Simulation through CFD of Different Flow Field Designs for Enhancing Proton Exchange Membrane Fuel Cell Performance

Simulation through CFD of Different Flow Field Designs for Enhancing Proton Exchange Membrane Fuel Cell Performance | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Simulation through CFD of Different Flow Field Designs for Enhancing Proton Exchange Membrane Fuel Cell Performance Manisha Singh Chauhan, Ajay Kumar Sharma, Arun Kumar Tiwari This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6988123/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The performance of Proton exchange membrane fuel cell, a promising energy conversion technology, is closely tied to the design of their flow fields. The Fuel cell architecture plays a critical role in distributing reactant gases, managing water, and dissipating heat within the system. For comprehension effect of FC s design on PEMFC functionality, a detailed computational model is developed to investigate four different channel shapes with the same cross-sectional area in a parallel flow field configuration. The aim of this study, to unravel the relationship between channel geometry and fuel cell behaviour, focusing on gas transport, water dynamics, thermal profiles and current density. The investigation revealed that the channel geometry significantly influences PEMFC performance. The findings highlighted the pivotal role of channel shape in modulating mass transport, thermal characteristics, and water management within the fuel cell. Notably, the square channel geometry outperformed the other designs, exhibiting a 17.20% improvement in efficiency compared to the semi-circular channel also at 0.40 V, the maximum velocities in square, rectangular, semi-circular, and triangular channels are 4.28618 m/s, 4.1856 m/s, 4.17292 m/s, and 4.78493 m/s, respectively. This is attributed to the more optimized flow profile and reduced parasitic losses in the square channel design. PEMFC s Channel shape Flow field design Cell performance Computational fluid dynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction Global energy demand is rising and greenhouse effects are escalating, creating an environmental, social, and economic crisis. This requires a shift to alternative power generation. Using renewable energy sources is crucial to reduce reliance on traditional sources [ 1 ]. Electrochemical reactions attract substantial research interest due to their excellent efficiency, low environmental effect, and enhanced stability, making them promising alternatives in the evolving energy landscape[ 2 ]. Developing fuel cells is a significant step toward addressing these challenges and providing cleaner, more sustainable energy solutions. The growing demand for unconventional energy sources is a primary driver in the expansion of fuel cell technology, which is gaining momentum as a viable solution for various applications, ranging from portable electronics to large-scale power generation. FC s efficiently convert the chemical energy of fuels into electrical energy via electrochemical reactions, offering a more direct and efficient energy conversion pathway compared to traditional heat engines that rely on combustion and thermodynamic cycles. Due to their advanced state of development and exceptional performance, PEMFC s are frequently chosen for use in automobiles and fixed power generation facilities. Flow field plates, often referred to as bipolar plates, represent a cornerstone technology in the architecture of PEMFC s , executing a multifaceted role that is pivotal to the operational efficiency and extended lifespan of the fuel cell stack[ 3 ]. Functioning as electrical conductors, these plates facilitate the crucial task of channelling electrical current generated within the fuel cell to external circuits, ensuring a seamless energy transfer for practical applications. Beyond their electrical conductivity, flow field plates lend structural fortitude to the membrane-electrode assembly, providing the necessary mechanical support to withstand operational stresses and maintain the integrity of the fuel cell structure[ 4 ]. Furthermore, the intricate design of flow channels within these plates dictates the distribution of reactant gases, such as hydrogen and oxygen (or air), to the electrodes, a process that directly influences the uniformity of the electrochemical reaction and overall cell performance[ 5 ]. An additional critical function is the management of water, a by-product of the electrochemical reaction; the flow channels are engineered to facilitate efficient water removal, preventing flooding of the electrodes and ensuring optimal gas diffusion to the reaction sites[ 6 ]. The design of flow field plates is therefore not merely an ancillary consideration but a critical determinant of fuel cell performance, durability, and overall system efficiency. Researchers have extensively studied various FC designs to enhance PEMFC s performance. The most prominent configurations include serpentine, parallel, pin-type, and interdigitated channels[ 7 ]. Among these, serpentine and interdigitated flow fields have received the most attention[ 8 ]. Serpentine flow fields, with their intricate, multi-turn single-channel pathway, actively drive reactant gases into the gas diffusion layer, promoting faster reaction kinetics and improved electrochemical performance[ 9 ]. This design also creates a substantial pressure drop, which encourages consistent and robust reactant flow from inlet to outlet, resulting in higher power output compared to parallel flow fields. However, the extended channel length in serpentine designs increases pressure drop, elevating the risk of channel blockage, flooding, and undesirable slug/plug flows[ 10 ]. These issues reduce overall efficiency by increasing auxiliary power demand and causing mechanical stress due to high-pressure differences between the inlet and outlet. On the other hand, the interdigitated flow field, characterized by its dead-end channels, enhances reaction rates by compelling reactants to diffuse into the gas diffusion layer, ensuring a high degree of reactant utilization[ 11 ]. However, both serpentine and interdigitated flow fields require significant initial pressures to effectively force reactants into the gas diffusion layer, which can lead to increased energy consumption and system complexity. Historically, the parallel flow field design stands out for its inherent simplicity and associated cost advantages, offering an uncomplicated and economical approach to gas distribution within PEMFCs. The manufacturing processes for parallel gas flow channels are also less complex and more easily implemented than those required for serpentine flow fields, which involve intricate geometries and precise channel routing, resulting in reduced production costs. Despite its simplicity and ease of manufacturing, the conventional parallel flow field design has historically received less attention from researchers due to a critical limitation: Uneven reactant gas dispersal over the fuel cell's active region. This uneven distribution can lead to localized reactant starvation, reduced electrochemical reaction rates, and diminished overall fuel cell performance, particularly under high current density conditions. To overcome the performance limitations associated with conventional parallel flow fields, and to capitalize on their inherent advantages, this study introduces a novel modified parallel flow field design engineered to promote uniform reactant distribution and enhanced FC characteristics which is shown in Fig. 1 below. The development of advanced flow field designs remains a crucial area of research aimed at optimizing the performance and durability of PEMFCs[ 12 ] . Computational fluid dynamics has become a crucial tool for simulating and optimizing proton exchange membrane fuel cell performance and durability. CFD allows researchers to study the complex interactions between reactant transport, electrochemical reactions, and water management within the fuel cell, providing insights that are difficult to obtain through experimentation alone[ 13 ]. CFD simulations can accurately model and predict critical electrochemical parameters, as well as identify the underlying causes of operational issues that may not be apparent from traditional experimental characterization, making it central to advancing fuel cell technology. By enabling virtual experimentation and detailed parametric studies, CFD significantly reduces the reliance on costly and time-intensive physical experimentation, accelerating the design optimization process and reducing overall development costs[ 14 ]. A well-optimized flow field design, particularly one that considers the specific dimensions of the flow channels, is essential for achieving a homogeneous distribution of reactant gases, ultimately leading to optimal fuel cell performance[ 3 , 15 ]. The flow field architecture plays a pivotal role in determining the efficiency and longevity of the PEMFC[ 16 ]. Innovative flow field designs, such as stepped flow fields, have demonstrated enhanced gas diffusion rates through strategic reductions in cross-sectional area[ 17 ]. The flow channel design in a fuel cell stack is crucial, as it controls the transport of reactant gases, water management, and thermal distribution, which directly impact electrochemical kinetics and overall performance. Numerical investigations have confirmed that stepped flow field designs outperform traditional parallel flow field configurations, due to the enhanced mass transport characteristics and more uniform reactant distribution facilitated by the stepped geometry. Research has also explored diverse flow field configurations, including leaf-shaped[ 18 ], snowflake-shaped[ 19 ], lung-shaped, honeycomb-shaped[ 20 ], rib-shaped, and fishbone-shaped structures[ 21 ]. Novel 3D flow fields have garnered increasing attention, as they can improve cell performance by enhancing forced convection[ 22 ]. Numerical models of PEMFC stacks can simulate the detailed distributions of fluid flow, species concentrations, heat, and current in the stack [ 23 , 24 ]. These simulations offer insights into the operational behavior of PEMFCs. Uniform flow distribution is crucial for PEMFC performance, as it reduces concentration losses in parallel channel configurations[ 15 ]. An optimal flow field design should ensure uniform gas distribution, minimize pressure drop, provide sufficient rib area for high conductivity, and efficiently manage water while maintaining membrane moisture[ 25 ]. Modified parallel flow fields with micro-distributors can achieve comparable performance to serpentine