In this article the constant and the continuous linear boundary elements methods (BEMs) are given to obtain the numerical solution of the coupled equations in velocity and induced magnetic field for the steady magneto-hydrodynamic (MHD) flow through a pipe of rectangular and circular sections having arbitrary conducting walls. In recent decades, the MHD problem has been solved using some variations of BEM for some special boundary conditions at moderate Hartmann numbers up to 300. In this paper we develop this technique for a general boundary condition (arbitrary wall conductivity) at Hartmann numbers up to 105 by applying some new ideas. Numerical examples show the behavior of velocity and induced magnetic field across the sections. Results are also compared with the exact values and the results of some other numerical methods. © 2012 Elsevier Inc.
Hosseinzadeh, H., Dehghan, M., & Mirzaei, D. (2013). The boundary elements method for magneto-hydrodynamic (MHD) channel flows at high Hartmann numbers. Applied Mathematical Modelling, 37(4), 2337–2351. https://doi.org/10.1016/j.apm.2012.05.020