Both the strongly implicit procedure and the alternating direction implicit finite difference (ADI) technique are used to simulate mass transport to a microdisc electrode located in a channel flow, taking account of diffusion in three dimensions and the parabolic laminar convective flow over the electrode surface. The effect of the latter on the shape of the disc diffusion layer is qualitatively identified. The flow rate dependence of the transport-limited disc current is predicted and shown to be in quantitative agreement with experiments conducted on the oxidation of ferrocene in acetonitrile solution.