designs while significantly reducing pressure drop[ 21 ]. The dimensions of channels and ribs are critical design parameters that affect mass transport and pressure drop, often studied using parallel flow field designs[ 16 ]. Flow field optimization commonly involves manipulating the channel cross-section, channel-to-rib width ratio, and aspect ratio[ 3 , 26 ]. The channel-rib position impacts current density distribution[ 27 ], and the flow field geometry is critical for heat and water management, affecting reactant distribution and water removal[ 10 , 12 , 28 ]. Additive manufacturing enables complex 3D flow field designs unachievable through conventional methods. Future research should focus on redesigning and optimizing flow fields specifically for anion exchange membrane fuel cells, given their distinct water management requirements. Model Construction Geometrical configuration This work used a 10 cm² computational model to thoroughly examine the performance characteristics of PEMFC s . The design of fuel cell includes a critical five-layer membrane electrode assembly strategically positioned between the anode and cathode flow fields, each designed with parallel flow to ensure uniform reactant distribution. This design allowed a comprehensive investigation of the complex reactant transport dynamics, enhancing understanding of their interactions and impact on the fuel cell's overall performance, including efficiency and power generation. The PEMFC component dimensions implemented in the computational model are documented in Table 1, providing a reference for the analysis and simulation validation. To evaluate the influence of channel geometry, the study incorporated four distinct cross-sectional shapes - square, rectangular, triangular, and semi-circular - each designed to maintain a uniform 4 mm² area, enabling fair comparison across configurations. These configurations identified as Cases A, B, C and D for square, rectangular, triangular and semi-circular shapes, respectively enabled a thorough analysis of how channel morphology affects various aspects of fuel cell performance, including pressure drop, mass transfer, and uniformity index, which are critical for optimizing fuel cell design and operation. Table.1 Geometrical specifications of the PEMFC model Region Parameter Value and Unit Cell Unit FC length, L cell FC width, W cell 50 mm 20 mm FFP Total width of channel and rib, W ribch Rib Height, H r Channel Number 4 mm 2.5 mm 5 GDL GDL thickness, t GDL GDL Porosity, 0.2 mm 0.78 CL CL thickness, CL Porosity 0.1 mm 0.3 PEM Membrane thickness 0.05 mm Model assumptions The flow of gases is treated as laminar, especially within the narrow channels and porous gas diffusion layers. Gases like H 2 and O 2 are assumed to behave as ideal gases due to the typical operating pressures and temperatures. PEMFC s operate under steady-state conditions. Porous materials such as GDL and CL are represented as identical and isotropic. The PEM is idealized as impermeable to reactant gases, preventing reactant crossover. Contact resistance between fuel cell components is often neglected to streamline the computational model. Computational fluid dynamics software is used, starting with importing a mesh grid file to discretize the fuel cell geometry[ 29 ]. The PEMFC s module then defines the model's parameters and boundary conditions[ 30 ], including membrane ionic conductivity, electrode kinetics, gas diffusion coefficients, inlet gas composition, flow rates, temperature, and applied voltage. This allows for simulating mass transport, heat transfer, and electrochemical reactions. CFD simulations are useful for designing and optimizing PEM fuel cells, potentially improving power density, lifespan, and costs. Boundary conditions and calculation parameters When setting up boundary conditions for PEMFC simulations, especially the inlet, it's often more practical to specify the \(\:{\dot{m}}_{f}\:\) rather than the fluid velocity. This is because, in real-world engineering applications, the available data for inlets and outlets of the FC s is commonly in terms of flow rate. Using the PEMFC module, directly calculate \(\:{\dot{m}}_{finlet}\) from known parameters. However, if we choose to define a velocity inlet, we need to convert the known parameters into velocity values. This conversion process can introduce potential inaccuracies due to approximations or empirical correlations, which can then lead to error propagation throughout the simulation. Therefore, flow rate specified as the inlet boundary condition can be a more accurate approach. The inlet boundary condition is defined using the mass flow rate: Mass flow rate entering the anodic side: \(\:\dot{{m}_{a}}\) = \(\:{\xi\:}_{ad}\) \(\:\frac{{I}_{ref}}{2F}\) ρ g . \(\:\frac{ad}{{C}_{H2}}\) , in A PEM (1) Mass flow rate entering the cathodic side: \(\:\dot{{m}_{c}}\) = \(\:{\xi\:}_{cd}\) \(\:\frac{{I}_{ref}}{2F}\:\) ρ g . \(\:\frac{cd}{{C}_{O2}}\) , in A PEM (2) In the context of PEMFC s , the stoichiometric coefficient, typically denoted as ξ, I ref represents the reference value for current density in A/cm 2 , F is Faraday’s constant, A PEM is the area of the PEM in cm 2 , and ρ is the inlet gas density in kg/m 3 . Anode inlet concentration $$\:{C}_{{H}_{2},in}\:=\:{p}_{ad,in}\:{RH}_{ad}\frac{{p}_{sat}}{{RT}_{in}}$$ 3 Cathode inlet concentration $$\:{C}_{{O}_{2,in}}\:=\:0.21\left(\frac{{p}_{cd,in}{RH}_{cd}{p}_{sat}}{{RT}_{in}}\right)$$ 4 Eqs. ( 3 ) and ( 4 ) involve: p in represents the pressure of the gas entering the system at the inlet, RH indicating the amount of moisture, p sat is the vapor pressure of water at its saturation point corresponding to the inlet temperature, R is the ideal gas constant, T in is the temperature of the gas at the inlet. Proper operating conditions, such as \(\:\dot{m}\) a , p,T, and \(\:\varnothing\:\) are critical for reliable fuel cell operation. These parameters significantly influence the electrochemical reactions and transport processes within the fuel cell, affecting its performance and lifespan. To compare water management and current density, the parallel and rib-channel configurations were tested under identical conditions. Temperature and humidity impact membrane hydration, which affects ionic conductivity and overall performance. Inadequate humidity can dehydrate the membrane, reducing proton conductivity and increasing ohmic losses, while excess humidity can flood the electrodes, hindering gas transport and reactions. Operating pressure also plays a crucial role by influencing the partial pressures of reactant gases, affecting the thermodynamic driving force for the electrochemical reactions. Higher pressures generally improve reaction rates and fuel cell performance. Controlling the mass flow rates of hydrogen and oxygen is essential to ensure adequate reactant supply to the active sites. The specific operational parameters can be found in Table 3 , while Table 4 presents the calculated anode and cathode component concentrations, as well as the inlet mass flow rates of the anode and cathode under these operating parameters. Governing Equations The numerical modelling of a PEMFC s requires a detailed mathematical framework. This framework describes the overall behaviour of the fuel cell by using specific governing equations for each component. These equations cover the fundamental principles of mass conservation, momentum transfer, energy balance, and species transport. Together, these principles dictate the electrochemical reactions and current conservation within the fuel cell, influencing its performance and efficiency. Which are detailed in the following sections respectively. Continuity equation: The continuity equation, often referred to as the mass conservation equation, describes the principle of mass balance in a system., applied to flow channel design in a PEM fuel cell, can be expressed as follows: $$\:\frac{\partial\:\left(\varnothing\:\rho\:\right)}{\partial\:t}+\nabla\:\left(\varnothing\:\rho\:\overrightarrow{u}\right)=\:S\text{T}$$ 5 where \(\:\varnothing\:\:\) is the porosity of porous medium, \(\:\rho\:\) is fluid density (kg/m³) and \(\:\overrightarrow{u\:}\) is the fluid velocity vector (m/s) Momentum conservation equation: Also called as the Navier-Stokes equation, applied to the entire computational domain of a PEMFC, can be written as: \(\:\frac{1}{{\phi\:}^{2}}\varDelta\:\left(\rho\:\overrightarrow{u}\overrightarrow{u}\right)\) = - \(\:\nabla\:p\) + \(\:\frac{1}{\varnothing\:}\) \(\:\nabla\:\left(\mu\:\nabla\:\overrightarrow{u}\right)\) + S n (6) where p is a pressure, \(\:\mu\:\) is the dynamic viscosity and S n is the momentum source term. Energy conservation equation: \(\:\partial\:\:\left(\varnothing\:\rho\:\overrightarrow{u}T{C}_{p}\:\right)\) = \(\:\nabla\:\left({\lambda\:}^{eff}\nabla\:T\right)\) + S h (7) where T is a temperature, C p is specific heat at constant pressure, \(\:{\lambda\:}^{eff}\) is the thermal conductivity and S h is the source heat term. Table 2 Physical Property Parameters Table Parameter Value and Unit Parameter Value and Unit Anodic current density 10000 (A/m 2 ) Cathodic current density 5 (A/m 2 ) Reactant concentration on the anode 0.035 (kmol/m 3 ) Reactant concentration on the cathode 0.006451 (kmol/m 3 ) Power factor of anode concentration 0.8 Power factor of cathode concentration 0.5 Anode-specific exchange parameter 0.5 Cathode-specific exchange parameter 0.8 Reference diffusion coefficient of H 2 1.1*10 − 4 (m 2 /s) Reference diffusion coefficient of O 2 7.3*10 − 5 (m 2 /s) Reference diffusion coefficient of H 2 O 1.1*10 − 5 (m 2 /s) Other reference diffusion coefficient 3.2*10 − 5 (m 2 /s) Contact angle of the diffusion layer 120 o Contact angle of the catalyst layer 100 o Table 3 Reactant concentrations and mass flow in cathode and anode Parameter Numerical value Parameter Numerical value Mass fraction of H 2 O at Cathode Side 0.1267 Mass fraction of H 2 O at Anode Side 0.6778 Mass fraction of O 2 at cathode side 0.1833 Mass fraction of H 2 at cathode side 0.3221 Cathode MFR * (kg/s) 1.31119*10 − 5 Anode MFR * (kg/s) 7.72215*10 − 7 Result & Discussion Cell performance Figure 2 (a) and (b) indicate how channel geometry impacts PEMFC performance curves. It is clear that at high voltages (> 0.65 V), there is no apparent difference in the cell performance; however, as the operating voltage drops, the cell's performance becomes increasingly sensitive to the flow field's configuration. In other words, the shape and design of the flow field become more critical in determining how well the fuel cell operates. The square channel achieves highest current density at the same voltage, followed by the triangle, rectangle