A three-dimensional model, considering mass, momentum, energy and charge conservation, was developed and the equations solved to describe the physico-chemical phenomena occurring within a single, micro-tubular hollow fibre solid oxide fuel cell (HF-SOFC). The model was used to investigate the spatial distributions of potential, current and reactants in a 10 mm long HF-SOFC. The predicted effects of location of current collectors, electrode conductivities, cathode thickness and porosity were analysed to minimise the ranges of current density distributions and maximise performance by judicious design. To decrease the computational load, azimuthal symmetry was assumed to model 50 and 100 mm long reactors in 2-D. With connectors at the same end of the HF-SOFC operating at a cell voltage of 0.5 V and a mean 5 kA m(-2), axial potential drops of ca. 0.14V in the cathode were predicted, comparable to the cathode activation overpotential. Those potential drops caused average current densities to decrease from ca. 6.5 to ca.1 kA m(-2) as HF-SOFC length increased from 10 to 100 mm, at which much of the length was inactive. Peak power densities were predicted to vary from 3.8 to <2.5 kW m(-2), depending on the location of the current collectors; performance increased with increasing cathode thickness and decreasing porosity. (C) 2010 Elsevier Ltd. All rights reserved.