Study on magnetohydrodynamic Kelvin-Helmholtz instability with mass transfer through porous media

We study the linear analysis of Kelvin-Helmholtz instability of the interface between two viscous and magnetic fluids in a fully saturated porous medium using viscous potential flow theory, when the fluids are subjected to a constant tangential magnetic field, and when there is heat and mass transfer across the interface. The Darcy-Brinkman model has been used for the investigation. A dispersion relation has been derived and stability is discussed theoretically as well as numerically. The stability criterion is given in terms of a critical value of relative velocity as well as the critical value of applied magnetic field. It has been observed that both tangential magnetic field and vapor fraction have stabilizing effect on the stability of the system while heat and mass transfer destabilizes the interface. Porosity stabilizes the interface while the porous medium has destabilizing effect.