Steady convection in the presence of an external magnetic field

The problem of the equilibrium of a liquid enclosed in a vessel heated from below has been considered by Sorokin [1], Iudovich and Ukhovskii [2] and Velt [3]. It has been established that if the Rayleigh number λ exceeds a certain critical value λ₀, then secondary steady flows arise in the liquid.

The stability of a conductive liquid heated from below has been studied by many authors. The most complete and general studies are those of Sorokin and Sushkin [4], whose paper contains the appropriate bibliography, and that of Shliomis [5]. The results of [4 and 5] make clear the physical picture of the phenomena associated with the heating of a conductive fluid and indicate the possible existence of secondary steady and periodic flows.

The existence of steady convective flows in a conductive liquid are proved below. Our study is based on the procedure set forth in [2].