Mathematical Modeling of Transport Phenomena in Polymer Electrolyte and Direct Methanol Fuel Cells

This thesis deals with modeling of two types of fuel cells: the polymer electrolyte fuel cell (PEFC) and the direct methanol fuel cell (DMFC), for which we address four major issues: a) mass transport limitations; b) water management (PEFC); c) gas management (DMFC); d) thermal management. Four models have been derived and studied for the PEFC, focusing on the cathode. The first exploits the slenderness of the cathode for a two-dimensional geometry, leading to a reduced model, where several nondimensional parameters capture the behavior of the cathode. The model was extended to three dimensions, where four different flow distributors were studied for the cathode. A quantitative comparison shows that the interdigitated channels can sustain the highest current densities. These two models, comprising isothermal gasphase flow, limit the studies to (a). Returning to a two-dimensional geometry of the PEFC, the liquid phase was introduced via a separate flow model approach for the cathode. In addition to conservation of mass, momentum and species, the model was extended to consider simultaneous charge and heat transfer for the whole cell. Different thermal, flow fields, and hydrodynamic conditions were studied, addressing (a), (b) and (d). A scale analysis allowed for predictions of the cell performance prior to any computations. Good agreement between experiments with a segmented cell and the model was obtained. A liquid-phase model, comprising conservation of mass, momentum and species, was derived and analyzed for the anode of the DMFC. The impact of hydrodynamic, electrochemical and geometrical features on the fuel cell performance were studied, mainly focusing on (a). The slenderness of the anode allows the use of a narrow-gap approximation, leading to a reduced model, with benefits such as reduced computational cost and understanding of the physical trends prior to any numerical computations. Adding the gas-phase via a multiphase mixture approach, the gas management (c) could also be studied. Experiments with a cell, equipped with a transparent end plate, allowed for visualization of the flow in the anode, as well as validation of the two-phase model. Good agreement between experiments and the model was achieved. Descriptors: Fuel cell; DMFC; PEFC; one-phase; two-phase; model; visual cell; segmented cell; scale analysis; asymptotic analysis.