Thermal Instability of Compressible and Rotating Viscoelastic Rivlin-Ericksen Fluid Permeated with Suspended Particles Saturating Porous Media in Hydromagnetics

Abstract

This paper deals with the instability of the plane interface between two uniform, superposed, electrically conducting and counterstreaming viscoelastic fluids saturating porous media in the presence of horizontal magnetic field. The rheology of the viscoelastic fluid is described by Walters’ (model B¢ ). The effects of medium porosity, surface tension and square of the Alfvén velocity, on the growth rate (both the real and the imaginary) of the most unstable mode have been investigated numerically. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if the perturbations in the direction of streaming are ignored. For perturbations in all other directions, there exists
instability for a certain wave number range. The simultaneous presenceof the magnetic field and the surface tension are able to suppress this  Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity has critical strength to suppress the instability on the  real growth rates of the most unstable mode. However, in case of imaginary growth rates of the most unstable modes remain uninfluenced by the increase in surface tension, the square of the Alfvén velocity and medium porosity. All these results have been computed numerically and depicted graphically.