Formulation Of The Problem Of Instability Of Streaming Walters’ Fluids In A Porous Medium

The instability of the plane interface separating the two uniforms, superposed, electrically conducting and counter - streaming elastico-viscous fluids through a porous medium is examined for visco-elastic polymer solutions in the presence of a horizontal magnetic field and also in the presence and absence of surface tension. These solutions are known as Walters’ (model B? ) fluiare approximatedeology is approximated by the Walters’ (model B? ) constitutive relations, proposed by Walters (1962). In the absence of surface tension, the perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions, there exists the instability for a certain wave number range. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wave length perturbations, and the medium porosity and the visco-elasticity reduce the stability range given in terms of a difference in streaming velocities and the Alfven velocity