and semi-circular channels. For instance, PEMFCs with square, triangle, rectangle and semicircle channel geometries have current densities of 1.5122 A cm − 2 , 1.4750 A cm − 2 , 1.4229 A cm − 2 and 1.28844 A cm − 2 at 0.32 V, respectively. In this scenario, the PEMFC equipped with square channels demonstrates an increase of approximately 17.36% in current density compared to the semicircular channel configuration. As illustrated in Fig. 2 (b), all channel designs reach their maximum power output at 0.4 V. Figure 2 (c) presents the peak power densities corresponding to the four channel geometries. The square channel design yields the highest peak power density, followed by the triangular, rectangular, and semicircular channels, with respective values of 0.504387 W/cm², 0.487884 W/cm², 0.470295 W/cm², and 0.430352 W/cm². In conclusion, the square channel configuration results in a 17.203% improvement in peak power density over the semicircular design. Table 4 System Parameters Operating Parameters Numerical value Operating Parameters Numerical value Pressure during operation 150 kPa Anodic vapor pressure (Pa) 28427.413 Working Temperature 353.16 Cathodic Vapor Pressure (Pa) 28427.4 Humidity at the anode inlet 100% Humidity at the cathode inlet 100% Activation area(m 2 ) 0.005 Anode/Cathode excess factor 2 Operating pressure & velocity The functionality of the PEMFCs is closely linked to operating pressure, a key factor that significantly affects the Nernst equation and Butler-Volmer equations. Analysis of the cathode flow field at 0.4 V shows a pressure gradient - pressure decreases in the direction of flow, highlighting the connection between fluid dynamics and electrochemical reactions. Comparing different channel geometries reveals how design impacts pressure drop. Triangular channels have the highest pressure drop due to increased friction and flow constriction, while square channels have lower pressure drop and enable better mass transport. Cell voltage and pressure in the anode and cathode channels are closely related. As voltage decreases, anode pressure increases while cathode pressure decreases. For example, in a rectangular channel, the pressure drop across the anode channel increased slightly from 39.7 Pa to 40.8 Pa as the cell voltage decreased from 0.65 V to 0.4 V. In contrast, the pressure drop in the cathode channel decreased from 68.1 Pa to 67.0 Pa over the same voltage change. This is driven by the stoichiometry of electrochemical reactions. Higher current density leads to more oxygen and water consumption at the cathode, and more water production at the anode. Pressure drop is also influenced by frictional forces between the fluid and channel walls, governed by fluid dynamics principles and the properties of the fluid species. $$\:{\Delta\:}\text{P}=\frac{32\text{u}\text{L}v}{{\text{D}}_{\text{h}}^{2}}\:=\:\frac{64}{{R}_{e}}\rho\:g.\frac{L}{{D}_{h}}\frac{v}{2g}$$ H 2 is much lower dynamics viscosity than O 2 , leading to significantly lower pressure drops in the anode channel compared to the cathode channel. This difference in pressure drop is observed in Fig. 3 (a) and (b). The characteristics of fluid flow in confined channels depend on the channel's geometry, which determines the velocity distribution and impacts various transport phenomena. Analyzing the velocity distribution across different channel shapes is depicted in Fig. 4 (a). The fluid velocity is low near channel walls due to viscous effects and the no-slip condition, while the maximum velocity occurs at the channel center, consistent with boundary layer theory. Fig. 4 (b) illustrates, the channel's geometric configuration significantly affects this velocity profile, resulting in notable differences in the maximum velocities across various shapes. The maximum velocity within these channels is influenced by the operational voltage, highlighting a correlation with the distinct cross-sectional geometry of each channel. The triangular channel has the highest maximum velocity, whereas the semicircular channel has the lowest, indicating the profound influence of channel shape on fluid dynamics. For instance, at 0.4 V, the maximum velocities in square, rectangular, semicircular, and triangular channels are 4.28618 m/s, 4.1856 m/s, 4.17292 m/s, and 4.78493 m/s, respectively, demonstrating that the sequence of maximum velocity is: triangular > square > rectangular > semicircular. This variation in maximum velocities arises from the interplay between the channel's cross-sectional geometry and the resulting flow dynamics. Temperature The performance of PEMFC s is highly sensitive to operating temperature due to the temperature-dependence of species transport parameters. This is because the channel outlet exhibits high temperatures, stemming from the poor thermal conductivity of the electrochemical reaction gases, leading to inefficient heat dissipation which is clearly shown in figure.5 (b). This underscores the vital need for effective thermal management strategies in PEMFC design and operation. The thermal behaviour is a key determinant of overall performance, as temperature variations significantly impact cell voltage, especially at varying current densities. Elevated temperatures, caused by inadequate heat dissipation from the low-conductivity reactant gases, necessitate sophisticated thermal management systems. These systems are essential for maintaining optimal PEMFC performance through precise temperature control and mitigating accelerated component degradation from thermal gradients and excessive heat buildup. Gas transfer The electrochemical reactions within PEMFC govern their operational efficiency. At the cathode, the rate at which H 2 O is consumed is twice the rate at which O 2 is used (Yuan & Wang, 2008). Conversely, at the anode, water is produced at twice the rate of hydrogen consumption. Hydrogen consumption and dilution by water lead to decreasing hydrogen concentration along the flow geometry. Paradoxically, amount of oxygen available at the cathode increases along the flow direction, due to different rates of water and oxygen consumption. At the anode, hydrogen concentration varies across channel geometries, with the square channel exhibiting the most uniform distribution is observed in Fig. 6 (a). On the cathode side, the PEMFC configuration featuring square channels exhibits the highest oxygen concentration, as illustrated in Fig. 6 (b), which corresponds to its superior overall performance, likely due to elevated current densities increasing the rate of cathode water consumption. The efficiency of water management, especially at the cathode, is critical to PEMFC performance. Channel geometry is a key design parameter that influences mass transport and electrochemical reaction kinetics, affecting the fuel cell's power output and efficiency. Water transport In PEMFC s , maintaining an optimal balance between liquid water and water vapor is crucial for high performance, especially below 100°C, as both phases influence membrane hydration, proton conductivity, and reaction kinetics. Effective water management is essential to sustain adequate membrane hydration while preventing electrode flooding and ensuring efficient gas transport. Local temperature and pressure variations can lead to water condensation, particularly in the cathode where water is produced; thus, understanding and controlling these parameters are key for optimizing fuel cell performance[ 31 ]. In this present work, investigating the transport of liquid water, water vapor, and membrane-bound H 2 O in PEMFC s is crucial, given the potential for phase interconversion and its impact on performance[ 32 ]. Along the flow direction, there is a gradual increase in anodic water vapor concentration, while the cathodic concentration exhibits the opposite trend, due to the electrochemical reactions. Elevated temperatures facilitate greater the movement of water from the membrane to the gas phase affects the concentration gradients. The BPP design significantly affects water vapor concentration gradients, highlighting the complex relationship between geometry and mass transport phenomena that determine fuel cell operational effectiveness. The distribution of water concentration at the anode is highest in semicircular channels, followed by rectangular, triangular and square with corresponding standard deviations of 0.9409, 0.8013, 0.6550 and 0.6501 mol m − 3 , respectively. Conclusions In this study, a high-quality three-dimensional, two-phase, non-isothermal numerical model is develop to investigate the influence of channel geometry on the performance of PEMFC. This model enabled a detailed examination of how different channel shapes within parallel flow field configurations affect PEMFC performance. The findings indicate that channel geometry plays a crucial role in influencing PEMFC performance, with the square channel demonstrating the highest efficiency 17.20% greater peak power density compared to the semicircular channel. It is clear that at high voltages (> 0.65 V), there is no apparent difference in the cell performance; however, as the operating voltage drops, the functionality of FC becomes strongly reliant on the flow field shape. The square channel achieves highest current density at the same voltage, followed by the triangle, rectangular and semi-circular channels. Triangular channels have the highest pressure drop due to increased friction and flow constriction, while square channels have lower pressure drop and enable better mass transport. The maximum velocity within these geometries is influenced by the operational voltage, highlighting a correlation with the distinct cross-sectional geometry of each channel. The triangular shape has the highest maximum velocity, whereas the semicircular channel has the lowest, indicating the profound influence of channel shape on fluid dynamics. For instance, at 0.40 V, the maximum velocities in square, rectangular, semicircular, and triangular channels are 4.28618 m/s, 4.1856 m/s, 4.17292 m/s, and 4.78493 m/s, respectively. Nomenclature Declarations Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author Contribution Conceptualization, writing original draft, formal analysis, Manisha Singh Chauhan; figures formation, tablesformation, review and editing, Ajay Kumar Sharma and Arun Kumar Tiwari. The final, published version ofthe paper has been read and approved by all authors. Acknowledgement Manisha Singh Chauhan expresses gratitude to Dr. A.P.J. Abdul Kalam Technical University, Lucknow, Uttar Pradesh, India, for awarding the fellowship as part of the Homi Bhabha Teaching cum Research Fellowship. 