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Magnetohydrodynamic flow on a half‐plane
Author(s) -
Sezgin Münevver
Publication year - 1988
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650080702
Subject(s) - magnetohydrodynamic drive , hartmann number , laminar flow , magnetohydrodynamics , magnetic field , fredholm integral equation , integral equation , plane (geometry) , flow (mathematics) , physics , boundary layer , mathematical analysis , mechanics , mathematics , classical mechanics , geometry , quantum mechanics
We investigate the magnetohydrodynamic flow (MHD) on the upper, half of a non‐conducting plane for the case when the flow is driven by the current produced by an electrode placed in the middle of the plane. The applied magnetic field is perpendicular to the plane, the flow is laminar, uniform, steady and incompressible. An analytical solution has been developed for the velocity field and the induced magnetic field by reducing the problem to the solution of a Fredholm's integral equation of the second kind, which has been solved numerically. Infinite integrals occurring in the kernel of the integral equation and in the velocity and magnetic field were approximated for large Hartmann numbers by using Bessel functions. As the Hartmann number M increases, boundary layers are formed near the non‐conducting boundaries and a parabolic boundary layer is developed in the interface region. Some graphs are given to show examples of this behaviour.