Homotopy simulation of oscillatory powell–eyring nanofluid under rotating MHD Forces with Hall–ion slip and thermophoretic deposition

This paper presents an analytical investigation of the unsteady magneto hydrodynamic (MHD) flow of a Powell–Eyring nanofluid over an oscillating vertical plate in a rotating frame. The combined effects of Hall current, ion slip, Brownian motion, and thermophoretic diffusion are incorporated to describe coupled momentum, heat, and mass transport. The governing nonlinear partial differential equations are rendered dimensionless using similarity transformations and solved analytically through an optimized Homotopy Analysis Method (HAM). The influence of the magnetic field, rotation rate, Hall and ion slip parameters, and nanoparticle diffusion mechanisms on flow and thermal characteristics is thoroughly examined. Results reveal that the magnetic parameter induces Lorentz damping, which suppresses the primary velocity by about 12–15%, while the Hall parameter enhances it by nearly 10–14%. A 20% increase in the rotation parameter promotes flow stabilization and enhances temperature uniformity across the boundary layer. The thermophoretic parameter intensifies nanoparticle migration, thickening the thermal boundary layer by approximately 18–22% and increasing wall temperature, whereas Brownian motion slightly elevates the diffusion rate. These combined electromagnetic and diffusion-driven effects strongly regulate the transport behavior of Powell–Eyring nanofluids under oscillatory and rotational conditions. Overall, the study provides a reliable analytical benchmark for optimizing magnetically controlled nanofluid systems. The findings have direct applications in the design of electromagnetic cooling devices, rotating machinery, and high-current electrical wiring systems, where precise control of heat and mass transfer under magnetic and rotational influences is crucial.