Summary
The laminar flow of an incompressible, viscous, electrically conducting fluid impinging normal to a plane in the presence of a transverse magnetic field is investigated. Using finite-differences and quasilinearization, an exact numerical solution is presented which takes into account the asymptotic boundary condition. It is demonstrated that iff denotes the dimensionless stream function, the value off″(0) increases monotonically withM, the Hartmann number, where a prime denotes the derivative normal to the plane.
This conclusion is supported by deriving a perturbation solution valid for smallM. Also, an analytical solution is obtained valid for largeM. Finally, an approximate solution is given which is simple and sufficiently accurate for the entire range of values ofM.
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Ariel, P.D. Hiemenz flow in hydromagnetics. Acta Mechanica 103, 31–43 (1994). https://doi.org/10.1007/BF01180216
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DOI: https://doi.org/10.1007/BF01180216