Boger Fluid Effects on MHD Tetra-Hybrid Nanofluid Flow over a Stretching Surface with Radiation and Slip Conditions

Tetra-hybrid nanofluids, formed by dispersing four distinct nanoparticles in a base fluid, offer enhanced thermal conductivity and momentum transport compared to mono-, hybrid-, and tri-hybrid nanofluids, making them attractive for advanced thermal management systems. This study numerically investigates the magnetohydrodynamic (MHD) flow and heat transfer of an Al₂O₃-Cu-SiO₂-TiO₂/water tetra-hybrid nanofluid over a permeable stretching sheet, incorporating Boger (viscoelastic) fluid characteristics, Darcy–Forchheimer porous drag, thermal radiation, velocity and thermal slip, heat source/sink, and viscous dissipation effects. The governing partial differential equations are transformed into a system of nonlinear ordinary differential equations using appropriate similarity variables and solved numerically via the bvp4c method in MATLAB. The present numerical scheme is validated against previously published results for limiting cases, showing close agreement. Results indicate that increasing the magnetic parameter and velocity slip parameter jointly reduce heat transfer efficiency, while the Boger fluid relaxation parameter enhances the velocity profile and the retardation parameter suppresses it. A deep neural network (DNN) surrogate model is additionally employed to predict the skin friction coefficient and Nusselt number across the parameter space, showing smooth, physically consistent trends and confirming the reliability of the numerical solution. These findings provide insight into controlling momentum and heat transport in tetra-hybrid nanofluid systems, with potential applications in cooling technologies, biomedical devices, and thermal management in industrial processes. It is noticed that, the TiO₂–SiO₂–Cu–Al₂O₃/water quadra-hybrid nanofluid provides a 23.63% enhancement in the Nusselt number relative to the base-fluid case, demonstrating its superior thermal transport capability. The Nusselt number enhances 5.6% improvement with relaxation parameter in observed.