A two-dimensional along-the-channel CFD (computational fluid dynamic) model, coupled with a two-phase flow model of liquid water and gas transport for a PEM (proton exchange membrane) fuel cell is described. The model considers non-isothermal operation and thus the non-uniform temperature distribution in the cell structure. Water phase-transfer between the vapour, liquid water and dissolved phase is modelled with the combinational transport mechanism through the membrane. Liquid water saturation is simulated inside the electrodes and channels at both the anode and cathode sides. Three types of models are compared for the HOR (hydrogen oxidation reaction) and ORR (oxygen reduction reaction) in catalyst layers, including Butler-Volmer (B-V), liquid water saturation corrected B-V and agglomerate mechanisms. Temperature changes in MEA (membrane electrode assembly) and channels due to electrochemical reaction, ohmic resistance and water phase-transfer are analysed as a function of current density. Nonlinear relations of liquid water saturations with respect to current densities at both the anode and cathode are regressed. At low and high current densities, liquid water saturation at the anode linearly increases as a consequence of the linear increase of liquid water saturation at the cathode. In contrast, exponential relation is found to be more accurate at medium current densities. (C) 2016 Elsevier Ltd. All rights reserved.