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Prod. 2019 , 214 , 738–748, doi:10.1016/j.jclepro.2018.12.293. Liu, H.; Yang, W.; Tan, J.; An, Y.; Cheng, L. Numerical Analysis of Parallel Flow Fields Improved by Micro-Distributor in Proton Exchange Membrane Fuel Cells. Energy Convers. Manag. 2018 , 176 , 99–109, doi:10.1016/j.enconman.2018.09.024. Chen, X.; Yu, Z.; Yang, C.; Chen, Y.; Jin, C.; Ding, Y.; Li, W.; Wan, Z. Performance Investigation on a Novel 3D Wave Flow Channel Design for PEMFC. Int. J. Hydrogen Energy 2021 , 46 , 11127–11139, doi:10.1016/J.IJHYDENE.2020.06.057. Kjeang, E.; Djilali, N.; Sinton, D. Microfluidic Fuel Cells: A Review. J. Power Sources 2009 , 186 , 353–369, doi:10.1016/j.jpowsour.2008.10.011. Imbrioscia, G.M.; Fasoli, H.J. Simulation and Study of Proposed Modifications over Straight-Parallel Flow Field Design. Int. J. Hydrogen Energy 2014 , 39 , 8861–8867, doi:10.1016/j.ijhydene.2013.11.079. Sauermoser, M.; Kizilova, N.; Pollet, B.G.; Kjelstrup, S. Flow Field Patterns for Proton Exchange Membrane Fuel Cells. Front. Energy Res. 2020 , 8 , 1–20, doi:10.3389/fenrg.2020.00013. Kerkoub, Y.; Benzaoui, A.; Haddad, F.; Ziari, Y.K. Channel to Rib Width Ratio Influence with Various Flow Field Designs on Performance of PEM Fuel Cell. Energy Convers. Manag. 2018 , 174 , 260–275, doi:10.1016/j.enconman.2018.08.041. Wang, M.; Ding, Y.; Hu, J.; Xu, L.; Yang, X. Numerical Simulation of Water and Heat Transport in the Cathode Channel of a PEM Fuel Cell. Int. J. Hydrogen Energy 2022 , 47 , 11007–11027, doi:10.1016/j.ijhydene.2022.01.143. Babuponnusami, A.; Muthukumar, K. A Review on Fenton and Improvements to the Fenton Process for Wastewater Treatment. J. Environ. Chem. Eng. 2014 , 2 , 557–572, doi:10.1016/J.JECE.2013.10.011. Iranzo, A.; Toharias, B.; Suárez, C.; Rosa, F.; Pino, J. Dataset and Mesh of the CFD Numerical Model for the Modelling and Simulation of a PEM Fuel Cell. Data Br. 2022 , 41 , 107987, doi:10.1016/J.DIB.2022.107987. Herlambang, Y.D.; Kurnianingsih; Roihatin, A.; Prasetyo, T.; Marliyati; Taufik; Shyu, J.C. A Numerical Study of Bubble Blockage in Microfluidic Fuel Cells. Processes 2022 , 10 , doi:10.3390/pr10050922. Rikukawa, M.; Sanui, K. Proton-Conducting Polymer Electrolyte Membranes Based on Hydrocarbon Polymers. Prog. Polym. Sci. 2000 , 25 , 1463–1502, doi:10.1016/S0079-6700(00)00032-0. Wu, H.; Li, X.; Berg, P. On the Modeling of Water Transport in Polymer Electrolyte Membrane Fuel Cells. Electrochim. Acta 2009 , 54 , 6913–6927, doi:10.1016/j.electacta.2009.06.070. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6988123","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":481170392,"identity":"aa28e5ab-ff3f-4c71-a319-3dad7803b5ca","order_by":0,"name":"Manisha Singh Chauhan","email":"","orcid":"","institution":"Institute of Engineering \u0026 Technology, Lucknow 226021, Uttar Pradesh, India","correspondingAuthor":false,"prefix":"","firstName":"Manisha","middleName":"Singh","lastName":"Chauhan","suffix":""},{"id":481170393,"identity":"baab3d59-37f1-49b9-94cf-5da8957d3e8f","order_by":1,"name":"Ajay Kumar Sharma","email":"data:image/png;base64,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","orcid":"","institution":"Institute of Engineering \u0026 Technology, Lucknow 226021, Uttar Pradesh, India","correspondingAuthor":true,"prefix":"","firstName":"Ajay","middleName":"Kumar","lastName":"Sharma","suffix":""},{"id":481170394,"identity":"f4b28da7-5b28-4b69-86f6-150722af50ce","order_by":2,"name":"Arun Kumar Tiwari","email":"","orcid":"","institution":"Institute of Engineering \u0026 Technology, Lucknow 226021, Uttar Pradesh, India","correspondingAuthor":false,"prefix":"","firstName":"Arun","middleName":"Kumar","lastName":"Tiwari","suffix":""}],"badges":[],"createdAt":"2025-06-27 05:38:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6988123/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6988123/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86145164,"identity":"7930ec68-2679-4329-a208-26757bea1a61","added_by":"auto","created_at":"2025-07-07 09:00:33","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":208741,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematic of (a) computational domain, (b) four different shapes\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6988123/v1/2f9bf2766cb1dd6b2a5557af.png"},{"id":86146567,"identity":"ece80a6f-95ce-4c2e-b818-6794c400c221","added_by":"auto","created_at":"2025-07-07 09:16:33","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":34594,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePerformance of PEMFC with different flow channel geometries: (a) Polarization curves; (b) Power density curve; (c) Peak power density.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6988123/v1/a4cdf1252be4999e15972b42.png"},{"id":86145717,"identity":"487903de-1ac6-4f30-ba22-eb066b4d625f","added_by":"auto","created_at":"2025-07-07 09:08:33","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":23995,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6988123/v1/25f821bb20fccdfce36fa208.png"},{"id":86145169,"identity":"d5277543-e471-45d9-a3c9-e407c71bbebb","added_by":"auto","created_at":"2025-07-07 09:00:33","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":138367,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eFlow Characteristics in the Cathode Channel: (a) Velocity Profile; (b) Maximum Flow Velocity\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6988123/v1/9fe3e1f2176af9dc4fc5dac4.png"},{"id":86145168,"identity":"126d7db6-ce8c-487f-947b-30458f662b7e","added_by":"auto","created_at":"2025-07-07 09:00:33","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":202526,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) Temperature profile on the cathode membrane surface at 0.4V; (b) Temperature across various voltages.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6988123/v1/e0108138d26753c4fbbbd9f7.png"},{"id":86145172,"identity":"c1420a71-62b5-41ab-a698-0980604fe8cc","added_by":"auto","created_at":"2025-07-07 09:00:33","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":43427,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e\"Non-uniform circulation of reactants along the y-direction: (a) H\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e concentration at the anode GDL-CL interface; (b) O\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e concentration at the cathode GDL-CL interface; (c) Index of H\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e concentration non-uniformity; (d) Index of O\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e concentration non-uniformity.\"\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6988123/v1/18e1e6772e4d863c4c653eed.png"},{"id":86145170,"identity":"1d9f6fd0-7830-4411-86fd-eb9fc504cd50","added_by":"auto","created_at":"2025-07-07 09:00:33","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":57766,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a) Water concentration profile at the anode GDL-CL surface in the y-direction;\u003cbr\u003e\n(b) Water concentration profile at the cathode GDL-CL surface in the y-direction.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6988123/v1/efd8eff34d4a7ba5126f2c6c.png"},{"id":87676330,"identity":"786f8be2-3432-4217-9cdd-dde47f80f56b","added_by":"auto","created_at":"2025-07-27 17:01:32","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1884028,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6988123/v1/9516bc30-dc5d-404d-8685-19481d80407f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Simulation through CFD of Different Flow Field Designs for Enhancing Proton Exchange Membrane Fuel Cell Performance","fulltext":[{"header":"Introduction","content":"\u003cp\u003eGlobal energy demand is rising and greenhouse effects are escalating, creating an environmental, social, and economic crisis. This requires a shift to alternative power generation. Using renewable energy sources is crucial to reduce reliance on traditional sources [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Electrochemical reactions attract substantial research interest due to their excellent efficiency, low environmental effect, and enhanced stability, making them promising alternatives in the evolving energy landscape[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Developing fuel cells is a significant step toward addressing these challenges and providing cleaner, more sustainable energy solutions. The growing demand for unconventional energy sources is a primary driver in the expansion of fuel cell technology, which is gaining momentum as a viable solution for various applications, ranging from portable electronics to large-scale power generation. FC\u003csub\u003es\u003c/sub\u003e efficiently convert the chemical energy of fuels into electrical energy via electrochemical reactions, offering a more direct and efficient energy conversion pathway compared to traditional heat engines that rely on combustion and thermodynamic cycles. Due to their advanced state of development and exceptional performance, PEMFC\u003csub\u003es\u003c/sub\u003e are frequently chosen for use in automobiles and fixed power generation facilities. Flow field plates, often referred to as bipolar plates, represent a cornerstone technology in the architecture of PEMFC\u003csub\u003es\u003c/sub\u003e, executing a multifaceted role that is pivotal to the operational efficiency and extended lifespan of the fuel cell stack[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Functioning as electrical conductors, these plates facilitate the crucial task of channelling electrical current generated within the fuel cell to external circuits, ensuring a seamless energy transfer for practical applications. Beyond their electrical conductivity, flow field plates lend structural fortitude to the membrane-electrode assembly, providing the necessary mechanical support to withstand operational stresses and maintain the integrity of the fuel cell structure[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Furthermore, the intricate design of flow channels within these plates dictates the distribution of reactant gases, such as hydrogen and oxygen (or air), to the electrodes, a process that directly influences the uniformity of the electrochemical reaction and overall cell performance[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. An additional critical function is the management of water, a by-product of the electrochemical reaction; the flow channels are engineered to facilitate efficient water removal, preventing flooding of the electrodes and ensuring optimal gas diffusion to the reaction sites[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. The design of flow field plates is