This dissertation investigates heat and mass transfer in two- and three-dimensional electrically conducting non-Newtonian hybrid nanofluid flow over a stretching surface embedded in a porous medium. The Tiwari–Das and Buongiorno nanofluid models are employed to derive the governing equations. The governing nonlinear partial differential equations are transformed into a coupled system of ordinary differential equations using similarity transformations and solved numerically using MATLAB’s bvp4c and bvp5c solvers, higher-order Runge–Kutta methods, and the finite element method. Validation with existing results confirms the accuracy and reliability of the numerical solutions. A detailed parametric study examines the influence of physical parameters on velocity, temperature, and concentration distributions, as well as on skin-friction coefficients, local Nusselt numbers, and local Sherwood numbers. The results indicate that increasing the Darcy number, magnetic parameter, Forchheimer number, and nanoparticle volume fraction suppresses the velocity field, while the curvature parameter improves the velocity profile. In addition, increasing nonlinear thermal radiation, viscous dissipation, and nanoparticle volume fraction enhances the temperature distribution, whereas the thermal relaxation parameter diminishes the temperature profile. Ternary hybrid nanofluids exhibit superior thermal performance compared to mono and hybrid nanofluids due to the synergistic interactions among multiple nanoparticle types, which enhance energy transport mechanisms. This study not only advances the theoretical understanding of non-Newtonian nanofluid dynamics under complex thermal, electromagnetic, and porousmedium effects but also provides valuable guidance for the design and optimization of advanced thermal systems. The results underscore the potential of ternary hybrid nanofluids for applications in aerospace cooling, high-performance heat exchangers, electronic thermal management, biomedical technologies, and renewable energy systems.