An innovative methodology in scrutinizing the nonlinear instability of two immiscible MHD viscoelastic liquids

This study examines the nonlinear stability of two distinct viscoelastic magneto-rheological planner fluids that are immersed in porous media. The lower zone is filled with the Reiner-Rivlin fluid (RRF); meanwhile, the upper one is occupied by the Eyring-Powell fluid (EPF). An unchanged magnetic field (MF) is applied to the whole structure, and the effects of surface tension (ST) and mass and heat transfer (MHT) are also documented. This approach offers insights into stability thresholds and flow dynamics crucial for applications in energy systems, medicinal devices, and industrial processes that involve multi-layered magneto-rheological fluids in porous settings. One use of these fluids is the real-time adjustment of damping qualities in adaptive vehicle suspension systems. Improvements in vehicle dynamic performance, comfort, and safety are directly impacted by this research. The calculations are shortened by making use of viscous potential theory (VPT). Therefore, the viscoelastic influences are considered in order to show how the nonlinear boundary conditions (BCs) produce their contributions. Consequently, the impacts of the viscoelasticity parameters are removed from the solution of the equations of motion. Merging the fundamental linear hydrodynamic equations with Maxwell's equations over the quasi-static approximations, the boundary-value problem is raised. A popular nonlinear ordinary differential equation (ODE) can be transformed into a linear via the He’s frequency formula (HFF), which forms the basis of the non-perturbative approach (NPA). The non-dimensional analysis reveals a set of physical dimensionless numerals. Additionally, they help to reduce the amount of variables that are needed to comprehend the framework. The stability constraints are numerically tested in the complex scenario, and the stability mechanism remains consistent for both real and imaginary coefficients within the nonlinear characteristic equation governing interface displacement. Polar plots of unstable solutions are omitted, since these solutions are not desired.