The flow of a conducting fluid under the influence of an imposed electric and magnetic field is analysed using Computational Fluid Dynamic techniques. A finite volume method is used to solve the Navier-Stokes equations for the fluid flow variables. The Lorentz force is obtained by solving Maxwell's equations via the same finite volume technique. Velocity profiles for a two dimensional flow are predicted for a number of different Hartmann numbers and compare well to the analytic solution. The more complex case of three dimensional flow is also modelled and demonstrates that the model is able to predict the Hartmann layer and high velocity regions which occur near walls.
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