Insights into Nonlinear Instability of a Fluid Jet Under a Tangential Periodic Magnetic Field

The study is driven by its importance in modern material processing and precision engineering, where understanding and controlling interfacial stability is crucial in maintaining reliable performance across various operating conditions. The interplay between the tangential magnetic field and temporal periodicity generates additional mechanisms of mode coupling and amplifies instability. These observations address critical shortcomings in nonlinear stability theory and suggest practical uses in flow regulation and the control of conductive fluids. The fluids are assumed as Eyring–Powell non-Newtonian and flow with uniform velocities through porous media. The analysis is conducted using a non-perturbative method that relies mainly on He’s frequency formulation. To facilitate the mathematical treatment, viscous potential theory is adopted. The governing linear partial differential equations describing the flow are then solved under nonlinear boundary conditions, resulting in a nonlinear characteristic equation that represents the displacement of the interface. A non-dimensional procedure is then applied to extract the key dimensionless physical parameters influencing the system behavior. A set of graphical results is provided to demonstrate how the system’s stability behavior is influenced by changes in the key dimensionless physical parameters. The validation of the innovative process is achieved using Mathematica Software. The study considers both uniform and periodically varying magnetic fields, and the associated stability conditions are evaluated for each case, where the impacts of various non-dimensional attributes are assessed. As density ratio increases, it stabilizes periodic magnetic fields while destabilizing uniform ones. A stronger MF enhances magnetic damping, reducing instability regions and promoting stable periodic interfacial motion. Enhanced conductivity improves Magnetohydrodynamic interactions, resulting in greater energy dissipation and stability.