Nonlinear stability and subcritical dynamics of ferroconvection with couple stresses under thermal non-equilibrium in porous media

The present work contributes to advancing the theoretical understanding of ferroconvection phenomena in porous media, which is critical for engineering applications involving magnetic nanofluids, such as biomedical cooling, energy systems, and microfluidics. This study aims to investigate the nonlinear stability and subcritical dynamics of ferroconvection in porous media under local thermal non-equilibrium (LTNE) conditions, with a focus on the mechanical behavior of ferrofluids influenced by couple stresses, magnetization, and medium properties. The ferrofluid flow is modeled using the Darcy–Brinkman framework, coupled with a two-field energy model to capture LTNE effects. Linear stability is analyzed via normal mode analysis, while nonlinear behavior is examined through the energy method. A single-term Galerkin approach is employed to solve the resulting eigenvalue problems under three thermal boundary conditions: free–free, rigid–free, and rigid–rigid. The results reveal the existence of a subcritical region characterized by differences between linear and nonlinear Rayleigh numbers. Key parameters, including magnetization, couple stresses, medium permeability, porosity-modified conductivity ratio, and interphase heat transfer coefficient, are examined for their influence on stability and subcritical behavior. These results provide important design insights for controlling ferrofluid behavior in porous systems under magnetic and thermal gradients.