Solving inhomogeneous magnetohydrodynamic flow equations in an infinite region using boundary element method

In this paper, the inhomogeneous magnetohydrodynamic (MHD) flow equations are solved in an infinite region (upper half plane). Change of variables is done to find homogeneous equations equivalent to inhomogeneous MHD flow equations, and then these homogeneous equations are solved using boundary element method (BEM) for three types of boundary conditions. The proposed boundary element method provides the solution of MHD flow equations in the infinite region for arbitrary angles of magnetic field radiation on the fluid surface and high Hartmann numbers. This demonstrates the effectiveness, efficiency, and robustness of the proposed boundary element method. Finally, by providing some numerical examples, the effect of radiation angle changing of the magnetic field on the fluid surface and high Hartmann numbers have been shown for solving the intended problem in three types of boundary conditions.