Mathematical Model of Instability Phenomenon with Magnetic Fluid through Homogeneous Porous Media

In this paper the mathematical model of instability phenomenon occurs during secondary oil recovery process is formulated under the external magnetic effect which is due to injection of magnetic fluid into injection wells. Mathematical formulation of the present model leads tonon-linear partial differential equation of parabolic type which has been solved in form of power series with appropriate initial and boundary conditions for any time T > 0. The solution represents saturation of injected phase for different time T > 0. The graph shows that saturation of injected phase increases for distanceX increases for different time T. It is given by using MATLAB coding. Keywords: Instability phenomenon, magnetic fluid, Power series solution 2010 Mathematics Subject Classification: 35Q35, 76S99