therefore not merely an ancillary consideration but a critical determinant of fuel cell performance, durability, and overall system efficiency. Researchers have extensively studied various FC designs to enhance PEMFC\u003csub\u003es\u003c/sub\u003e performance. The most prominent configurations include serpentine, parallel, pin-type, and interdigitated channels[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Among these, serpentine and interdigitated flow fields have received the most attention[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Serpentine flow fields, with their intricate, multi-turn single-channel pathway, actively drive reactant gases into the gas diffusion layer, promoting faster reaction kinetics and improved electrochemical performance[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. This design also creates a substantial pressure drop, which encourages consistent and robust reactant flow from inlet to outlet, resulting in higher power output compared to parallel flow fields. However, the extended channel length in serpentine designs increases pressure drop, elevating the risk of channel blockage, flooding, and undesirable slug/plug flows[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. These issues reduce overall efficiency by increasing auxiliary power demand and causing mechanical stress due to high-pressure differences between the inlet and outlet. On the other hand, the interdigitated flow field, characterized by its dead-end channels, enhances reaction rates by compelling reactants to diffuse into the gas diffusion layer, ensuring a high degree of reactant utilization[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. However, both serpentine and interdigitated flow fields require significant initial pressures to effectively force reactants into the gas diffusion layer, which can lead to increased energy consumption and system complexity.\u003c/p\u003e \u003cp\u003eHistorically, the parallel flow field design stands out for its inherent simplicity and associated cost advantages, offering an uncomplicated and economical approach to gas distribution within PEMFCs. The manufacturing processes for parallel gas flow channels are also less complex and more easily implemented than those required for serpentine flow fields, which involve intricate geometries and precise channel routing, resulting in reduced production costs. Despite its simplicity and ease of manufacturing, the conventional parallel flow field design has historically received less attention from researchers due to a critical limitation: Uneven reactant gas dispersal over the fuel cell's active region. This uneven distribution can lead to localized reactant starvation, reduced electrochemical reaction rates, and diminished overall fuel cell performance, particularly under high current density conditions. To overcome the performance limitations associated with conventional parallel flow fields, and to capitalize on their inherent advantages, this study introduces a novel modified parallel flow field design engineered to promote uniform reactant distribution and enhanced FC characteristics which is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e below. The development of advanced flow field designs remains a crucial area of research aimed at optimizing the performance and durability of PEMFCs[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] .\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eComputational fluid dynamics has become a crucial tool for simulating and optimizing proton exchange membrane fuel cell performance and durability. CFD allows researchers to study the complex interactions between reactant transport, electrochemical reactions, and water management within the fuel cell, providing insights that are difficult to obtain through experimentation alone[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. CFD simulations can accurately model and predict critical electrochemical parameters, as well as identify the underlying causes of operational issues that may not be apparent from traditional experimental characterization, making it central to advancing fuel cell technology. By enabling virtual experimentation and detailed parametric studies, CFD significantly reduces the reliance on costly and time-intensive physical experimentation, accelerating the design optimization process and reducing overall development costs[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. A well-optimized flow field design, particularly one that considers the specific dimensions of the flow channels, is essential for achieving a homogeneous distribution of reactant gases, ultimately leading to optimal fuel cell performance[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. The flow field architecture plays a pivotal role in determining the efficiency and longevity of the PEMFC[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Innovative flow field designs, such as stepped flow fields, have demonstrated enhanced gas diffusion rates through strategic reductions in cross-sectional area[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The flow channel design in a fuel cell stack is crucial, as it controls the transport of reactant gases, water management, and thermal distribution, which directly impact electrochemical kinetics and overall performance. Numerical investigations have confirmed that stepped flow field designs outperform traditional parallel flow field configurations, due to the enhanced mass transport characteristics and more uniform reactant distribution facilitated by the stepped geometry. Research has also explored diverse flow field configurations, including leaf-shaped[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], snowflake-shaped[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], lung-shaped, honeycomb-shaped[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], rib-shaped, and fishbone-shaped structures[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Novel 3D flow fields have garnered increasing attention, as they can improve cell performance by enhancing forced convection[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Numerical models of PEMFC stacks can simulate the detailed distributions of fluid flow, species concentrations, heat, and current in the stack [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. These simulations offer insights into the operational behavior of PEMFCs. Uniform flow distribution is crucial for PEMFC performance, as it reduces concentration losses in parallel channel configurations[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. An optimal flow field design should ensure uniform gas distribution, minimize pressure drop, provide sufficient rib area for high conductivity, and efficiently manage water while maintaining membrane moisture[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Modified parallel flow fields with micro-distributors can achieve comparable performance to serpentine designs while significantly reducing pressure drop[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The dimensions of channels and ribs are critical design parameters that affect mass transport and pressure drop, often studied using parallel flow field designs[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Flow field optimization commonly involves manipulating the channel cross-section, channel-to-rib width ratio, and aspect ratio[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. The channel-rib position impacts current density distribution[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e], and the flow field geometry is critical for heat and water management, affecting reactant distribution and water removal[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Additive manufacturing enables complex 3D flow field designs unachievable through conventional methods. Future research should focus on redesigning and optimizing flow fields specifically for anion exchange membrane fuel cells, given their distinct water management requirements.\u003c/p\u003e"},{"header":"Model Construction","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eGeometrical configuration\u003c/h2\u003e \u003cp\u003eThis work used a 10 cm\u0026sup2; computational model to thoroughly examine the performance characteristics of PEMFC\u003csub\u003es\u003c/sub\u003e. The design of fuel cell includes a critical five-layer membrane electrode assembly strategically positioned between the anode and cathode flow fields, each designed with parallel flow to ensure uniform reactant distribution. This design allowed a comprehensive investigation of the complex reactant transport dynamics, enhancing understanding of their interactions and impact on the fuel cell's overall performance, including efficiency and power generation. The PEMFC component dimensions implemented in the computational model are documented in Table\u0026nbsp;1, providing a reference for the analysis and simulation validation. To evaluate the influence of channel geometry, the study incorporated four distinct cross-sectional shapes - square, rectangular, triangular, and semi-circular - each designed to maintain a uniform 4 mm\u0026sup2; area, enabling fair comparison across configurations. These configurations identified as Cases A, B, C and D for square, rectangular, triangular and semi-circular shapes, respectively enabled a thorough analysis of how channel morphology affects various aspects of fuel cell performance, including pressure drop, mass transfer, and uniformity index, which are critical for optimizing fuel cell design and operation.\u003c/p\u003e \u003cp\u003e \u003cb\u003eTable.1 Geometrical specifications of the PEMFC model\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRegion\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValue and Unit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCell Unit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFC length, L\u003csub\u003ecell\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eFC width, W\u003csub\u003ecell\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e50 mm\u003c/p\u003e \u003cp\u003e20 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFFP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTotal width of channel and rib, W\u003csub\u003eribch\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eRib Height, H\u003csub\u003er\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eChannel Number\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4 mm\u003c/p\u003e \u003cp\u003e2.5 mm\u003c/p\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGDL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGDL thickness, t\u003csub\u003eGDL\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eGDL Porosity,\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2 mm\u003c/p\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCL thickness,\u003c/p\u003e \u003cp\u003eCL Porosity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1 mm\u003c/p\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePEM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMembrane thickness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.05 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eModel assumptions\u003c/h3\u003e\n\u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe flow of gases is treated as laminar, especially within the narrow channels and porous gas diffusion layers.