Electrohydrodynamic Instability of Two Superposed Viscous Dielectric Fluids Flowing down an Inclined Plane with Thermal Conductivity Variation

Abstract

The linear electrohydrodynamic instability of two superposed viscous dielectric fluids flowing down an inclined plane in the presence of thermal conductivity variation and applied electric fields is investigated. Using long-wavelength approximation, a new instability is presented. It is shown that when there is a variation in thermal conductivity in the fluid even in absence of electric fields or when applied electric fields are present even in absence of thermal conductivity variation, instability can occur under a longitudinal gravitational field. The effects of various parameters as Prandtl number, Reynolds number, electric field, inclination angle, and thermal conductivity variation on the stability of the system are discussed analytically and numerically in detail. The presence of electric field is important to prevent the drop out of the analysis when there is no stratification in thermal conductivity. Key words: Hydrodynamic stability; Viscous fluids; Flows down an inclined plane; Thermal conductivity; Electro-hydrodynamics