A two-dimensional, along-the-channel, two-phase flow, non-isothermal model is developed which represents a low temperature proton exchange membrane (PEM) fuel cell. The model describes the liquid water profiles and heat distributions inside the membrane electrode assembly (MEA) and gas flow channels as well as effectiveness factors of the catalyst layers. All the major transport and electrochemical processes are taken into account except for reactant species crossover through the membrane. The catalyst layers are treated as spherical agglomerates with inter-void spaces, which are in turn covered by ionomer and liquid water films. Liquid water formation and transport at the anode is included while water phase-transfer between vapour, dissolved water and liquid water associated with membrane/ionomer water uptake, desorption and condensation/evaporation are considered. The model is validated by experimental data and used to numerically study the effects of electrode properties (contact angel, porosity, thickness and platinum loading) and channel geometries (length and depth) on liquid water profiles and cell performance. Results reveal low liquid water saturation with large contact angle, low electrode porosity and platinum loading, and short and deep channel. An optimal channel length of 1 cm was found to maximise the current densities at low cell voltages. A novel channel design featured with multi-outlets and inlets along the channel was proposed to mitigate the effect of water flooding and improve the cell performance.