Effect of mass and heat transfer on EHD stability of two dusty liquid layers between two inclined rigid plates

The electrohydrodynamics (EHD) instability of two separate overlapping viscous particle fluids moving in a porous medium is the subject of this paper. The incompressible packaging contains microscopic, uniformly sized fine dust particles. The system is influenced by a tangential electric field that remains constant. The abbreviated formulation of Hsieh is employed to account for the impact of mass and heat transfer (MHT). The problem solution follows the viscous potential theory (VPT) because of the problem complexity in mathematics. The significance of fluid-particle mixing in several applications of practical physics and engineering operates as the guiding force behind this investigation. The standard normal modes methodology is used to examine the standard fundamental equations of motion. The essential mechanisms of the nonlinear technique are the formulations of the linear controlling fundamental formulae and the application of the appropriate nonlinear boundary criteria. A number of nondimensional characteristic parameters are produced by the technique. The nonlinear stability results in a nonlinear Landau–Ginzburg equation. By giving the physical parameter numerical values, the stability designs have been graphically represented. Therefore, both linear and nonlinear approaches are depicted to illustrate the impacts of different physical quantities. Using the homotopy perturbation approach and the idea of extended frequency, a uniform approximate solution for a nonlinear interface displacement is provided. He’s frequency approach yields another nonperturbative solution of the surface displacement solution, which is validated using the Runge–Kutta method.