Magnetohydrodynamic flow constructions with fundamental solutions

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Abstract
In this paper steady flows of an incompressible, viscous, electrically conducting fluid are constructed from fundamental solutions of magnetohydrodynamics in which the applied magnetic field is parallel to the velocity at infinity. The flat plate and the sphere are considered as examples, and approximate solutions are presented for the limiting cases of large and small Reynolds and magnetic Reynolds numbers. The effects of currents in the body are also considered, and it is found that unless the magnetic Prandtl number is larger than unity, currents in the body have negligible effect on the flow.

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