Solution of a magnetohydrodynamic boundary - value problem with a periodic boundary condition

Yu. I. Malov - L. K. Martinson - K. B. Pavlov

Abstract
The steady flow of a viscous incompressible isotropically conducting fluid is considered in a plane channel with the conductivity of the walls being an arbitrary periodic function. The solution of the problem is in the form of an expansion in trigonometric series with coefficients satisfying an infinite linear algebraic system. Justification is provided for reducing the problem to the solution of this system. The results are given of calculations for a channel with walls having periodically alternating sections with different conductivity. The effect of the conductivity of the different sections of the channel walls on the velocity of the fluid u is ascertained, as is the dependence of 6 =umax-umin on the periodicity parameter.