Influence of Magnetic Field Dependent Viscosity on Thermal Instability in a Ferrofluid Layer Saturating a Porous Medium with Permeable Boundaries

Abstract

In this study, we explore the stability of a ferrofluid layer saturating a densely packed porous medium, situated between two horizontal permeable boundaries, influenced by magnetic-field-dependent (MFD) viscosity and a vertically oriented magnetic field. The analysis is carried out using linear stability theory and the normal mode method to derive the eigenvalue problem. A single-term Galerkin method is adopted for solving the eigenvalue problem, facilitating the calculation of critical wave number and critical magnetic Rayleigh number and for distinct boundary combinations. The principle of exchange of stabilities is upheld, indicating that convection begins solely via the stationary mode. Through numerical calculations and graphical representations, the study evaluates the impact of various important factors, such as the MFD viscosity parameter, medium permeability, permeable boundary parameters, and magnetic parameters $M_1$ and $M_3$, on the initiation of stationary convection. The findings reveal that the viscosity stabilizes the system across all boundary combinations, while medium permeability destabilizes it. Furthermore, the transition in the nature of permeable boundaries from free to rigid results in an increase in the magnetic Rayleigh number, indicating that convection occurs later in the former case, which corresponds to greater stability in the system. These results are essential for advancing various industrial, engineering and environmental applications involving convection in ferrofluids.