Stability of conducting medium flows between plane continuous electrodes inclined to the horizon

The mathematical formulation of the problem of analysis of the stability of flows of a conducting continuous medium associated with Joule heat generation in an inclined plane layer in the presence of the gravity force is formulated. A one-dimensional steady-state background solution is found. Volt-ampere characteristics (VAC) are constructed and investigated. It is shown that S -shaped voltage dependences of the current density can exist under certain conditions when three solutions with different current densities are possible for a given voltage. The solution with the mean current density that corresponds to the VAC fragment with a negative differential resistance is unstable. A model of analysis of two-dimensional perturbations based on the Oberbeck-Boussinesq equations and a thermal discharge model is proposed.