MATHEMATICAL MODELING OF FINGERO-IMBIBITION UNDER GRAVITATIONAL, HETEROGENEITY, AND MAGNETIZATION EFFECTS

This investigation mathematically models the fingero-imbibition process in a heterogeneous porous medium under magnetic influences. Many natural and manmade systems rely on fingero-imbibition, or the preferential flow of a wetting liquid through porous surfaces when magnetic fields are present. The study focuses on vertical heterogeneity, considering how magnetization and gravity-driven flow impede fluid movement. The governing equations are solved using the Variational Iteration Method (VIM) under appropriate initial and boundary conditions. MATLAB-generated graphical representations and numerical data are used to demonstrate how the system performs under various parameter situations.