STUDY OF MAGNETO-HYDRODYNAMIC FLOW OF VISCOUS FLUID THROUGH DIFFERENT POROUS STRUCTURES EMBEDDED IN POROUS MEDIUM

The study of the magneto-hydrodynamic flow of a viscous fluid through different structures embedded by a porous medium has been discussed by many researchers. In this investigation, the concept of fluid motion embedded in a porous medium in the presence of a magnetic field has been introduced. The objective of this article is to discuss the flow of viscous fluid past a porous circular cylinder and porous sphere embedded in a porous medium in the presence of a magnetic field. The Brinkman model is used for discussing the motion of fluid in porous media, and matching conditions suggested by Williams have been taken for both structures. The solutions to the problems have been obtained analytically; MATLAB software is used for graphical investigation. The streamlines are plotted and the drag on the porous sphere as well as the cylinder have been analyzed. It is observed that in the case of the sphere, as well as inside the cylinder, the drag increases sharply with the decrease of the permeability of the embedding medium, but outside the cylinder, the drag increases with the decrease of the porous material of the cylinder. Results obtained in this analysis are compared with the results obtained by applying the Ochoa Tapia and Whitaker matching conditions at the interface.