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Magnetohydrodynamic flow in an infinite channel. (English) Zbl 0597.76116
Summary: The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in an infinite channel, under an applied magnetic field has been investigated. The MHD flow between two parallel walls is of considerable practical importance because of the utility of induction flowmeters. The walls of the channel are taken perpendicular to the magnetic field and one of them is insulated, the other is partly insulated, partly conducting.
An analytical solution has been developed for the velocity field and magnetic field by reducing the problem to the solution of a Fredholm integral equation of the second kind, which has been solved numerically. Solutions have been obtained for Hartmann numbers M up to 200. All the infinite integrals obtained are transformed into finite integrals which contain modified Bessel functions of the second kind. So, the difficulties associated with the computation of infinite integrals with oscillating integrands which arise for large M have been avoided. It is found that, as M increases, boundary layers are formed near the non- conducting boundaries and in the interface region for both velocity and magnetic fields, and a stagnant region in front of the conducting boundary is developed for the velocity field. Selected graphs are given showing these behaviours.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
65R20 Numerical methods for integral equations
76M99 Basic methods in fluid mechanics
45B05 Fredholm integral equations
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