Combined effect of MFD viscosity and fluid-permeable, magnetic boundaries on convective instabilities in a hot ferrofluid layer

The present analysis examines the effect of magnetic field-dependent (MFD) viscosity on convective instability in a ferrofluid layer heated from below and subjected to a uniform vertical magnetic field, with fluid-permeable magnetic boundaries. Given its broad implications across various disciplines, the use of such boundaries adds novelty to this research. The parameters characterizing the permeable nature and magnetic susceptibility of the boundaries are varied to explore more realistic scenarios. The governing PDEs are reduced to non-dimensional linearized ODEs using linear stability theory followed by normal mode analysis. It is mathematically proven that the Principle of Exchange of Stabilities (PES) holds, thereby ruling out the oscillatory mode of convection. The critical values of the convective instability parameter for a stationary mode of convection are then obtained using the single-term Galerkin method. The study reveals that the magnetic parameter [Formula: see text] accelerates the onset of convection, while the impact of [Formula: see text], which represents the nonlinearity of the ferrofluid's magnetization, depends on the magnitude of δ, showing a destabilizing effect at lower δ values and a dual role at higher δ values.The MFD viscosity (δ) of the ferrofluid and magnetic susceptibility (χ) of the bounding surface stabilize the system. However, increasing the permeability of both boundaries leads to the opposite effect. Therefore, the system exhibits stronger stabilization when the permeability of the boundary layer is at its minimum, accompanied by larger magnetic susceptibility. The results documented in prior studies for free-free and rigid-rigid boundaries are also derived as special cases from this study.