Magneto-Rotatory Convection in Couple-Stress Fluid

Abstract

Background: Thermal convection is the most convective instability when crystals are produced from a single element like silicon and the thermal instability of a fluid layer heated from below plays an important role in geophysics, oceanography, atmospheric physics, etc. The flow through porous media is of considerable interest for petroleum engineers, for geophysical fluid dynamicists and has importance in chemical technology and industry. Many of the flow problems in fluids with couple-stresses indicate some possible experiments, that could be used for determining the material constants, and the results are found to differ from those of Newtonian fluid. Keeping this in view, the present work was to study the effect of a uniform vertical magnetic field on the couple-stress fluid heated from below in the presence of a uniform vertical rotation through permeable media. Methodology: The present problem is studied using the linearized stability theory, Boussinesq approximation, normal mode analysis, and the dispersion relation is obtained. Results: The stationary convection, stability of the system, and oscillatory modes are discussed. In the case of stationary convection, the rotation postpones the onset of convection. The magnetic field and couple-stress may hasten the onset of convection in the presence of rotation while in the absence of rotation; they always postpone the onset of convection. The medium permeability hastens the onset of convection in the absence of rotation while in the presence of rotation, it may postpone the onset of convection. The rotation and magnetic field are found to introduce oscillatory modes in the system which was non-existent in their absence. A sufficient condition for the non-existence of overstability is also obtained.