Specific of a viscous fluid flow under the action of a transverse magnetic field

Abstract

Annotation. In this article we considered the flow of viscous electrically conductive fluids in the field of action forces which have a magnetic nature. Done the analysis of the case when the flow is unstabilized, but in their characteristics close to the flow in the hydrodynamic initial section. In this case, besides the viscous friction forces,have a significant effect on the flow the inertial forces from convective acceleration and mass forces, related with the action of ponderomotive forces arising in the presence of a magnetic field. In this case, the term appears in the equations of motion characteristic of the description of the hydrodynamic initial section, which characterize the action of forces with a magnetic nature, that is, the value    shows on the effect of the manifestation of ponderomotive forces in the hydrodynamic initial section and related with the value of the ratio between the forces of inertia and the forces of viscous friction. The Hartman flow characterizes when the inertia forces are insignificant in this case. On the other side the inertia forces from convective acceleration are much greater than the ponderomotive forces, the flow under consideration is characteristic of the hydrodynamic initial section and is described in the article quite fully. Finally, these equations can be used to describe the Poiseuille motion, when ponderomotive forces and inertia forces are too small. In general case, in the presence of all types of forces represented in the equation of motion, we are working with a hydrodynamic initial section, whose value depends on both the Reynolds criterion and the Hartman criterion. The nature of this dependence is presented in the article as a picture, where the differential pressure in the general case can be represented as the sum of the differential pressure for a stabilized flow and additional, related with the action of inertia and ponderomotive forces. The experiments show, that the action of ponderomotive forces appear itself in the form of a flow-inhibiting effect. At the same time, inertial forces from convective acceleration contribute to the accelerated movement of fluid in flow core in the hydrodynamic initial section and inhibition within the forming boundary layer. Finally, the process of flow formation in the hydrodynamic initial section depends on the relationship between these forces. In the work, this process is characterized by the relationship between the Reynolds criterion and the Hartman criterion.