Numerical Approach based Study of MHD Viscous and Viscoelastic Immiscible Fluids Flow through Porous Channel

Abstract

The study and application of multiphase magnetohydrodynamic (MHD) fluid flow in porous media extend to several fields including petroleum engineering, environmental engineering, polymer processing and manufacturing, and several others. In these industries, the flow of viscous and viscoelastic fluids prevails through various channels where the many flow issues exist and require extensive investigation. In the present study, the viscous and viscoelastic immiscible magnetohydrodynamic (MHD) fluid flow through a porous horizontal channel between two plates is examined. In the channel, the viscoelastic fluid flows in upper region and the viscous fluid flows in the lower region. The flow is considered to be through a constant pressure gradient. The porous media of the upper and lower regions have two different permeabilities. The governing equations and boundary conditions are derived as per the channel geometry for these flows. These differential equations are solved analytically. The roots of the cubic equation in the viscoelastic fluid governing equation are obtained for different values of the viscoelastic parameter and permeability coefficient. The boundary conditions are applied to these solutions and obtained equations are solved numerically to obtain the values of coefficients involved in the solution using a MATLAB program. Finally, the effect of various flow governing parameters is shown on velocity profiles through various graphs. The results show that on applying the magnetic field velocity decreases. It has been shown that the MHD field application causes a drop in shear stress at the lower plate while increasing in the upper plate. The magnetic field effect on volume flow rate is also analysed and found that it increases with increasing magnetic field values. The effect of other parameters is also shown on shear stress and flow rate and the results are discussed through various graphs and tables.