On Compressible Couple-Stress Fluid Heated and Soluted From Below in Porous Medium in Presence of Rotation and Magnetic Field

Abstract

The thermosolutal convection in a compressible couple-stress fluid in a porous medium in the presence of uniform rotation and uniform magnetic field (separately) is studied. Using linearized stability theory and normal mode analysis, the dispersion relation is obtained in each case. In the case of incompressible magneto thermosolutal convection, the stable solute gradient, the magnetic field and couple-stress parameter postpone the onset of convection, whereas medium permeability hastens the onset of convection for stationary convection. For rotatory compressible thermosolutal convection the stable solute gradient and rotation have postponed the onset of convection whereas medium permeability and couple-stress have both hastened the onset of convection as well as postpone the onset of convection. We also found that the effect of compressibility is to postpone the onset of thermal instability. Further the solute gradient, magnetic field, and rotation are found to introduce oscillatory modes which were non- existent in their absence, and then principle of exchange of stability is valid. The sufficient conditions for non-existence of overstability are also obtained.