−CNT−Al₂O₃ with different shapes of nanoparticles such as Cylindrical−Platelets−Spherical are considered. The non-dimensionalized governing equations are solved using Galerkin finite element method (GFEM) and the results are produced graphically for different values of the physical parameters. Herewith the obtained results concluded that Average Nusselt number results are increased or decreased for the larger values of Ra or Da⁻¹ respectively. Not to be overlooked is the fact that the water − Cu − Ag − Cuo ternary hybrid nanofluid combination is improving heat transfer more than the other combination of nanofluids. Based on these findings, the authors advise the industries to think about using the water − Cu − Ag − Cuo combination to increase the rate of heat transfer.