Experiments with a laminar flow-based membrane-less fuel cell (LFMFC) have been conducted by many scientists. Choban et al. reported that the cell's performance is cathode limited. Accordingly, we have established half-cell models in our paper to study two types of redox reactions occurring at the cathode of the LFMFC without considering the fuel reaction. Our two-dimensional models are solved by using the spectral method where the eigenvalues are obtained by employing the Galerkin method. The similarity transform is applied to separate the concentrations of the oxidant and the intermediate product from their coupled boundary conditions. As shown in our results, the limiting average current density increases with the stoichiometry coefficient of electrons in the case of no intermediate product, yet the maximum electric power is independent of this coefficient. Given the concentrations of the oxidant and the intermediate product at the inlet end of the cell, we have obtained a condition increasing the current density. However, we also found the principle of generating a great deal of electric power by increasing the concentration of the intermediate product at the inlet end of the cell. (c) 2006 Elsevier B.V. All rights reserved.