Study of squeezed ferrofluid flow through fibrous porous media

This study explores the unsteady squeezed flow of ferrofluid through a fibrous porous medium confined between two circular disks. The lower disk remains stationary, while the upper disk undergoes sinusoidal oscillations in the axial direction, inducing time-periodic compression of the porous matrix. The variation in the inter-disk gap drives transient deformation, altering porosity and permeability over time. A normalized Kozeny–Carman relation is employed to model the deformation-dependent permeability, effectively capturing the relationship between porosity evolution and flow resistance. The combined influence of oscillatory squeezing motion, fibrous microstructure, and magnetic effects significantly alters flow resistance, mixing behavior, and heat transfer characteristics. A similarity transformation reduces the governing momentum and energy equations to a set of coupled nonlinear ordinary differential equations, which are solved numerically using the MATLAB built-in boundary value problem solver (bvp5c). The results reveal that increasing the squeezing parameter intensifies axial flow and enhances thermal transport, while stronger ferromagnetic interactions redirect streamlines radially and suppress vertical compression, contributing to flow stabilization. The overall velocity magnitude increases under stronger compression of the porous medium, enhancing ferrofluid displacement and axial pumping effects. The heat transfer of ferrofluid is found to be damped by augmented ferromagnetic interactions, whereas it is enhanced with increasing oscillatory compression. The skin friction coefficient and Nusselt numbers on both disks exhibit distinct oscillatory patterns, with sharp peaks occurring during early compression phases. These insights provide a foundation for engineering adaptive thermal and lubrication systems, where oscillatory compression and magnetic field are harnessed to regulate transport and stability.