A solution of two-dimensional magnetohydrodynamic flow using the finite element method

A numerical code based on the finite element method (FEM) was developed to solve the two-dimensional, steady-state magnetohydrodynamic (MHD) flow in a rectangular channel. In order to apply the FEM, the Galerkin weak formulation was used. In this analysis, in contrast with the previous works, the thickness of the duct wall is taken into account and the results are compared to those obtained in the limit case when the thickness is much smaller than a characteristic dimension of the duct. In this case, convergence behaviour of several iterative methods, for high Hartmann numbers, was also investigated