A new second order theoretical model of the combined interaction of externally applied electric and magnetic fields and viscous incompressible fluid flows has been rewritten as a system of first order partial differential equations. The system was solved using least-squares finite element model on an unstructured grid. The numerical algorithm is very stable and accurate. The accuracy was confirmed by comparing the numerical results against simple analytical results for a magnetohydrodynamic flow between two parallel isothermal infinite stationary plates. Effects of Joule heating and reverse pressure gradient are correctly predicted with this algorithm which is applicable to arbitrary planar flow configurations.

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