Author	Title / Keywords	Abstract	Journal
H. Meng	A three-dimensional mixed-domain PEM fuel cell model with fully coupled transport phenomena PEM fuel cell; Mixed-domain model; Interfacial boundary condition; Fully-coupled transport phenomena; Water content	A three-dimensional mixed-domain PEM fuel cell model with fully-coupled transport phenomena has been developed in this paper. In this model, after fully justified simplifications, only one set of interfacial boundary conditions is required to connect the water content equation inside the membrane and the equation of the water mass fraction in the other regions. All the other conservation equations are still solved in the single-domain framework. Numerical results indicate that although the fully-coupled transport phenomena produce only minor effects on the overall PEM fuel cell performance, i.e. average current density, they impose significant effects on current distribution, net water transfer coefficient, velocity and density variations, and species distributions. Intricate interactions of the mass transfer across the membrane, electrochemical kinetics, density and velocity variations, and species distributions dictate the detailed cell performances. Therefore, for accurate PEM fuel cell modeling and simulation, the effects of the fully-coupled transport phenomena could not be neglected.	J. Power Sources 2007, 164, 688-696
A. Bı yı koğ lu	Review of proton exchange membrane fuel cell models Proton exchange membrane fuel cells; Fuel cell modeling; Computational modeling	In the present study, fuel cell models are described in the light of the open literature. Proton exchange membrane fuel cell (PEMFC) components and its functions are introduced and explained briefly. The state of the art of fuel cell modeling is presented. Comparisons of both modeling and experimental studies are also presented in tables. Governing equations and assumptions are briefly reviewed and presented for PEMFCs.	Int. J. Hydrogen Energy 2005, 30, 1181-1212
H. Meng & C.Y. Wang	Large-scale simulation of polymer electrolyte fuel cells by parallel computing Computational fuel cell dynamics (CFCD); Parallel computing; Water management; Polymer electrolyte fuel cell; Low humidity operation	A three-dimensional, electrochemical–transport fully coupled numerical model of polymer electrolyte fuel cells (PEFC) is introduced. A complete set of conservation equations of mass, momentum, species, and charge are numerically solved with proper account of electrochemical kinetics and water management. Such a multi-physics model combined with the need for a large numerical mesh results in very intense computations that require parallel computing in order to reduce simulation time. In this study, we explore a massively parallel computational methodology for PEFC modeling, for the 8rst time. The physical model is validated against experimental data under both fully and low-humidi8ed feed conditions. Detailed results of hydrogen, oxygen, water, and current distributions in a PEFC of 5-channel serpentine ;ow-8eld are discussed. Under the fully humidi8ed condition, current distribution is determined by the oxygen concentration distribution. Cell performance decreases in low-humidity inlet conditions, but good cell performance can still be achieved with proper water management. Under low-humidity conditions, current distribution is dominated by the water distribution at high cell voltages. When the cell voltage is low, the local current density initially increases along the ;ow path as the water concentration rises, but then starts to decrease due to oxygen consumption. Under both fully and low-humidi8ed conditions, numerical results reveal that the ohmic losses due to proton transport in anode and cathode catalyst layers are comparable to that in the membrane, indicating that the catalyst layers cannot be neglected in PEFC modeling.	Chem. Eng. Sci. 2004, 59, 3331-3343
P.T. Nguyen; T. Berning & N. Djilali	Computational model of a PEM fuel cell with serpentine gas flow channels PEM fuel cells; Fuel cell modeling; Overpotential; Simulation; CFD	Athree-dimensional computational fluid dynamics model of a PEM fuel cell with serpentine flowfield channels is presented in this paper. This comprehensive model accounts for the major transport phenomena in a PEM fuel cell: convective and diffusive heat and mass transfer, electrode kinetics, and potential fields. A unique feature of the model is the implementation of a voltage-to-current (VTC) algorithm that solves for the potential fields and allows for the computation of the local activation overpotential. The coupling of the local activation overpotential distribution and reactant concentration makes it possible to predict the local current density distribution more accurately. The simulation results reveal current distribution patterns that are significantly different from those obtained in studies assuming constant surface overpotential. Whereas the predicted distributions at high load show current density maxima under the gas channel area, low load simulations exhibit local current maxima under the collector plate land areas.	J. Power Sources 2004, 130, 149-157
