Nonlinear instability of two streaming-superposed magnetic Reiner-Rivlin Fluids by He-Laplace method

Magnetic properties play an important role in electrocatalysis and electrodeposition. The current study is concerned with a novel mathematical approach to the Kelvin Helmholtz instability (KHI) saturated in porous media with heat and mass transfer. The system consists of two finite horizontal magnetic fluids, which is acted upon by a uniform tangential magnetic field. The field permits the presence of surface charges on the surface of separation. The rheological behavior of the visco-elastic fluid is characterized by Reiner-Rivlin model. Typically, the solutions of the governing equations of motion in accordance with the appropriate nonlinear boundary conditions resulted in a characteristic nonlinear second-order partial differential equation of a complex nature. This equation controls the behavior of the surface deflection and may be treated to yield the Helmholtz-Duffing equation. By means of He-Laplace method, an approximate bounded analytic solution is obtained and plotted. Additionally, the technique of the nonlinear expanded frequency is applied to attain the stability criteria. In the nonlinear stability approach, the numerical calculations reveal additional physical parameters in the stability configuration. The implication of the linear/nonlinear curves shows that stability is judged only by the linear curve.