Influence of Arrhenius activation energy and thermal radiation on unsteady MHD hybrid nanofluid flow with inclined stretching sheet in the presence of Brownian motion, and thermophoresis

This study investigates the unsteady magneto-hydrodynamic (MHD) mixed convection heat and mass transfer of a hybrid nanofluid flowing through a Darcy porous medium over a stretching inclined sheet, considering the influences of thermal radiation, Arrhenius activation energy, Brownian motion, and thermophoresis effects. A hybrid nanofluid is formulated by dispersing titanium oxide (TiO2) and alumina oxude (Al2O3) nanoparticles in water as the base fluid. The governing nonlinear partial differential equations (PDEs) describing the fluid flow and heat transfer are transformed into a set of ordinary differential equations (ODEs) using similarity transformations and nondimensional variables. These equations are then solved numerically using the fourth-order Runge–Kutta method combined with the shooting technique. The results comprise visual depictions and detailed explanations demonstrating the influence of key parameters on velocity, temperature, and concentration, which are graphically represented. Additionally, skin friction, Nusselt number, and Sherwood number are evaluated and tabulated to highlight their dependence on governing parameters. Key findings indicate that an increase in the magnetic field parameter (M) significantly reduces velocity due to the Lorentz force, while higher thermal radiation (Rd) enhances temperature profiles. Brownian motion (Nb) and thermophoresis (Nt) parameters exhibit significant effects on the thermal and solutal boundary layers, with Brownian motion enhancing temperature distribution and thermophoresis increasing nanoparticle concentration gradients. A rise in the activation energy parameter (E) leads to a notable reduction in concentration profiles, thereby influencing the chemical reaction rate. Additionally, an increase in the unsteady parameter results in a decrease in both velocity and thermal boundary layer thickness. These findings provide insights into optimizing heat and mass transfer in various industrial applications, including cooling systems, chemical processing, and energy storage technologies. The inclusion of Brownian motion and thermophoresis effects further enhances the understanding of hybrid nanofluid transport mechanisms, making this study valuable for applications in nanotechnology, biomedical fluid dynamics, and advanced thermal energy systems. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.