Use of RDTM (Reduced Differential Transform Method) in solution of fingero-instability phenomenon with effect of magnetic field in porous media

Abstract

This paper studies the efficiency of the Reduced Differential Transform Method (RDTM) in simulating fingering instability in the flow of two immiscible fluids water and oil through a homogeneous porous medium under the influence of a vertically downward variable magnetic field. The problem is of direct relevance to secondary oil recovery processes, where two of the dominant mechanisms, fingering and imbibition, play very important roles in influencing the displacement efficiency of the fluid. The use of a variable magnetic field is thought to increase the velocity of the injected conductive fluid, thus affecting the flow dynamics. The result of mathematical formulation is followed by a non-linear partial differential equation (PDE), the reduced differential transform method (RDTM) is, used to suitable initial and boundary conditions. RDTM is demonstrated to be a very good analytical method that offers a basic but accurate method for the solution of hard nonlinear systems without resort to computationally intensive numerical methods. The study offers quantitative results as well as graphical schemes to illustrate the physical behavior of the fluid system under the influence of the magnetic field. The physical implications of the solution are explained along with numerical data and graphical representations.