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eGases like H\u003csub\u003e2\u003c/sub\u003e and O\u003csub\u003e2\u003c/sub\u003e are assumed to behave as ideal gases due to the typical operating pressures and temperatures.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePEMFC\u003csub\u003es\u003c/sub\u003e operate under steady-state conditions.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003ePorous materials such as GDL and CL are represented as identical and isotropic.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe PEM is idealized as impermeable to reactant gases, preventing reactant crossover.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eContact resistance between fuel cell components is often neglected to streamline the computational model.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eComputational fluid dynamics software is used, starting with importing a mesh grid file to discretize the fuel cell geometry[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The PEMFC\u003csub\u003es\u003c/sub\u003e module then defines the model's parameters and boundary conditions[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], including membrane ionic conductivity, electrode kinetics, gas diffusion coefficients, inlet gas composition, flow rates, temperature, and applied voltage. This allows for simulating mass transport, heat transfer, and electrochemical reactions. CFD simulations are useful for designing and optimizing PEM fuel cells, potentially improving power density, lifespan, and costs.\u003c/p\u003e\n\u003ch3\u003eBoundary conditions and calculation parameters\u003c/h3\u003e\n\u003cp\u003eWhen setting up boundary conditions for PEMFC simulations, especially the inlet, it's often more practical to specify the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\dot{m}}_{f}\\:\\)\u003c/span\u003e\u003c/span\u003erather than the fluid velocity. This is because, in real-world engineering applications, the available data for inlets and outlets of the FC\u003csub\u003es\u003c/sub\u003e is commonly in terms of flow rate. Using the PEMFC module, directly calculate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\dot{m}}_{finlet}\\)\u003c/span\u003e\u003c/span\u003e from known parameters. However, if we choose to define a velocity inlet, we need to convert the known parameters into velocity values. This conversion process can introduce potential inaccuracies due to approximations or empirical correlations, which can then lead to error propagation throughout the simulation. Therefore, flow rate specified as the inlet boundary condition can be a more accurate approach. The inlet boundary condition is defined using the mass flow rate:\u003c/p\u003e \u003cp\u003eMass flow rate entering the anodic side:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{{m}_{a}}\\)\u003c/span\u003e \u003c/span\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\xi\\:}_{ad}\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{I}_{ref}}{2F}\\)\u003c/span\u003e\u003c/span\u003e ρ\u003csub\u003eg\u003c/sub\u003e.\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{ad}{{C}_{H2}}\\)\u003c/span\u003e\u003c/span\u003e, in A\u003csub\u003ePEM\u003c/sub\u003e (1)\u003c/p\u003e \u003cp\u003eMass flow rate entering the cathodic side:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{{m}_{c}}\\)\u003c/span\u003e \u003c/span\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\xi\\:}_{cd}\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{I}_{ref}}{2F}\\:\\)\u003c/span\u003e\u003c/span\u003eρ\u003csub\u003eg\u003c/sub\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{cd}{{C}_{O2}}\\)\u003c/span\u003e\u003c/span\u003e, in A\u003csub\u003ePEM\u003c/sub\u003e (2)\u003c/p\u003e \u003cp\u003eIn the context of PEMFC\u003csub\u003es\u003c/sub\u003e, the stoichiometric coefficient, typically denoted as ξ, I\u003csub\u003eref\u003c/sub\u003e represents the reference value for current density in A/cm\u003csup\u003e2\u003c/sup\u003e, F is Faraday\u0026rsquo;s constant, A\u003csub\u003ePEM\u003c/sub\u003e is the area of the PEM in cm\u003csup\u003e2\u003c/sup\u003e, and ρ is the inlet gas density in kg/m\u003csup\u003e3\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAnode inlet concentration\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{C}_{{H}_{2},in}\\:=\\:{p}_{ad,in}\\:{RH}_{ad}\\frac{{p}_{sat}}{{RT}_{in}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eCathode inlet concentration\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{C}_{{O}_{2,in}}\\:=\\:0.21\\left(\\frac{{p}_{cd,in}{RH}_{cd}{p}_{sat}}{{RT}_{in}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEqs.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e3\u003c/span\u003e) and (\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e4\u003c/span\u003e) involve: p\u003csub\u003ein\u003c/sub\u003e represents the pressure of the gas entering the system at the inlet, RH indicating the amount of moisture, p\u003csub\u003esat\u003c/sub\u003e is the vapor pressure of water at its saturation point corresponding to the inlet temperature, R is the ideal gas constant, T\u003csub\u003ein\u003c/sub\u003e is the temperature of the gas at the inlet.\u003c/p\u003e \u003cp\u003eProper operating conditions, such as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{m}\\)\u003c/span\u003e\u003c/span\u003e\u003csub\u003ea\u003c/sub\u003e, p,T, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varnothing\\:\\)\u003c/span\u003e\u003c/span\u003e are critical for reliable fuel cell operation. These parameters significantly influence the electrochemical reactions and transport processes within the fuel cell, affecting its performance and lifespan. To compare water management and current density, the parallel and rib-channel configurations were tested under identical conditions. Temperature and humidity impact membrane hydration, which affects ionic conductivity and overall performance. Inadequate humidity can dehydrate the membrane, reducing proton conductivity and increasing ohmic losses, while excess humidity can flood the electrodes, hindering gas transport and reactions. Operating pressure also plays a crucial role by influencing the partial pressures of reactant gases, affecting the thermodynamic driving force for the electrochemical reactions. Higher pressures generally improve reaction rates and fuel cell performance. Controlling the mass flow rates of hydrogen and oxygen is essential to ensure adequate reactant supply to the active sites. The specific operational parameters can be found in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e3\u003c/span\u003e, while Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the calculated anode and cathode component concentrations, as well as the inlet mass flow rates of the anode and cathode under these operating parameters.\u003c/p\u003e\n\u003ch3\u003eGoverning Equations\u003c/h3\u003e\n\u003cp\u003eThe numerical modelling of a PEMFC\u003csub\u003es\u003c/sub\u003e requires a detailed mathematical framework. This framework describes the overall behaviour of the fuel cell by using specific governing equations for each component. These equations cover the fundamental principles of mass conservation, momentum transfer, energy balance, and species transport. Together, these principles dictate the electrochemical reactions and current conservation within the fuel cell, influencing its performance and efficiency. Which are detailed in the following sections respectively.\u003c/p\u003e \u003cp\u003eContinuity equation:\u003c/p\u003e \u003cp\u003eThe continuity equation, often referred to as the mass conservation equation, describes the principle of mass balance in a system., applied to flow channel design in a PEM fuel cell, can be expressed as follows:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\frac{\\partial\\:\\left(\\varnothing\\:\\rho\\:\\right)}{\\partial\\:t}+\\nabla\\:\\left(\\varnothing\\:\\rho\\:\\overrightarrow{u}\\right)=\\:S\\text{T}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varnothing\\:\\:\\)\u003c/span\u003e\u003c/span\u003e is the porosity of porous medium, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:\\)\u003c/span\u003e\u003c/span\u003e is fluid density (kg/m\u0026sup3;) and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{u\\:}\\)\u003c/span\u003e\u003c/span\u003eis the fluid velocity vector (m/s)\u003c/p\u003e \u003cp\u003eMomentum conservation equation:\u003c/p\u003e \u003cp\u003eAlso called as the Navier-Stokes equation, applied to the entire computational domain of a PEMFC, can be written as:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{{\\phi\\:}^{2}}\\varDelta\\:\\left(\\rho\\:\\overrightarrow{u}\\overrightarrow{u}\\right)\\)\u003c/span\u003e \u003c/span\u003e = -\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\nabla\\:p\\)\u003c/span\u003e\u003c/span\u003e + \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{\\varnothing\\:}\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\nabla\\:\\left(\\mu\\:\\nabla\\:\\overrightarrow{u}\\right)\\)\u003c/span\u003e\u003c/span\u003e + S\u003csub\u003en\u003c/sub\u003e (6)\u003c/p\u003e \u003cp\u003ewhere p is a pressure, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003e is the dynamic viscosity and S\u003csub\u003en\u003c/sub\u003e is the momentum source term.\u003c/p\u003e \u003cp\u003eEnergy conservation equation:\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\partial\\:\\:\\left(\\varnothing\\:\\rho\\:\\overrightarrow{u}T{C}_{p}\\:\\right)\\)\u003c/span\u003e \u003c/span\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\nabla\\:\\left({\\lambda\\:}^{eff}\\nabla\\:T\\right)\\)\u003c/span\u003e\u003c/span\u003e+ S\u003csub\u003eh\u003c/sub\u003e (7)\u003c/p\u003e \u003cp\u003ewhere T is a temperature, C\u003csub\u003ep\u003c/sub\u003e is specific heat at constant pressure, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\lambda\\:}^{eff}\\)\u003c/span\u003e\u003c/span\u003e is the thermal conductivity and S\u003csub\u003eh\u003c/sub\u003e is the source heat term.