Two-dimensional analysis of the stability of conducting medium flows between permeable plane electrodes inclined to the horizon

Flows of a conducting continuous medium due to Joule heat generation in an inclined plane layer in the presence of the gravity force are considered on the basis of the Oberbeck-Boussinesq equations and a thermal discharge model. One-dimensional steady-state background solutions are constructed and volt-ampere characteristics (VAC) are studied for a model temperature dependence (linearly decreasing) of the specific electric resistance of the interelectrode medium. The investigation is carried out taking the electrode permeability into account for a conducting medium in the presence of blowing through a single electrode and suction through the other. An analysis of stability carried out in the electrical engineering (one-dimensional) approximation shows that under certain conditions there exist solutions corresponding to a VAC fragment with negative differential resistance. Flows of the continuous medium corresponding to these solutions can be unstable in the interelectrode discharge gap. The results of calculations of the instability growth rate of a horizontal layer are given in the electrothermal approximation when there are no velocity perturbations.