Abstract The magnitude of the current is numerically computed for a mass transfer limited electrochemical reaction at a plane electrode in a rectangular channel under conditions of steady state, fully developed laminar flow. The procedure is based on the backward implicit finite difference numerical method, applied to solve the differential equation governing convective diffusion. The, convergence and error limits inherently present in the procedure are evaluated over a wide range of conditions, and compared with results obtained for the explicit finite difference method and the implicit Crank-Nicolson method. The backward implicit method is highly advantageous, for solving problems of the type investigated. Very good agreement is obtained with other experimental and semi-empirical studies over a wide range of operational parameters of the channel electrode.