Analysis of Convective Instability in Dusty Ferromagnetic Fluids with Magnetic Field-Dependent Viscosity Under Fluid-Permeable Magnetic Boundaries

The subject under consideration finds manifold applications across various disciplines, including biological, industrial, and environmental sectors. Therefore, this study aims to analytically investigate the onset of convective instability in a dusty ferromagnetic fluid layer, influenced by magnetic field-dependent viscosity and fluid-permeable magnetically active boundaries, when subjected to a uniform transverse magnetic field. The eigenvalue problem is formulated through the utilization of linear stability theory followed by normal mode analysis. To address this problem, a single-term Galerkin method is employed, followed by a numerical calculation of the critical magnetic Rayleigh number. It is investigated numerically and graphically that (N_c)_Free ≤ (N_c)_permeable ≤ (N_c)_Rigid. It has been observed that as the dust particle parameter h₁ increase, the critical Rayleigh number decreases, indicating the destabilizing nature of h₁ On the other hand, the viscosity parameter δ and magnetic susceptibility χ and permeability parameter Da_s demonstrate a stabilizing effect on the system. Initially, measure of nonlinearity of magnetization M₃ exhibits a destabilizing effect, but beyond a certain threshold, it switches to a stabilizing effect within the system.