Mathematical modeling for nonlinear slippery-hybrid nanofluid flow with radiation impacts and thermophoretic diffusion via a porous medium.

This study addresses the growing need for advanced thermal regulation by investigating the nonlinear flow behavior of a hybrid nanofluid within a porous medium under realistic physical conditions. The primary objective is to evaluate how slip effects, variable viscosity, and thermophoresis influence heat and mass transfer performance when multiple physical mechanisms act simultaneously. A comprehensive mathematical model is developed to describe the momentum, thermal, and concentration transport of a water-based hybrid nanofluid containing two distinct nanoparticle species, subjected to magnetic field effects, thermal radiation, and internal heat generation. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and solved numerically via a shooting technique under appropriate boundary conditions. The novelty of this work lies in the combined consideration of slip velocity, thermophoresis-driven nanoparticle migration, and variable viscosity within a magnetohydrodynamic porous framework. The present study is relevant to practical applications, including microelectronics cooling, advanced heat exchangers, and maritime thermal management. The results indicate that increasing thermophoretic effects and internal heat generation significantly influence transport behavior, as enhanced particle migration reduces concentration gradients while internal heating shifts the heat transfer mechanism toward convection-dominated regimes. Further, the findings reveal that hybrid nanofluids exhibit enhanced thermal control capabilities, with thermophoresis and slip mechanisms playing a key role in improving heat and mass transfer rates, highlighting their potential for high-performance cooling applications.