Numerical simulations have been performed to analyze the electric current density in an aqueous solution of CuSO4, flowing in a two-dimensional channel with finite electrodes placed symmetrically on opposite sides. A Butler-Volmer law is chosen as a boundary condition on the electrodes for current densities below the limiting current. At limiting current density, two modified boundary conditions at the cathode are derived. For 0 less than or equal to Pe less than or equal to 25000, comparisons are made with results of other studies, and the agreement is excellent for large values of Pe but differ for Pe similar to 1. For small values of the applied voltage and large values of Pe, a semi-analytic solution of the electric potential is derived.