Influence of permeable boundaries and temperature-dependent viscosity on thermal instability in a dusty ferrofluid-saturated porous layer

This study examines the influence of permeable boundaries on thermal convection in a dusty ferrofluid-saturated porous layer with temperature-dependent viscosity, considering three distinct viscosity variation laws: linear, exponential, and inverse. The incorporation of permeable boundaries and temperature-dependent viscosity introduces a novel theoretical extension to the study of thermal convection in porous dusty ferrofluid systems. A linear stability analysis is performed, and Pellew and Southwell’s technique is employed to validate the principle of exchange of stabilities, confirming that instability occurs via a stationary convection mode. The eigenvalue problem for stationary convection is solved using a single-term Galerkin method. The study investigates the influence of various parameters on the onset of convection under different hydrodynamic conditions, providing key insights into system stability. It is observed that parameters governing boundary permeability ($k_0^{{}^{\prime }},k_1^{{}^{\prime }}$), as well as those characterizing the porous medium ($D{a}_s^{-1}$) and the Brinkman number ($\Lambda$), delay the onset of convection, thereby exerting a stabilizing effect. In contrast, the non-linearity of the magnetization parameter ($M_3$) and the dust particles parameter ($h^{{}^{\prime }}$) promote convection, leading to the opposite effect. The temperature-dependent viscosity variation parameter ($\delta$) enhances stability for linear and exponential variations but induces destabilization under inverse variation. Additionally, the influence of these parameters on convection cell size is analyzed. The findings of previous studies are retrieved as special cases within the framework of this analysis, reinforcing the validity of the results.