S. Shimpalee; S. Greenway; D. Spuckler & J.W. Van Zee	Predicting water and current distributions in a commercial-size PEMFC PEM fuel cell; CFD modeling; Parallel computing; STAR-CD; Flow-field design; Water management; Large-scale PEMFC	Many researchers have experimentally studied small (10–50 cm2), single cell PEMFC systems to understand the behavior and electrochemistry of PEMFC. Also, three-dimensional electrochemical models have been used to predict the distributions of current, temperature, and species mole fractions as a function of the operating conditions and geometry of small cells and these predictions have been compared with experimental data. However, the commercial viability of PEMFC systems depends on understanding the mass transport and electrochemistry of large-scale electrodes with reacting area on the order of 200–600 cm2 and numerical investigation of PEMFCs of this size have been effectively impossible without the recent advances in parallel computation and processor speed. This paper applies a parallelized three-dimensional computational fluid dynamics (CFD) model to a 480 cm2 PEMFC flow-field selected from US patent literature to demonstrate that analysis of large-scale cells is possible. The distributions of pressure, temperature, and electrochemical variables for stationary and automotive operating conditions are examined. Using parallel computing techniques, the computational time is shown to be significantly reduced by increasing the number of processors while maintaining less than 1% error in mass balance.	J. Power Sources 2004, 135, 79-87
C.Y. Wang	Fundamentals models for fuel cell engineering		Chem. Rev. 2004, 104, 47274766
A.Z. Weber & J. Newman	Modeling transport in polymer-electrolyte fuel cells		Chem. Rev. 2004, 104, 4679-4726
K.Z. Yao; K. Karan; K.B. McAuley; P. Oosthuizen; B. Peppley & T. Xie	A review of mathematical models for hydrogen and direct methanol polymer electrolyte membrane fuel cells Polymer Electrolyte Membrane; Fuel Cell; Direct Methanol Fuel Cell; Mathematical Modeling	This paper presents a review of the mathematical modeling of two types of polymer electrolyte membrane fuel cells: hydrogen fuel cells and direct methanol fuel cells. Models of single cells are described as well as models of entire fuel cell stacks. Methods for obtaining model parameters are briefly summarized, as well as the numerical techniques used to solve the model equations. Effective models have been developed to describe the fundamental electrochemical and transport phenomena occuring in the diffusion layers, catalyst layers, and membrane. More research is required to develop models that are validated using experimental data, and models that can account for complex two-phase flows of liquids and gases.	Fuel Cells 2004, 4, 3-29
D. Natarajan & T. Van Nguyen	Three-dimensional effects of liquid water flooding in the cathode of a PEM fuel cell Fuel cell; Conventional gas distributor; Interdigitated gas distributor; Cathode; Electrode; Mathematical model; Pseudo-three-dimensional	A two-dimensional model available in the literature for conventional gas distributors was expanded to account for the dimension along the length of the channel. The channel was discretized into control volumes in series that were treated as well mixed. An iterative solution procedure was incorporated in each control volume to determine the average current density and the corresponding oxygen consumption and water generation rates. Downstream channel concentrations were calculated based on stoichiometric flow rates and the solution obtained from the preceding control volumes. Comparison of the model results with experimental data and the existing two-dimensional model showed that accounting for the oxygen concentration variations along the channel and its effect on the current density is critical for accurately predicting the cathode performance. Variations in the current density along the channel were strongly influenced by the changes in oxygen concentration caused by consumption due to reaction and dilution caused by water evaporation. Operating parameters that facilitated better water removal by evaporation like higher temperature and stoichiometric flow rates and lower inlet stream humidity resulted in higher net current. Operating conditions that resulted in minimal loss in oxygen concentrations resulted in a more uniform current density distribution along the channel.	J. Power Sources 2003, 115, 66-80
