Formation of Thermomagnetic Convection of Stratified Magnetic Fluid in a Hele–Shaw Cell

This paper touches upon the formation of thermomagnetic convection in a stratified magnetic colloid that fills up a Hele–Shaw cell placed in an external nonuniform magnetic field and heats up from the side of a narrow edge in such a way that the constant field strength gradient is codirected with the temperature gradient. The Galerkin method is applied to obtain critical magnetic Rayleigh numbers for the cases of monotonous convection and oscillatory convection arising due to the nonuniformity of the concentration of magnetic nanoparticles caused by thermal diffusion and magnetophoresis. In the case of oscillatory instability, the dependence of the neutral oscillation frequency on the mixture separation parameter and the concentration Rayleigh number is determined. For supercritical monotonous and oscillatory convection regimes, the stream function, temperature, and concentration distributions are presented, and the behavior of the amplitudes of various spatial harmonics is investigated.