Thermal Convection in a Horizontal Layer of Magnetic Fluids

The linear instability is investigated for a horizontal magnetic fluid layer confined between two ferromagnetic boundaries and heated from below in the presence of a vertical magnetic field. Galerkin method is used for solving the disturbance equations. The resultant eigenvalue problem is solved numerically. The critical Rayleigh number varies with the magnetic number, N , as R a c =106.7(1- N / N 0 ), where N 0 is a function of M 3 , a measure of the nonlinear magnetization of fluid, and decreases from 141.7 to 106.7 as M 3 increases from 0 to ∞. The linear relation between R a c and N is proved analytically for very large values of M 3 . It is concluded that the magnetization of the boundaries and the non-linearity of fluid magnetization both reduces R a c , and that the effects of magnetic force and buoyancy compensate each other.