Mass transfer processes in an electrochemical system can be strongly influenced by an applied external magnetic field. A simplified model to characterize this influence in diffusion controlled regime is proposed. The presence of a supporting electrolyte in excess in the bath is the major simplifying hypothesis for the electric current calculation. Moreover, the interface reaction is supposed to be sufficiently fast so that the wall current density, proportional to the concentration wall gradient of the active species, controls the velocity distribution via the electromagnetic forces. The problem is then characterized by a strong coupling between the species transport equation and the Navier Stokes equation. The model is applied to numerically simulate magnetically induced flow of electrolyte in a short duct. The results are found to compare favorably with available experimental data obtained by Aogaki et al.