Computational study of oscillatory convection in an infinite ferromagnetic fluid layer: Impact of rotation, MFD viscosity, and variable gravity using the Galerkin method for free–free, rigid–free, and rigid–rigid boundaries

This study examines ferrofluid convection, a process important in many technical, industrial, and environmental applications, providing guidance on optimizing stability through control of rotation, viscosity, magnetization, and gravitational effects. We examine the impact of uniform rotation, varying gravity, magnetic-field-dependent (MFD) viscosity, and different boundary conditions on oscillatory ferromagnetic convection. Six types of variation of the gravitational field are analyzed, and the governing equations are nondimensionalized using linear stability theory. The Galerkin-type weighted residual method is employed to determine the critical Rayleigh and magnetic Rayleigh numbers for various boundary conditions. MATLAB R2021a software is employed to compute critical wavenumbers and magnetic Rayleigh numbers and to generate graphical results. The findings reveal that rotation consistently enhances system stability for all types of gravitational variation. Both MFD viscosity and magnetization parameters further stabilize the system, delaying the onset of convection under all types of gravity variation and boundary conditions. For rigid–rigid, free–free, and rigid–free boundaries, decreasing gravitational field variations stabilize the system, whereas increasing gravitational variations tend to destabilize it. Among the gravity profiles studied, the system shows highest stability for G(z)=z2−2z and lowest stability for G(z)=ez, regardless of boundary conditions. Regarding boundary effects, free–free conditions yield the greatest stability, while rigid–free boundaries are least stable at lower Taylor numbers. However, at higher Taylor numbers, rigid–rigid boundaries become the least stable. The present results generalize and validate earlier studies as special cases within this analysis.