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This study examines the thermal instability in a magnetized rotating ferrofluid layer with magnetic field-dependent (MFD) viscosity, confined between two horizontal permeable boundaries using the Darcy-Brinkman model. Normal mode analysis is performed, followed by a single-term Galerkin approach to solve the eigenvalue problem for the Rayleigh number. The findings reveal that rotation and permeable boundaries significantly influence the onset of convective instability. At lower Taylor numbers Formula: see text, viscosity stabilizes the system, whereas at higher values of Formula: see text, it promotes instability. Beyond a certain threshold of Formula: see text, free-free boundaries exhibit greater stability than other boundary combinations. The effects of medium permeability, buoyancy, and non-buoyancy magnetization are also analyzed. An attempt is also made to examine the oscillatory convection, revealing that it is not the preferred mode of instability. The results closely address limiting cases, ensuring accuracy and significance.
Thakur et al. (Wed,) studied this question.