Flow in magnetohydrodynamic channels at large magnetic Reynolds numbers

V. I. Kovbasyuk - S. A. Medin

Abstract
The variational problem of the flow of a conducting fluid in the channel of a magnetohydrodynamic generator at large magnetic Reynolds numbers is considered. The magnetic induction equation is written for a magnetic system containing steel. The possibility of partial saturation of the magnet is allowed. The minimum is sought for the functional of a generalized channel coordinate (for example, the length or volume). An analysis is carried out of the boundary conditions of the problem, and the conditions are considered at the magnetic-field inflection point when the saturation induction is reached. A numerical solution of the problem is obtained for compressible fluid having a variable conductivity. In the case of an incompressible fluid the analytic solution is given. A comparison is made between the solutions of variational problems and the solutions of nonvariational ones.