L. Wang; A. Husar; T. Zhou & H. Liu	A parametric study of PEM fuel cell performances Fuel cells; PEM fuel cells	The effects of different operating parameters on the performance of proton exchange membrane (PEM) fuel cell have been studied experimentally using pure hydrogen on the anode side and air on the cathode side. Experiments with different fuel cell operating temperatures, different cathode and anode humidi1cation temperatures, different operating pressures, and various combinations of these parameters have been carried out. The experimental results are presented in the form of polarization curves, which show the effects of the various operating parameters on the performance of the PEM fuel cell. The possible mechanisms of the parameter effects and their interrelationships are discussed. In addition, a comprehensive three-dimensional fuel cell model is briefly presented and the modeling results are compared with our experimental data. The comparison shows good agreements between the modeling results and the experimental data.	Int. J. Hydrogen Energy 2003, 28, 1263-1272
T. Berning; D.M. Lu & N. Djilali	Three-dimensional computational analysis of transport phenomena in a PEM fuel cell PEM fuel cells; PEFC; Fuel cell modelling; CFD	A comprehensive non-isothermal, three-dimensional computational model of a polymer electrolyte membrane (PEM) fuel cell has been developed. The model incorporates a complete cell with both the membrane-electrode-assembly (MEA) and the gas distribution flow channels. With the exception of phase change, the models accounts for all major transport phenomena. The model is implemented into a computational fluid dynamics code, and simulations are presented with an emphasis on the physical insight and fundamental understanding afforded by the detailed three-dimensional distribution of reactant concentrations, current densities, temperature and water fluxes. The results show that significant temperature gradients exist within the cell, with temperature differences of several degrees K within the MEA. The three-dimensional nature of the transport is particularly pronounced under the collector plates land area and has a major impact on the current distribution and predicted limiting current density.	J. Power Sources 2002, 106, 284-294
L. You & H. Liu	A two-phase flow and transport model for the cathode of PEM fuel cells Two-phase flow; Porous electrode; Proton exchange membrane (PEM); Fuel cells; Mathematical model; Simulation; Water and thermal management	A unified two-phase flow mixture model has been developed to describe the flow and transport in the cathode for PEM fuel cells. The boundary condition at the gas diffuser/catalyst layer interface couples the flow, transport, electrical potential and current density in the anode, cathode catalyst layer and membrane. Fuel cell performance predicted by this model is compared with experimental results and reasonable agreements are achieved. Typical two-phase flow distributions in the cathode gas diffuser and gas channel are presented. The main parameters influencing water transport across the membrane are also discussed. By studying the influences of water and thermal management on twophase flow, it is found that two-phase flow characteristics in the cathode depend on the current density, operating temperature, and cathode and anode humidification temperatures.	Int. J. Heat Mass Tran. 2002, 45, 2277-2287
P. Costamagna	Transport phenomena in polymeric membrane fuel cells Fuel cells; Chemical reactors; Electrochemistry; Energy; Mathematical modelling; Transport processes	Transport phenomena of mass, energy, momentum and electrical charges play a significant role in proton exchange membrane fuel cells (PEMFCs). In this study the transport and balance equations are the basis of a simulation model which allows the evaluation of the distribution of the physico-chemical parameters within the structure of a PEMFC reactor. Model validation is presented; the validated model is then used to investigate the behaviour of the reactor, with particular attention to critical operating conditions. Critical conditions arise in a number of cases: flooding, membrane drying and degradation due to temperature peaks are discussed in this paper.	Chem. Eng. Sci. 2001, 56, 323-332
S. Dutta; S. Shimpalee & J.W. Van Zee	Numerical prediction of mass-exchange between cathode and anode channels in a PEM fuel cell	A numerical model is developed to predict the mass flow between channels in a Polymer Electrolyte Membrane (PEM) fuel cell with a serpentine flow path. The complete three-dimensional Navier-Stokes equations with multispecies mixture are solved and electro-chemical reactions are modeled as mass source/sink terms in the control volumes. The results indicate that flow distribution in both anode and cathode channels are significantly affected by the mass consumption patterns on the Membrane Electrode Assembly (MEA). The water transport is governed by both electroosmosis and diffusion processes. Further, the overall pressure drop is less than that expected for a regular straight channel flow.	Int. J. Heat Mass Tran. 2001, 44, 2029-2042
