Magnetohydrodynamic flows in coupled rectangular channels are numerically investigated under an external, horizontally applied magnetic field. The flows are driven by constant pressure gradients in the channels, which are separated with a thin partly insulating and partly conducting barrier. A direct boundary element formulation is utilized to solve these two-dimensional steady, convection-diffusion type coupled partial differential equations in terms of velocity and induced magnetic fields. The resulting system of linear equations is solved by reordering the unknown vector due to the insertion of the coupled boundary conditions along the conducting partition of the barrier. This study aims to examine the consequence of high values of Hartmann number on the velocity and induced magnetic fields. Further, the alteration in flow behavior due to the variations in the length of the conducting partition along the thin barrier and in the value of ratio of the pressure gradients of two channels is also analyzed. (C) 2012 Elsevier Ltd. All rights reserved.