Instability analysis of a streaming electrified cylindrical sheet through porous media

Abstract

The current study deals with the influence of a uniform electric field on a cylindrical streaming sheet. This paper investigates a few representatives of porous media. These media are considered to be uniform, homogeneous and isotropic. The analysis is based on viscous potential theory, which assumes that the viscous forces affect only the interface between the fluids. The mathematical treatment is based on the normal modes analysis. For convenience, cylindrical coordinates are used. The boundary-value problem yields coupled second-order and damped differential equations with complex coefficients. These equations are combined with a single equation under the concepts of the symmetric and antisymmetric deformations. The Routh–Hurwitz criterion is adopted to govern the stability of the system. Several special cases are recovered upon appropriate data choices. The effects of various parameters on the interfacial stability are theoretically presented and illustrated graphically through some sets of figures. These parameters are the Darcy’s coefficients, basic velocities, dielectric constants, viscosity and thickness of the inner cylinder. We have found that the thickness of the inner cylinder plays a dual role on the stability picture. Also, the Darcy’s coefficient and dielectric constants have stabilising influence and the dynamic viscosity has a destabilising effect.