Insights in the nonlinear instability of a ferromagnetic fluid jet

The objective of the current study is to scrutinize the nonlinear instability of a cylindrical interface linking two distinct viscoelastic magnetic fluids. The viscoelastic fluid obeys the Eyring-Powell non-Newtonian (EPF) type. It is supposed that the liquids are initially streaming with uniform velocities and saturated in a permeable media. Additionally, an unchanged axial magnetic field (MF) is pervaded by the presence of surface tension (ST). The motivation of the current matter is essential for sophisticated material processing and precision engineering, as it enhances their stability and responsiveness under diverse situations, facilitating more efficient devices and novel applications in microfluidics and soft robotics. It is also improved the material processing, biomedical devices, flexible electronics, and drug delivery systems, in addition to optimizing ferrofluid-based actuators and sensors in MFs. The methodology of the analysis is grounded in the non-perturbative approach (NPA). This methodology is established mainly on He's frequency formula (HFF). To relax the calculated manipulation, the viscous potential theory (VPT) is employed. The linear partial differential equations (PDEs) governing the motion are solved in light of the nonlinear boundary conditions (BCs). This organization produced a complicated nonlinear characteristic PDE. A procedure concerning the non-dimensional analysis is adopted to reveal a set of dimensionless physical parameters. A compound nonlinear specific formula with complex factors has resulted in the form of the former procedure. It is discovered that ignoring the Weber number excludes all the imaginary components. The nonlinear characteristic ODE is studied in instances of the real besides the complex coefficients. A set of diagrams is plotted to display the stability configuration with the variation of diverse physical pertinent parameters. The stability zones fluctuate between increasing and decreasing due to various characteristics, although remains predominantly stable. Additionally, a collection of PolarPlots moreover time variation and phase plane diagrams are illustrated for the equivalent solution to grantee stable solutions. The damping in the complex solution is increasing and speeding with the rise of the amplitude factor and the wave number.