Krzysztof Mizerski

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79005

## Abstract

A magnetohydrodynamic flow of a viscous and conducting fluid confined between two parallel differentially moving boundaries is considered. The whole system is in a strong magnetic field chosen in such a way that the Hartmann boundary layers which form in this problem become singular at the points where the magnetic field becomes tangent to the boundary. Two geometries are taken into account: plane and spherical. Within the class of such configurations, the velocity field of the fluid and the influence of the conductivity of the boundaries on the fluid's motion are reviewed here. In the region of singularity, where the magnetic field is tangent to the boundary, the fluid's velocity exceeds that of the moving boundary. The effect of nonzero conductivity of the boundaries on the super-speeding jets is vital and has been enlightened in a series of papers, including experimental and theoretical findings. The mechanism of the formation of super-speeding jets in the considered configurations has been explained, which is based on strong Hartmann currents allowed to enter the boundary layer due to the singularity. In the case of both perfectly conducting boundaries, the ˜ ° <sup>M</sup><sup>1</sup>=<sup>2</sup> super velocity was shown to be as strong as to scale with the Hartmann number as <sup>O</sup> .

Keywords: super rotation, magnetohydrodynamics, MHD boundary layers, Hartmann layer singularity, nonzero conductivity
