The Effect of Suction and Injection on MHD Flow Between Two Porous Concentric Cylinders Filled with Porous Medium

S.E E Hamza

doi:10.24297/jap.v16i1.8273

Abstract

This Paper deals wit the effects of suction (injection) on magnetohydrodynamic (MHD) steady flow of a viscous and electrically conducting fluid in an annular porous region between two concentric cylinders. The inner cylinder is rotating with uniform angular velocity and the outer one is fixed. The two cylinders are porous with uniform permeability. It is assumed that the suction rate at the inner cylinder is equal to the injection rate at the outer cylinder. A uniform axial magnetic field was applied perpendicular to the flow direction. The flow resistance presented by the porous medium is governed by the Darcy law. By using similarity transformation, the governing partial differential equations have been transformed to a system of nonlinear ordinary differential equations. The solution of the obtained system in its general form has been obtained. Analytical expression for velocity field is obtained in terms of Bessel function of first and second kind. The effects of various parameters such as susction (injection), magnetic and permeability parameters on the flow are discussed and the obtained results are presented graphically. The obtained figures show that, the velocity distribution increased with the increase of permeability parameter of the the porous medium and with suction process. On the other hand, the velocity distribution decreased with the increase of magnetic parameter and with injection parameter.

Highlights

Flow in porous medium has been extensively investigated due to its numerous applications in geophysics, petroleum industry and chemical engineering etc
In the present problem we have studied the steady and laminar flow of a viscous, incompressible fluid in an annular porous concentric cylinders filled saturated porous medium under the uniform axial magnetic field
In order to understand the physical situation of the problem and the effect of suction, magnetic and porousity parameters, we have found the variation of velocity field for 1 r in all special cases and for values of the included physical parameters

Summary

Introduction

Flow in porous medium has been extensively investigated due to its numerous applications in geophysics, petroleum industry and chemical engineering etc. Concentric cylinders, Navier Stocks equation, Suction, Injection, MHD flow, Bessel function, Porous medium, Darcy law, Permeability parameter, Magnetic parameter. Srivastava et al [34] have concedred Poiseuille and Couette flow of an electrically conducting fluid through a porous medium of variable permeability under the transverse magnetic field.

Results

Conclusion