A two dimensional, along the channel, non-isothermal, two-phase flow, anode partial flooding model was developed to investigate the effects of relative humidity, stoichiometric flow ratio and channel length, as well as their interactive influence, on the performance of a PEM (proton exchange membrane) fuel cell. Liquid water formation and transport at the anode due to the condensation of supersaturated anode gas initiated by hydrogen consumption was considered. The model considered the heat source/sink in terms of electrochemical reaction, Joule heating and latent heat due to water phase-transfer. The non-uniform temperature distributions inside the MEA (membrane electrode assembly) and channels at various stoichiometric flow ratios were demonstrated. The Peclet number was used to evaluate the contributions of advection and diffusion on liquid water and heat transport. Results indicated that higher anode relative humidity is required to the improved cell performance. As the decrease in the anode relative humidity and increase in channel length, the optimal cathode relative humidity was increased. The initial increase in stoichiometric flow ratio improved the limiting current densities. However, the further increases led to limited contributions. The Peclet number indicated that the liquid water transport through the electrode was mainly determined by the capillary diffusion mechanism. (C) 2016 Elsevier Ltd. All rights reserved.