In this paper, we investigate the flow of a viscous, Incompressible, electrically conducting fluid through a rectangular duct in the presence of a magnetic field, when one of the boundaries perpedicular to the magnetic field is partly conducting and partly Insulating, by a modified Boundary Integral Method.

Three problems are considered (i) flow through an infinite channel, (ii) flow through a rectangular duct when the conducting part is symmetrically situated, and (iii) flow through a rectangular duct when the conducting part is arbltrarily positioned.

Such problems have been studied before by asymptotic means for large values of M, the Hartmann number. Hoverer, the present modification of the Boundary Integral Method renders the problem computationally efficient and provides a reliable numerical solution for all values of M. For large M, our coputation time decreases significantly.