BOUNDARY-ELEMENT METHOD SOLUTION OF MHD FLOW IN A RECTANGULAR DUCT

The magnetohydrodynamic (MHD) flow of an incompressible, viscous, elec trically conducting fluid in a rectangular duct with an external magne tic field applied transverse to the flow has been investigated. The wa lls parallel to the applied magnetic field are conducting while the ot her two walls which are perpendicular to the field are insulators. The boundary element method (BEM) with constant elements has been used to cast the problem into the form of an integral equation over the bound ary and to obtain a system of algebraic equations for the boundary unk nown values only. The solution of this integral equation presents no p roblem as encountered in the solution of the singular integral equatio ns for interior methods. Computations have been carried out for severa l values of the Hartmann number (1 less-than-or-equal-to M less-than-o r-equal-to 10). It is found that as M increases, boundary layers are f ormed close to the insulated boundaries for both the velocity and the induced magnetic field and in the central part their behaviours are un iform. Selected graphs are given showing the behaviours of the velocit y and the induced magnetic field.