A new theoretical ternary hybrid nanofluid, by suspending three types of nanoparticles with different physical and chemical bonds in a porous square cavity, is proposed in this paper. The ternary hybrid nanofluid is formed by suspending three types of nanoparticles with different physical and chemical bonds into a base fluid. In this study, the nanoparticles Alumina (Al2O3), Copper (Cu) and Titania (TiO2) are suspended into water (H2O) thus forming the combination. The system of governing partial differential equations, are numerically solved using finite element formulation based on the Galerkin along with ADINA software (Adina v 9.20) method. The average Nusselt number ¯Nu is computed for three values of the Rayleigh number: 10, 100 and 1000, with the results of other authors from the open literature. An excellent agreement, and therefore, we are deeply confident that the numerical results obtained are correct and very accurate. We wish to point out that the numerical results of the present paper are completely new and original with very important results for practical applications of the ternary hybrid nanofluid in the modern industry. To our best of knowledge, the results of the present paper were never published by any researcher.