Electrohydrodynamic linear stability of finitely conducting flows through porous fluids with mass and heat transfer

In this work, a linear stability analysis is used to investigate a capillary surface waves between two horizontal finite fluid layers. The system is acted upon by a vertical periodic electric field. The problem examines few representatives of porous media. It is also includes finite conductivity, mass and heat transfer. It is assumed that the basic flow is two-dimensional streaming flow. A general dispersion relation governing the linear stability is derived. In contrast with our previous work [23], the present problem shows that the stability criterion depends on the mass and heat transfer parameter. The present study recovers some special cases upon appropriate data choices. The presence of finite conductivity’s together with the dielectric permeability’s make the uniform electric field plays a dual role in the stability criterion. This shows some analogy with the nonlinear stability theory. In addition, the mass and heat transfer parameter as well as the Darcy’s coefficients play a stabilizing role in the stability picture. In case of the Rayleigh–Taylor instability, by means of the Whittaker technique, the parametric excitation of the electrohydrodynamic surface waves is obtained. The transition curve equations are calculated up to the fourth order for a small dimensionless parameter. The analytical results are numerically confirmed.