Single diffusive magnetohydrodynamic pressure driven miscible displacement flows in a channel

Abstract

We investigate the influence of a magnetic field on the single diffusive pressure driven miscible displacement of a low viscous fluid by a high viscous one in a channel using the streamline upwind Petrov-Galerkin based finite element method. We perform transient numerical simulations of the governing continuity and Navier–Stokes equations with magnetohydrodynamic effects coupled with the convection–diffusion solute concentration equation. We have assumed concentration-dependent viscosity and neglected the density contrast. Our computational results are found to match quite well with the other results from the literature. We report that the presence of a magnetic field can suppress the interface instabilities characterized by intense convective mixing and roll-up phenomena for the classical situation of a less viscous fluid displacing a more viscous one. We have found various new types of instability patterns with the combined influences of the Hartmann number, Reynolds number, and Schmidt number. We show that the mushroomlike structure at the tip of the leading finger grows in volume with enhancing magnetic field strength, whereas follows the reverse trend as the Reynolds number is increased. Finally, to examine the effect of magnetic field on the global stability characteristics, we have performed a dynamic mode decomposition analysis. Our analysis demonstrates that by effectively maneuvering the dimensionless parameters, the displacement rate can be enhanced, and this is attributed to the acceleration in fluid mixing. Apart from the fundamental importance, we trust that the results obtained from this study may help in improving the operating efficiency of the modern generation process industries.