Summary
The nonlinear partial differential equation of motion for an incompressible fluid flowing over a flat plate under the influence of a magnetic field and a pressure gradient, and with or without fluid injection (or ejection) through the plate is transformed to a nonlinear, third order ordinary differential equation by using a stream function and a similarity transformation.
The necessary boundary conditions are developed for flow with and without fluid injection (or ejection), and an example is presented to illustrate the solution to the flow problem.
The controlling equation reduces to the well known Falkner-Skan equation when the magnetic field is zero, and if additionally the pressure gradient is zero, the equation reduces to the Blasius equation.
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Ibid.
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Cobble, M.H. Magnetofluiddynamic flow with a pressure gradient and fluid injection. J Eng Math 11, 249–256 (1977). https://doi.org/10.1007/BF01535969
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DOI: https://doi.org/10.1007/BF01535969