In recent years, many researches were promoted to find new efficient and green energy sources. Fuel cell is an attractive power generatuion device which is transformed chemical energy to electricity directly. This technique was established based on hydrogen energy. The energy shortage crisis in the world and production of green house gases reduces fossil fuel demand. The hydrogen can eliminate fossil fuel consumption and global warming. Since then, many researchers contributed in energy production of hydrogen in recent decade. In addition, various power systems were developed besde on energy of hydrogen rections [1], [2].

The initial fuel cell was introduced by Grove in 1843 [3]. The first work was developed on platinum electrodes and sulfuric acide that acts as electrolite. The electricity was obtained by reacting hydrogen and oxygen molecules in stochiometric rate. The water and vapor are two byproducts which may be produced and discharged through vent or drain. Since then, the solid and carbonate fuel cell were developed to promote the current density and efficiency of fuel cell. Low efficiency, safety problems and enviromental issues conducted the researches to new generation of fuel cells that was called Proton Exchange Membrane Fuel Cell (PEMFC). The temperature range 90ºC-180ºC was mentioned in various refrences. This technlogy is more viable for portable applications such as automoiles and space capsules.

In order to gain higher efficiency, differnt parameters were studied that help to commercialize the fuel cells.Temperature, electrolite, membrane charactristics and particularly catalyst layer, affect efficiency of fuel cell. The fuel cells are connected together in series configuration that builds a fuel cell stack. A stack obtains required voltage and current continously in the presence of H2 and O2.

Modeling of fuel cell systems plays a crucial role in improving the design, manufacturing, and operation of these systems. The use of numerical and analytical models leads to a reduction in experimental costs, enhancement of efficiency, and acceleration of fuel cell technology development. Reliable models must possess sufficient accuracy and robustness to predict fuel cell behavior under various operating conditions. An appropriate model should be capable of simulating fuel cell performance over a wide range of operating conditions, and even relatively simple models can exhibit significant predictive capability.

Models play a fundamental role in fuel cell development, as they provide deeper insight into the effects of key parameters on the performance of individual cell components as well as the overall system. Steady-state models describe fuel cell performance at a specific operating point, typically under constant temperature and reactant pressure, and are mainly used to predict experimental results. In contrast, dynamic models are employed to predict the transient behavior of fuel cells under time-varying operating conditions. These models are particularly useful for analyzing start-up and shutdown processes and for optimizing system response to load variations.

Siegel [4] presented a comprehensive review of published fuel cell models, addressing issues such as grid resolution, computational tools, and simulation time. In this study, one-dimensional, two-dimensional, and three-dimensional models were examined, and it was shown that one- and two-dimensional models are sufficient for many analyses. In addition, various modeling strategies, implementation approaches, as well as their advantages and limitations were discussed, and an overview of available fuel cell modeling software was provided.

In the context of developing new membrane materials for fuel cells, numerous studies have employed computational approaches. Cheddie and Munroe [5] developed a three-dimensional model to investigate the performance of a fuel cell employing a polybenzimidazole membrane, which is more advanced than one- and two-dimensional models. This type of membrane enables operation at higher temperatures, leading to increased reaction rates and reduced adverse effects of catalyst poisoning caused by carbon monoxide. The modeling results showed good agreement with experimental data.

One of the important applications of three-dimensional modeling in fuel cells is the optimization of flow channel design. Chen et al. [6] analyzed and simulated a wavy flow channel and validated their results using experimental data and the findings reported by Kaiser et al. [7]. The presence of obstacles in flow channels induces forced mixing regions and improves gas transport toward the Gas Diffusion Layer (GDL). The results demonstrated that wavy flow channels provide superior fuel cell performance compared to straight channels. Modeling also enables the identification of faults and deficiencies during simulations. Such models can distinguish defective regions from the actual fuel cell behavior and prevent numerical errors from being misinterpreted as real performance degradation. These approaches are particularly important for predicting fuel cell behavior under sudden failure conditions [8].

Other studies have focused on cold-start conditions of fuel cells. At very low temperatures, fuel cell performance is severely affected, and phenomena such as ice formation and reduced membrane conductivity become significant. The results indicate a direct relationship between cathode gas humidity and ice formation, with the highest ice accumulation occurring in the cathode catalyst layer. Furthermore, increasing the gas flow rate can mitigate the adverse effects of cold-start operation.

Water formation and transport in flow channels and Gas Diffusion Layers (GDLs) represent key aspects of fuel cell performance. Numerous models have been developed to predict water formation and two-phase flow behavior. In some models, water droplets are represented as spherical particles suspended in the gas flow, which is a reasonable assumption at low current densities; however, at higher current densities, this assumption may lead to deviations from experimental observations [9].

Modeling of cooling channels is also of great importance, particularly in simulations of fuel cell stacks where significant heat generation occurs. Proper temperature control prevents component degradation and ensures long-term system performance. Some studies have utilized system-level models to design effective control strategies for coolant temperature regulation.

Moreover, innovative flow field designs such as interdigitated, serpentine, and radial channels have been investigated using Computational Fluid Dynamics (CFD) methods. The results of these studies indicate that modifying flow channel geometry can lead to a more uniform current density distribution, reduced pressure drop, and ultimately improved overall fuel cell performance.

Overall, the review of previous studies demonstrates that numerical modeling—particularly CFD-based approaches—is a powerful tool for the analysis, design, and optimization of fuel cells, providing deep insight into mass and heat transfer phenomena, electrochemical reactions, and transient system behavior [10].

This PEM fuel cell model was solved using ANSYS FLUENT 15.0 software. The hexahederal mesh was selected in order to descritize the fuel cell geometry. Sensitivity analysis was carried out to test the accuracy of the proposed model. The model was solved for different mesh number and iteration. Velocity vector residual, energy residual, mass concentration residual, electrical potential residual and voltage residual were measured, compared and depicted in various graphs in Fig. 2. The results show that the best convergency was obtained at 500 iteration and 224280 mesh number. Although the precision for iteration number =200 is acceptable (single precision order) but due to the low run time, the results are reported at iteration number 500.

4.01E-04 5.01E-04 3.51E-04 100 4.01E-04 200 3.01E-04 200 500 500 3.01E-04 2.51E-04 2.01E-04 2.01E-04

The molar concentration of hydrogen from the anode flow channel to the anode catalyst layer decreases.Molar concentration of oxygen from the cathode flow channel to the catalyst layer decreases.Also, due to the consumption of oxygen, its concentration along the fuel celldecreases.Note that the overall reaction in fuel cells is associated with the production of the water and heat, the molar concentration of water and temperature raise in the cathode catalyst layer is high and the temperature achieve to 346 K. The amount of entropy and enthalpy of both the anode and cathode side also increases.

All aspects of the research and manuscript preparation were carried out by the author. The author has read and approved the final version of the manuscript.

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This study does not involve any research conducted on human participants or animals.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

All data are included in the text.

The authors declare no conflict of interest.