[en] A new science that treats three-dimensional phenomena in MHD generators is introduced. Parabolized Navier-Stokes equations are solved together with the kappa-epsilon two-equation turbulence model and with the electrodynamic equations. The rational Runge-Kutta method is used along the main flow direction and the Galerkin finite element method in the perpendicular cross section. It is shown that, even when the MHD interaction is still low, three-dimensional effects become clear near open- and short-loading conditions in the case of a diagonal-type generator, since a relatively large J(x) component is induced. 9 references