Transport of Immiscible Non-Newtonian Fluid Layers in Composite Anisotropic Porous Structures under MHD Influence

Abstract Multilayer transport of non-Newtonian fluids through anisotropic porous media under magnetic fields is central to many engineering and biomedical applications, yet the combined influence of permeability anisotropy and magnetic control on layered flows remains insufficiently understood. The steady, incompressible, and laminar flow of a Casson–Jeffrey fluid system between two parallel plates filled with an anisotropic porous medium is analyzed in the presence of a uniform inclined magnetic field. The immiscible multilayer configuration consists of a Casson fluid core sandwiched between two Jeffrey fluid layers (J–C–J), enabling detailed examination of interfacial and anisotropic effects. A rigorous magnetohydrodynamic model incorporating directional permeability is developed, and the governing equations are nondimensionalized to introduce the anisotropic permeability ratio, anisotropy angle, Hartmann number, and Casson and Jeffrey fluid parameters. Exact analytical solutions for the velocity field are obtained. The results reveal that increasing permeability anisotropy and magnetic field strength suppress fluid velocity and interfacial shear, while the applied magnetic field provides an effective mechanism to regulate and stabilize multilayer flow in anisotropic porous channels. These findings offer physical insight into flow control in anisotropic porous systems, with applications in enhanced oil recovery, biomedical transport, composite material processing, and magnetically tunable microfluidic devices.