Cilia-assisted flow for the Johnson–Segalman fluid inside a convergent complex wavy passage with the magnetic field, hall effect, and porous medium

Abstract

This study investigates the cilia-driven flow of a Johnson–Segalman (J–S) non-Newtonian fluid through a two-dimensional converging channel under the influence of a vertically applied magnetic field. The problem is motivated by its relevance to biological fluid transport and the design of bio-inspired microfluidic devices. Key physical effects such as the Hall current, magnetic field interaction, and porous medium resistance are incorporated to reflect realistic conditions found in physiological and industrial settings. The governing equations, derived under the assumptions of low Reynolds number and long wavelength approximations, are numerically solved using the bvp4c method. The results reveal that the interplay between geometric convergence, complex ciliary wall undulations, magnetic forces, and Hall currents significantly alters the fluid's axial velocity, pressure gradient, and shear stress distributions. In particular, increases in the Darcy number and Hall parameter enhance fluid transport, while stronger magnetic fields and higher wall slip lengths tend to suppress flow. The novelty of this work lies in its comprehensive coupling of cilia-induced transport with Hall magnetohydrodynamics in a converging porous duct, an area scarcely explored in existing literature. These insights offer potential applications in optimizing next-generation microfluidic designs, peristaltic transport systems, and bio-mimetic pumping technologies.