Effect of Wave Number on Thermal Convection in Couple-Stress Fluid in The Presence of Rotation and Magnetic Field

The effect of wave number and rotation on the thermal convection in couple-stress fluid heated from below in the presence of uniform magnetic field is investigated. The paper established the regime for all non-oscillatory and nondecaying slow motions starting from rest; the necessary condition for the existence of 'overstability' and the sufficient condition for the validity of the 'exchange principle' is also derived, when both the bounding planes are rigid. Further, the stationary convection at marginal state with free horizontal boundaries is analyzed numerically and graphically, showing that the rotation has a stabilizing effect on the system. In the presence of rotation; the magnetic field and couple-stress parameter has stabilizing (or destabilizing) effect on the system depending upon conditions satisfied. In the absence of rotation, both magnetic field and couple-stress parameter has stabilizing effect. However, for the constant magnitude of any of the couple-stress parameter, magnetic field and rotation, the wave number has a destabilizing effect for a value less than the critical value, which varies with the magnitude of the couple-stress parameter, magnetic field and rotation; and for higher values than the critical value of the wave number; it has a stabilizing effect on the system.