A numerical, asymptotic and analytical study of the steady laminar MHD flow driven by a rotating disk situated at the top of a cylinder, filled with a liquid metal, is presented. The governing equations in cylindrical coordinates are solved by a finite volume method. The effect of an axial magnetic field on the flow is investigated for an aspect ratio, H/R, equal to 1. The magnetic Reynolds number is assumed to be small whereas the interaction parameter, N, is large compared to unity. This allows to derive asymptotic results for the flow solution which are in good agreement with the numerical calculations. The effect of the top, bottom and vertical walls conductivity on the flow is studied.