Abstract
The Kelvin-Helmholtz instability of two viscoelastic Oldroydian superposed conducting fluids permeated with suspended particles in a porous medium is studied when the whole system is immersed in a uniform magnetic field. The dispersion equation for the considered system is obtained, which also yields the dispersion relation for Maxwellian fluids as a limiting case in the presence of suspended particles through a porous medium in hydromagnetics. It is found that both the magnetic field and sur ace tension have stabilizing effects and completely suppress the Kelvin-Helmholtz instability for small wavelengths. The medium porosity reduces the stability range given in terms of the fluids and Alfven velocities. The stability conditions are discussed analytically in detail. The numerical results show that the stress relaxation time, number density of the suspended particles, porosity of the porous medium, Stokes's drag coefficient, and the strain retardation time have destabilizing as well as stabilizing effects for small and large wave numbers. The medium permeability is found to have an opposite effect. The magnetic field has a stabilizing effect only for small wave numbers; otherwise, it has no effect on the stability of the system. Both the kinematic viscosity and fluid velocity are found to have destabilizing effects. The corresponding results in the limiting case of Maxwellian fluids have been compared with the previous results of Oldroydian fluids.