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePhysical Property Parameters Table\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValue and Unit\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eValue and Unit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnodic current density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10000 (A/m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCathodic current density\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5 (A/m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReactant concentration on the anode\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.035 (kmol/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReactant concentration on the cathode\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.006451 (kmol/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePower factor of anode concentration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePower factor of cathode concentration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAnode-specific exchange parameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCathode-specific exchange parameter\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReference diffusion coefficient of H\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.1*10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e (m\u003csup\u003e2\u003c/sup\u003e/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eReference diffusion coefficient of O\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7.3*10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e(m\u003csup\u003e2\u003c/sup\u003e/s)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReference diffusion coefficient of H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.1*10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e (m\u003csup\u003e2\u003c/sup\u003e/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOther reference diffusion coefficient\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.2*10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e(m\u003csup\u003e2\u003c/sup\u003e/s)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eContact angle of the diffusion layer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e120\u003csup\u003eo\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eContact angle of the catalyst layer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e100\u003csup\u003eo\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eReactant concentrations and mass flow in cathode and anode\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumerical value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNumerical value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMass fraction of H\u003csub\u003e2\u003c/sub\u003eO at Cathode Side\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.1267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMass fraction of H\u003csub\u003e2\u003c/sub\u003eO at Anode Side\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.6778\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMass fraction of O\u003csub\u003e2\u003c/sub\u003e at cathode side\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.1833\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMass fraction of H\u003csub\u003e2\u003c/sub\u003e at cathode side\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3221\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCathode MFR\u003csup\u003e*\u003c/sup\u003e (kg/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.31119*10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAnode MFR\u003csup\u003e*\u003c/sup\u003e\u003c/p\u003e \u003cp\u003e(kg/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.72215*10\u003csup\u003e\u0026minus;\u0026thinsp;7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"Result \u0026 Discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eCell performance\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a) and (b) indicate how channel geometry impacts PEMFC performance curves. It is clear that at high voltages (\u0026gt;\u0026thinsp;0.65 V), there is no apparent difference in the cell performance; however, as the operating voltage drops, the cell's performance becomes increasingly sensitive to the flow field's configuration. In other words, the shape and design of the flow field become more critical in determining how well the fuel cell operates. The square channel achieves highest current density at the same voltage, followed by the triangle, rectangle and semi-circular channels. For instance, PEMFCs with square, triangle, rectangle and semicircle channel geometries have current densities of 1.5122 A cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, 1.4750 A cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, 1.4229 A cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e and 1.28844 A cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e at 0.32 V, respectively. In this scenario, the PEMFC equipped with square channels demonstrates an increase of approximately 17.36% in current density compared to the semicircular channel configuration. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), all channel designs reach their maximum power output at 0.4 V. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c) presents the peak power densities corresponding to the four channel geometries. The square channel design yields the highest peak power density, followed by the triangular, rectangular, and semicircular channels, with respective values of 0.504387 W/cm\u0026sup2;, 0.487884 W/cm\u0026sup2;, 0.470295 W/cm\u0026sup2;, and 0.430352 W/cm\u0026sup2;. In conclusion, the square channel configuration results in a 17.203% improvement in peak power density over the semicircular design.\u003c/p\u003e \u003cp\u003eTable 4 System Parameters\u003c/p\u003e\u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOperating Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumerical value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOperating Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNumerical value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePressure during operation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e150 kPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAnodic vapor pressure (Pa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28427.413\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWorking Temperature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e353.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCathodic Vapor Pressure (Pa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28427.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHumidity at the anode inlet\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e100%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHumidity at the cathode inlet\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e100%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eActivation area(m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAnode/Cathode excess factor\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eOperating pressure \u0026 velocity\u003c/h3\u003e\n\u003cp\u003eThe functionality of the PEMFCs is closely linked to operating pressure, a key factor that significantly affects the Nernst equation and Butler-Volmer equations. Analysis of the cathode flow field at 0.4 V shows a pressure gradient - pressure decreases in the direction of flow, highlighting the connection between fluid dynamics and electrochemical reactions. Comparing different channel geometries reveals how design impacts pressure drop. Triangular channels have the highest pressure drop due to increased friction and flow constriction, while square channels have lower pressure drop and enable better mass transport. Cell voltage and pressure in the anode and cathode channels are closely related. As voltage decreases, anode pressure increases while cathode pressure decreases. For example, in a rectangular channel, the pressure drop across the anode channel increased slightly from 39.7 Pa to 40.8 Pa as the cell voltage decreased from 0.65 V to 0.4 V. In contrast, the pressure drop in the cathode channel decreased from 68.1 Pa to 67.0 Pa over the same voltage change. This is driven by the stoichiometry of electrochemical reactions. Higher current density leads to more oxygen and water consumption at the cathode, and more water production at the anode. Pressure drop is also influenced by frictional forces between the fluid and channel walls, governed by fluid dynamics principles and the properties of the fluid species.\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{\\Delta\\:}\\text{P}=\\frac{32\\text{u}\\text{L}v}{{\\text{D}}_{\\text{h}}^{2}}\\:=\\:\\frac{64}{{R}_{e}}\\rho\\:g.\\frac{L}{{D}_{h}}\\frac{v}{2g}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eH\u003csub\u003e2\u003c/sub\u003e is much lower dynamics viscosity than O\u003csub\u003e2\u003c/sub\u003e, leading to significantly lower pressure drops in the anode channel compared to the cathode channel. This difference in pressure drop is observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a) and (b).\u003c/p\u003e \u003cp\u003eThe characteristics of fluid flow in confined channels depend on the channel's geometry, which determines the velocity distribution and impacts various transport phenomena. Analyzing the velocity distribution across different channel shapes is depicted in Fig. \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(a). The fluid velocity is low near channel walls due to viscous effects and the no-slip condition, while the maximum velocity occurs at the channel center, consistent with boundary layer theory. Fig. \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b) illustrates, the channel's geometric configuration significantly affects this velocity profile, resulting in notable differences in the maximum velocities across various shapes. The maximum velocity within these channels is influenced by the operational voltage, highlighting a correlation with the distinct cross-sectional geometry of each channel. The triangular channel has the highest maximum velocity, whereas the semicircular channel has the lowest, indicating the profound influence of channel shape on fluid dynamics. For instance, at 0.4 V, the maximum velocities in square, rectangular, semicircular, and triangular channels are 4.28618 m/s, 4.1856 m/s, 4.17292 m/s, and 4.78493 m/s, respectively, demonstrating that the sequence of maximum velocity is: triangular \u0026gt; square \u0026gt; rectangular \u0026gt; semicircular. This variation in maximum velocities arises from the interplay between the channel's cross-sectional geometry and the resulting flow dynamics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eTemperature\u003c/h2\u003e \u003cp\u003eThe performance of PEMFC\u003csub\u003es\u003c/sub\u003e is highly sensitive to operating temperature due to the temperature-dependence of species transport parameters. This is because the channel outlet exhibits high temperatures, stemming from the poor thermal conductivity of the electrochemical reaction gases, leading to inefficient heat dissipation which is clearly shown in figure.5 (b). This underscores the vital need for effective thermal management strategies in PEMFC design and operation. The thermal behaviour is a key determinant of overall performance, as temperature variations significantly impact cell voltage, especially at varying current densities. Elevated temperatures, caused by inadequate heat dissipation from the low-conductivity reactant gases, necessitate sophisticated thermal management systems. These systems are essential for maintaining optimal PEMFC performance through precise temperature control and mitigating accelerated component degradation from thermal gradients and excessive heat buildup.