A. Rowe & X. Li	Mathematical modeling of proton exchange membrane fuel cells Proton exchange membrane (PEM); Electrodes; Catalyst layers; Fuel cells; Modeling		J. Power Sources 2001, 102, 82-96
Z.H. Wang; C.Y. Wang & K.S. Chen	Two-phase flow and transport in the air cathode of proton exchange membrane fuel cells Two-phase transport; PEM fuel cells; Analytical modeling; Numerical simulation; Water management	Two-phase flow and transport of reactants and products in the air cathode of proton exchange membrane (PEM) fuel cells is studied analytically and numerically. Single- and two-phase regimes of water distribution and transport are classified by a threshold current density corresponding to first appearance of liquid water at the membrane/cathode interface. When the cell operates above the threshold current density, liquid water appears and a two-phase zone forms within the porous cathode. A two-phase, multicomponent mixture model in conjunction with a finite-volume-based computational fluid dynamics (CFD) technique is applied to simulate the cathode operation in this regime. The model is able to handle the situation where a single-phase region co-exists with a two-phase zone in the air cathode. For the first time, the polarization curve as well as water and oxygen concentration distributions encompassing both single- and two-phase regimes of the air cathode are presented. Capillary action is found to be the dominant mechanism for water transport inside the two-phase zone of the hydrophilic structure. The liquid water saturation within the cathode is predicted to reach 6.3% at 1.4 A cm-2 for dry inlet air.	J. Power Sources 2001, 94, 40-50
E. Hontañón; M.J. Escudero; C. Bautista; P.L. Garcia_Ybarra & L. Daza	Optimisation of flow-field in polymer electrolyte membrane fuel cells using computational fluid dynamics techniques Polymer electrolyte membrane fuel cells; Gas flow distribution; Computational fluid dynamics; Grooved plate; Porous materials	The purpose of this work was the enhancement of performance of Polymer Electrolyte Membrane Fuel Cells (PEMFC) by optimising the gas flow distribution system. To achieve this, 3D numerical simulations of the gas flow in the assembly, consisting of the fuel side of the bipolar plate and the anode, were performed using a commercial Computational Fluid Dynamics (CFD) software, the ‘‘FLUENT’’ package. Two types of flow distributors were investigated: a grooved plate with parallel channels of the type commonly used in commercial fuel cells, and a porous material. The simulation showed that the permeability of the gas flow distributor is a key parameter affecting the consumption of reactant gas in the electrodes. Fuel utilisation increased when decreasing the permeability of the flow distributor. In particular, fuel consumption increased significantly when the permeability of the porous material decreased to values below that of the anode. This effect was not observed in the grooved plate, which permeability was higher than that of the anode. Even though the permeability of the grooved plate can be diminished by reducing the width of the channels, values lower than 1 mm are difficult to attain in practice. The simulation shows that porous materials are more advantageous than grooved plates in terms of reactant gas utilisation.	J. Power Sources 2000, 86, 363-368
V. Gurau; H. Liu & S. Kaka	Two-dimensional model for Proton exchange membrane fuel cells	A 2-0 mathematical model for the entire sandwich of a proton-exchange membrane fuel cell including the gas channels was developed. The self-consistent model for porous media was used for the equations describing transport phenomena in the membrane, catalyst layers, and gas difisers, while standard equations of Navier-Stokes, energy transport, continuity, and species concentrations are solved in the gas channels. A special handling of the transport equations enabled us to use the same numerical method in the unified domain consisting of the gas channels, gas difusers, catalyst layers and membrane. It also eliminated the need to prescribe arbitrary or approximate boundary conditions at the interfaces between different parts of the fuel cell sandwich. By solving transport equations, as well as the equations for electrochemical reactions and current density with the membrane phase potential, polarization curves under various operating conditions were obtained. Modeling results compare very well with experimental results from the literature. Oxygen and water vapor mole fiaction distributions in the coupled cathode gas channel-gas difiser were studied for various operating current densities. Liquid water velocity distributions in the membrane and influences of various parameters on the cell performance were also obtained.	AIChE J. 1998, 44, 2410-2422