COMBINED EFFECTS OF MECHANICAL VIBRATION AND MAGNETIC FIELD ON THE ONSET OF BUOYANCY-DRIVEN CONVECTION IN AN ANISOTROPIC POROUS MODULE

The combined impacts of mechanical variation and the applied magnetic field on the onset of convection in an infinite flat liquid permeated anisotropic porous module are investigated subject to an adverse temperature gradient. The Brinkman model is taken to describe the flow momentum in the porous module, and the Boussinesq approximation is implicated in the field of buoyancy-driven flow. Floquet theory is applied to govern the onset condition within the framework of linear stability analysis. The present study is focused on the small amplitude gravity vibration, and the thresholds are found using Mathieu's functions and stability charts. Specific attention is paid to examine the effects on anisotropies in permeability and thermal conductivity of the porous module along the transverse direction. The emerging instabilities of synchronous and subharmonic modes and the exact point of the transition between them are examined for the control parameters. The applied magnetic field is more effective in stabilizing the system subject to gravity modulation than the system subject to gravity modulation alone. The findings of this analysis will give additional knowledge in controlling convective streams in designing highly perfect crystals or materials with improved mechanical properties.