This study computationally investigated the thermodynamic optimization of magnetohydrodynamic (MHD) Casson and Ellis tetra-hybrid ( \({\text{EG - Ag/TiO}}_{{2}} {\text{/Cu/Al}}_{{2}} {\text{O}}_{{3}}\) ) nanofluid flow over a rotating three-dimensional exponentially stretching sheet within an enhanced Darcy–Forchheimer porous medium. Ethylene glycol was used as the base fluid, and a comparative analysis was performed for mono, hybrid tri-hybrid and tetra-hybrid nanofluid systems. The governing nonlinear equations we resolved numerically using the shooting technique and the bvp4c MATLAB solver. The system behavior was analyzed in terms of the velocity and temperature fields, entropy generation, Bejan number, skin friction coefficient, Nusselt number, and streamline patterns. The results indicate that the volume fraction parameters significantly influenced the skin friction in both Casson and Ellis tetra-hybrid nanofluids under three-dimensional flow conditions. Furthermore, the entropy generation increases with thermal radiation owing to the enhanced temperature gradients, leading to higher irreversibility. It was also observed that the Ellis fluid exhibited slightly higher entropy generation than the Casson fluid, which was attributed to its stronger thermal transport characteristics. The Casson fluid showed a minimum response value of approximately − 2.8, whereas the Ellis fluid attains values close to − 2.2, highlighting the distinct fluid behavior under identical physical conditions. These findings demonstrate the importance of rotating three-dimensional flows in optimizing heat transfer systems, with applications in solar collectors, thermal energy storage devices, and photovoltaic cooling technologies.
