LAUSR

Abstract The current article is concerned with a nonlinear stability analysis of cylindrical Walters B' fluids. The system is pervaded by an axial time periodic electric field. A cylindrical interface is supposed to be disconnected from two dielectric fluids. The fluids are fully saturated in porous media. The motivation to scrutinize this area is attributed to the great attention it receives in many practical situations in physics and engineering applications. The implementation of the appropriate nonlinear boundary conditions of the linearized equations of motion yields a nonlinear characteristic dispersion equation. This equation manages the surface deflection of the surface waves. The use of the non-dimensional analysis resulted in various well-known non-dimensional numbers. A new approach to the characteristic equation is inspected by employing the Homotopy perturbation method (HPM). This new methodology resulted in a Klein-Gordon equation. Utilizing a travelling-wave solution to the linear part of the characteristic equation, a new restriction of the stability analysis appears. The investigation reveals the non-resonance as well as the resonance cases, and the stability criteria are established in both arguments. A set of diagrams is plotted to display the influence of various non-dimensional physical numbers on the stability profile and shows interesting features.