Estimation of Hall current infusion on blood filtration devices containing magnetized Cosserat fluids flow induced by metachronal transport system

• Developed a Darcy–Brinkman Cosserat blood-flow model with Hall current and Saffman slip for cilia-driven transport in magnetized porous channels relevant to blood filtration devices. • Derived closed-form analytical solutions for velocity, microrotation, pressure gradient, pressure rise–flow rate relationship and streamlines, and validated a limiting case against an existing micropolar MHD peristaltic flow solution. • Showed that magnetic field suppresses velocity, volumetric flow rate, bolus trapping and wall shear via Lorentz forces, while Hall current counteracts this damping and enhances pumping performance. • Demonstrated that Cosserat (micropolar) rheology yields higher velocities, flow rates and stronger trapping than Newtonian flow under identical MHD–porous conditions, highlighting the role of microrotation in blood rheology. • Quantified how Darcy permeability, Saffman slip and cilia length can be tuned to control pressure rise, flow rate and trapping, providing design insight for magnetically controlled blood filtration and micro-pumping devices. Blood, being a conducting fluid, interacts with magnetic fields, allowing MHD principles to be used for pumping, separation, and filtration processes. Infusion of Hall current in magnetic fields has found numerous applications in monitoring these pumping, separation, and filtration systems. This novel characteristic enables the application of magnetohydrodynamic (MHD) principles in biomedical technologies, particularly in contactless pumping, filtration, and separation processes. This study captures these novel applications through mathematical modelling tools. When blood is induced by a sufficiently strong magnetic field, the Hall Effect emerges, introducing an additional current component that plays a significant role in monitoring and regulating these systems. The problem to be modelled contains the magneto-hydrodynamic motion of a Cosserat fluid through a channel having a porous matrix and ciliated walls actuated by a transverse magnetic field. The model determines Lorentz body forces, Hall current effects, and micropolar property in which micro-rotational vectors are incorporated to expand the classical Navier-Stokes system to a nonlinear and coupled system of equations. With pathology, there exist internal blocks brought on by the deposit of substances like cholesterol, which require modelling using porous media like Darcy Brinkman structures. To make the problem analytically tractable, a long-wavelength calculation approximation in the creeping flow regime adopting the theory of lubrication approximation, is used. Galilean transformations are also used on a steady wave frame of reference, leading to the derivation of analytical expressions of axial velocity, micro-rotation component, pressure gradient, pressure rise flow rate, and stream function. The generalized model proposed herein uses the physiological flow properties to realize the key aspects of electromechanical, magneto-hydrodynamic pumping behavior, which provides a sound theoretical basis for the physiological and ionic fluid flows under non-Newtonian and magnetically driven conditions. The analytical technique is used to find the solution of rheological equations for flow features, such as velocity profile, microrotation, pressure gradient, flow rate, and streamlines. The comparison between Newtonian and Cosserat fluids is also highlighted. When it comes to flow and trapping in MHD porous circumstances, the Cosserat fluid consistently outperforms the other fluids due to its microrotation and structural flexibility. The fluid velocity is sharply affected under magnetic influence. It is found that the implication of Hall current exhibits noticeable impacts on manipulating the real-world applications of magnetic fields in surgical, blood filtration, biomedical Pumping, and blood separation processes.