Nonlinear Electrohydrodynamic Kelvin-Helmholtz Instability through Two Porous Layers with Suction / Injection : Viscous Potential Theory

Abstract

The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of an interface between two porous layers with heat and mass transfer is investigated. The fluid flow is considered to be through semi permeable boundaries above and below at which the fluids may either be flows in or sucked out, in a direction normal to the main streaming direction. Through the linear stability analysis, a general dispersion relation is obtained. The Ginzburg–Landau equation is obtained by employing the method of multiple scale expansion according to the nonlinear stability theorem. The stability of the system is discussed and is presented graphically. It is found that the injection of the two fluids at both boundaries has a stabilizing effect in contrast with the suction at both boundaries. The stable and unstable regions in the nonlinear case are drawn and discussed. Keywords Nonlinear Kelvin-Helmholtz instability ; Viscous potential flow; Interfacial instability; Heat transfer ; Mass transfer; Flow through porous media; Electrohydrodynamic; Multiple scale methods; Suction/Injection.