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eGas transfer\u003c/h2\u003e \u003cp\u003eThe electrochemical reactions within PEMFC govern their operational efficiency. At the cathode, the rate at which H\u003csub\u003e2\u003c/sub\u003eO is consumed is twice the rate at which O\u003csub\u003e2\u003c/sub\u003e is used (Yuan \u0026amp; Wang, 2008). Conversely, at the anode, water is produced at twice the rate of hydrogen consumption. Hydrogen consumption and dilution by water lead to decreasing hydrogen concentration along the flow geometry. Paradoxically, amount of oxygen available at the cathode increases along the flow direction, due to different rates of water and oxygen consumption. At the anode, hydrogen concentration varies across channel geometries, with the square channel exhibiting the most uniform distribution is observed in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(a). On the cathode side, the PEMFC configuration featuring square channels exhibits the highest oxygen concentration, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e(b), which corresponds to its superior overall performance, likely due to elevated current densities increasing the rate of cathode water consumption. The efficiency of water management, especially at the cathode, is critical to PEMFC performance. Channel geometry is a key design parameter that influences mass transport and electrochemical reaction kinetics, affecting the fuel cell's power output and efficiency.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eWater transport\u003c/h2\u003e \u003cp\u003eIn PEMFC\u003csub\u003es\u003c/sub\u003e, maintaining an optimal balance between liquid water and water vapor is crucial for high performance, especially below 100\u0026deg;C, as both phases influence membrane hydration, proton conductivity, and reaction kinetics. Effective water management is essential to sustain adequate membrane hydration while preventing electrode flooding and ensuring efficient gas transport. Local temperature and pressure variations can lead to water condensation, particularly in the cathode where water is produced; thus, understanding and controlling these parameters are key for optimizing fuel cell performance[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. In this present work, investigating the transport of liquid water, water vapor, and membrane-bound H\u003csub\u003e2\u003c/sub\u003eO in PEMFC\u003csub\u003es\u003c/sub\u003e is crucial, given the potential for phase interconversion and its impact on performance[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. Along the flow direction, there is a gradual increase in anodic water vapor concentration, while the cathodic concentration exhibits the opposite trend, due to the electrochemical reactions. Elevated temperatures facilitate greater the movement of water from the membrane to the gas phase affects the concentration gradients. The BPP design significantly affects water vapor concentration gradients, highlighting the complex relationship between geometry and mass transport phenomena that determine fuel cell operational effectiveness. The distribution of water concentration at the anode is highest in semicircular channels, followed by rectangular, triangular and square with corresponding standard deviations of 0.9409, 0.8013, 0.6550 and 0.6501 mol m\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e, respectively.\u003c/p\u003e "},{"header":"Conclusions","content":"\u003cp\u003eIn this study, a high-quality three-dimensional, two-phase, non-isothermal numerical model is develop to investigate the influence of channel geometry on the performance of PEMFC. This model enabled a detailed examination of how different channel shapes within parallel flow field configurations affect PEMFC performance.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe findings indicate that channel geometry plays a crucial role in influencing PEMFC performance, with the square channel demonstrating the highest efficiency 17.20% greater peak power density compared to the semicircular channel.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eIt is clear that at high voltages (\u0026gt;\u0026thinsp;0.65 V), there is no apparent difference in the cell performance; however, as the operating voltage drops, the functionality of FC becomes strongly reliant on the flow field shape. The square channel achieves highest current density at the same voltage, followed by the triangle, rectangular and semi-circular channels.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eTriangular channels have the highest pressure drop due to increased friction and flow constriction, while square channels have lower pressure drop and enable better mass transport.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe maximum velocity within these geometries is influenced by the operational voltage, highlighting a correlation with the distinct cross-sectional geometry of each channel. The triangular shape has the highest maximum velocity, whereas the semicircular channel has the lowest, indicating the profound influence of channel shape on fluid dynamics. For instance, at 0.40 V, the maximum velocities in square, rectangular, semicircular, and triangular channels are 4.28618 m/s, 4.1856 m/s, 4.17292 m/s, and 4.78493 m/s, respectively.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"Nomenclature","content":"\u003cp\u003e\u003cimg 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\" width=\"471\" height=\"587\"\u003e\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eDeclaration of competing interest\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, writing original draft, formal analysis, Manisha Singh Chauhan; figures formation, tablesformation, review and editing, Ajay Kumar Sharma and Arun Kumar Tiwari. The final, published version ofthe paper has been read and approved by all authors.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eManisha Singh Chauhan expresses gratitude to Dr. A.P.J. Abdul Kalam Technical University, Lucknow, Uttar Pradesh, India, for awarding the fellowship as part of the Homi Bhabha Teaching cum Research Fellowship. The authors extend their appreciation for the support received from the Department of Mechanical Engineering at the Institute of Engineering and Technology, Lucknow, India.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eManso, A.P.; Marzo, F.F.; Mujika, M.G.; Barranco, J.; Lorenzo, A. Numerical Analysis of the Influence of the Channel Cross-Section Aspect Ratio on the Performance of a PEM Fuel Cell with Serpentine Flow Field Design. \u003cem\u003eInt. J. 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On the Modeling of Water Transport in Polymer Electrolyte Membrane Fuel Cells. \u003cem\u003eElectrochim. Acta\u003c/em\u003e\u003cstrong\u003e2009\u003c/strong\u003e, \u003cem\u003e54\u003c/em\u003e, 6913\u0026ndash;6927, doi:10.1016/j.electacta.2009.06.070.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"PEMFC s , Channel shape, Flow field design, Cell performance, Computational fluid dynamics","lastPublishedDoi":"10.21203/rs.3.rs-6988123/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6988123/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe performance of Proton exchange membrane fuel cell, a promising energy conversion technology, is closely tied to the design of their flow fields. The Fuel cell architecture plays a critical role in distributing reactant gases, managing water, and dissipating heat within the system. For comprehension effect of FC\u003csub\u003es\u003c/sub\u003e design on PEMFC functionality, a detailed computational model is developed to investigate four different channel shapes with the same cross-sectional area in a parallel flow field configuration. The aim of this study, to unravel the relationship between channel geometry and fuel cell behaviour, focusing on gas transport, water dynamics, thermal profiles and current density. The investigation revealed that the channel geometry significantly influences PEMFC performance. The findings highlighted the pivotal role of channel shape in modulating mass transport, thermal characteristics, and water management within the fuel cell. Notably, the square channel geometry outperformed the other designs, exhibiting a 17.20% improvement in efficiency compared to the semi-circular channel also at 0.40 V, the maximum velocities in square, rectangular, semi-circular, and triangular channels are 4.28618 m/s, 4.1856 m/s, 4.17292 m/s, and 4.78493 m/s, respectively. This is attributed to the more optimized flow profile and reduced parasitic losses in the square channel design.\u003c/p\u003e","manuscriptTitle":"Simulation through CFD of Different Flow Field Designs for Enhancing Proton Exchange Membrane Fuel Cell Performance","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-07 09:00:29","doi":"10.21203/rs.3.rs-6988123/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"795bd528-98e0-4443-852c-ccd7337eb8dc","owner":[],"postedDate":"July 7th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-27T16:53:23+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-07 09:00:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6988123","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6988123","identity":"rs-6988123","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}