Thermal convection in micropolar ferrofluid in the presence of rotation

A linear stability analysis is performed for a micropolar ferrofluid layer, heated from below subjected to a transverse uniform magnetic field in the presence of uniform vertical rotation. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using normal mode analysis method. For the case of stationary convection, the effect of various parameters like rotation, magnetic parameter M3 (measures the departure of linearity in the magnetic equation of state), micropolar parameters (coupling, spin diffusion and micropolar heat conduction) has been analysed. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of magnetic parameter M1 (ratio of the magnetic to gravitational forces) and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the micropolar ferrofluid heated from below in the absence of micropolar viscous effect, microinertia and rotation. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia and rotation, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained