Viscous corrections for the viscous potential flow analysis of magnetohydrodynamic Kelvin-Helmholtz instability with heat and mass transfer

Abstract

Viscous corrections for the viscous potential flow analysis of Kelvin-Helmholtz instability at the interface of two viscous fluids in the presence of a tangential magnetic field has been carried out when there is heat and mass transfer across the interface. Both fluids are taken as incompressible, viscous and magnetic with different kinematic viscosities and different magnetic permeabilities. In the viscous potential flow theory, viscosity enters through the normal stress balance whereas the effect of shearing stresses is completely neglected. We include the viscous pressure in the normal stress balance along with the irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface for two fluids. A dispersion relation has been derived and stability is discussed theoretically as well as numerically. A stability criterion is given in terms of a critical value of relative velocity as well as a critical value of applied magnetic field. It has been observed that the tangential magnetic field and the vapor fraction both have stabilizing effect on the stability of the system while heat and mass transfer destabilize the interface. Also, it has been found that the effect of irrotational shearing stresses stabilizes the system.