An innovative methodology of inspecting nonlinear stability of a cylindrical interface separating two magnetic liquids

Studying the nonlinear stability of a cylindrical interface between two magnetic liquids is novel due to its complex interaction of Magnetohydrodynamic (MHD) effects, interfacial deformations, and thermodynamic gradients, relevant to industrial applications and astrophysical phenomena. Consequently, this study examines the nonlinear stability of a cylindrical interface between two liquids in MHD, focusing on applications like MHD technologies, industrial processes, and geophysical inflows. The inner region contains a Power-law fluid (PLF), meanwhile, the outer one is filled by an Eyring-Powell fluid (EPF), both of them are immersed in a permeable medium under a uniform magnetic field (MF). Surface tension (ST), mass, and heat transfer (MHT) are analyzed employing Hsieh's streamlined formulation. To summarize the mathematical manipulation, the investigation utilizes the viscous potential theory (VPT), which simplifies calculations by regarding normal stress equilibrium, however ignoring shear stresses. Through quasi-static approximations of Maxwell's equations, a boundary-value problem is derived. Nonlinear boundary conditions (BCs) are established by linearizing the movement equations. A nonlinear ordinary differential equation (ODE) is converted into a linear one using He's frequency formula (HFF), which supports a novel procedure named the non-perturbative approach (NPA). Dimensionless quantities simplify the framework, revealing the impact of MFs, viscoelastic parameters, and Lorentz forces on interfacial performance. It is found that the Weber numbers, the linear factor of MHT as well as Darcy number have stabilized influences. The characteristic nonlinear ODE possesses real coefficients in the absence of the Weber number. The PolarPlot graphics demonstrate stability criteria, which remain reliable in both real and complex coefficients, except for variations in the transitional curve.