Convective instability of magnetic fluids

A theoretical investigation of the convective instability problem in the thin horizontal layer of a magnetic fluid heated from below is carried out. The effects of the relaxation time tau and the vortex (rotational) viscosity xi are considered and discussed. The Chebyshev pseudospectral method is employed to solve the eigenvalue problems and numerical calculations are carried out for a number of magnetic fluids and in full range of the magnetic field. A variety of results under gravity-free conditions are also presented and the critical temperature gradient are determined for a variety of situations. It is shown that the consideration of (xi,tau), in the stability analysis, is most effective in the thin layer of the fluid and at low values of Langevin parameter alpha(L).