Three-Dimensional MHD Flow of Hybrid Nanofluid over a Moving Slender Parabolic Needle with Viscous Dissipation and Hall Current Effects

The efficient management of high flux heat and mass transport continues to be a challenging engineering problem that is essential to the development of micro fluidic devices, electronic thermal management systems, and aerospace surface coatings. While conventional mono nanofluids offer a small amount of thermal enhancements, they suffer significant drop in performance in complex multi physical conditions, such as coupled electromagnetic interactions and geometrically complex flow configurations. Particularly, boundary layer behavior over slender curved surfaces, like continuously moving needles, can be quite complicated on highly curved surfaces, due to the strong surface shear stresses and boundary layer curvature effects. The steady, three-dimensional laminar flow of a non-Newtonian polymer-based hybrid nanofluid over a moving parabolic slender needle under the presence of Hall currents, porous medium drags and thermal source variations has not been extensively studied. This unaddressed gap fundamentally limits the rational design of advanced thermal management architectures in which multi directional cross flows interact with complex structural geometries. To fill this gap, the present study numerically investigates the steady, three-dimensional, incompressible boundary layer flow of a Carboxymethyl Cellulose (CMC) - water-based hybrid nanofluid containing gold (Au) and molybdenum disulfide (MoS 2 ) nanoparticles past a slender parabolic needle moving horizontally. The treatment of the carrier fluid is performed in a generic Newtonian framework with dilute and weakly non-Newtonian suspension approximations for consistency in terms of both rheology and mathematics. The multi-physical transport model is based on a uniform transverse magnetic field and the generalized Ohm’s law, incorporating Hall current effects in a Darcy-Forchheimer porous medium, and also considers viscous dissipation, joule heating and volumetric heat generation and absorption. The dual-mechanism Buongiorno formulation, which combines Brownian motion and thermophoretic migration, yields a passive control of the hybrid nanoscale suspensions. The governing nonlinear partial differential equations (PDEs) are systematically reduced to a coupled system of ordinary differential equations (ODEs) by using a customized similarity transformation and solved by adaptive Runge-Kutta-Fehlberg 45 (RKF-45) shooting method along with Newton-Raphson iteration. The numerical scheme is strictly convergent and the shooting residuals are always kept less than 10[Formula: see text]. The imposed transverse magnetic field M gives rise to a resistive Lorentz force that decreases the primary axial velocity[Formula: see text] and increases the gradient of the wall velocityf[Formula: see text]. It is found that activation of the Hall current parameter [Formula: see text] redistributes electromagnetic resistance, which increases the secondary velocity component and a characteristic hydrodynamic swirl profile. Both the Brownian motion parameter (Nb) and thermophoresis parameter (Nt) play an important role in enhancement of the thermal field. Nb intensifies the collisions between particles at micro scale, while in the case of Nt, the nanoparticles begin to move toward the bulk flow due to their thermal conductivity, effectively trapping thermal energy within the hydrodynamic boundary layer. The thermal overshoot [Formula: see text] is observed in the near-wall region when the volumetric heat generation[Formula: see text] and local fluid temperatures exceed the prescribed surface boundary condition. The comparative study demonstrates that local skin friction, Nusselt number, and Sherwood number of the hybrid nanofluid (Au-MoS 2 ) are higher than the conventional mono nanofluids, as it has better effective density and dynamic viscosity. This article presents a rigorous computational tool for studying complex 3D magnetohydrodynamic (MHD) transport for slender aerodynamic configurations. The identified parametric restrictions for swirl intensification and near wall thermal overshoot offer physical insights that are useful for accurate thermal control in advanced manufacturing and material processing. The model is validated against the standard solutions from the literature and showed good predictive reliability and applicability. The outcomes provide particular design recommendations to enhance the thermal efficiency and reduce frictional energy losses in thermally challenging micro fluidic devices, chemical reactor channels, and electromagnetic coating technologies.