The use of the variation method in research of the MHD-interface of variable electrical conductivity

Zoran Boričić ; Dragiša Nikodijević ; Dragan Živković

Theoretical and applied mechanics, Tome 13 (1987) no. 1, p. 31 .

Résumé

In this paper, we study a flat MHD boundary layer of an incompressible electrically conductive fluid. It is assumed that the external magnetic field is perpendicular to the surface of the body which the fluid flows around and is at rest to this body. There is no external electric field. The electrical conductivity of a liquid is assumed in a familiar form. \[ igma=igma_0\frac v{U^2}\frac{ tial u}{ tial y}. \] To calculate the detected problem, a variational method with a vanishing parameter is used. For this purpose, the Lagrange function is defined and the problem is reduced to a variational problem. To solve the resulting variational problem, the Kantorovich method is used. An equation is obtained for the offending form of the ratio of the velocity $\phi=u/u$ and for the case when $\phi$ has the form of a third-order polynomial. At the end, a special example of a boundary layer on a cylinder with a sinusoidal distribution of the scale of the number $N$ is calculated. The characteristic values of the tyrannical layer $\delta^{**},\delta^*,\tau_w$ are calculated and presented graphically.