Abstract
Passive thermal management using a phase-change material (PCM) for proton exchange membrane fuel cells (PEMFCs) has been proposed and widely used in the thermal management of Li-ion batteries. A three-dimensional and nonisothermal numerical model of a PEMFC with a PCM cooling channel (PCC) is established in this study. The PCC is better than an air-cooling channel (ACC) in terms of reactant distribution and water removal. Its temperature at the interface of the gas diffusion layer and catalyst layer is lower, and the uniformity of temperature is better. The peak current and power density of the PCC are 4.60% and 5.14% higher than those of the ACC, respectively. Furthermore, the PCC does not increase parasitic power, unlike the ACC. In addition, owing to the high temperature near the outlet, the cooling effects of filling 1/3 PCM and filling 2/3 PCM near the outlet and filling of all PCM are investigated, which shows that the filling of 2/3 PCM provides a better cooling performance.
1. Introduction
Proton exchange membrane fuel cells (PEMFCs) are used as environmentally friendly power equipment [1] with a high energy density, absence of pollution, low operating temperature, and low noise [2, 3]. However, their use is hindered by their high manufacturing cost and short service life. Improving the performance through channel design and better thermal management is necessary for large-scale commercialisation [4]. In recent years, the design of channels and the thermal management of PEMFC have been of interest worldwide. Heat is generated during the electrochemical reaction in a PEMFC. Mainly, electrochemical reaction heat, Ohmic heat, and latent heat of phase change [5], which affect the operation of the PEMFC, including the transport of reactants and conductivity of the membrane electrode, are observed [6]. Research on enhancing the water and thermal management of PEMFCs has been focused mainly on improving the arrangement of channels and adding air-cooling channels (ACCs) and liquid-cooling channels. In-depth studies demonstrated that the bionic channel not only increases the power but also improves the uniformity of the temperature in the PEMFC [7]. Huang et al. [8] designed a bionic channel based on the structural characteristics of the human mesenteric artery and reported that its thermal management was stronger than that of a serpentine channel. Limjeerajarus and Santiprasertkul [9] proposed a hybrid serpentine-interdigitated channel and analysed the effects of different numbers of inlets and outlets on water transport and heat distribution in a PEMFC. These studies demonstrated that an optimal channel design can improve the thermal management performance of the PEMFC.
The optimal design of channels in water and the thermal management of the PEMFC are limited. The temperature affects almost all parameters related to the PEMFC [10], such as the catalyst activity, Ohmic impedance, reactants, and product diffusion coefficient. Therefore, it is necessary to perform passive thermal management for the PEMFC. The addition of ACCs and liquid-cooling channels is a common approach [11, 12]. Shen et al. [13] analysed the reverse flow cooling of an interlayer channel and the bidirectional circulating cooling; they reported that the bidirectional circulating cooling could reduce the temperature difference. Pei et al. [14] studied the effects of gas diffusion layer (GDL) characteristics and air flow rate in an ACC on the stack temperature and reported that an increase in the air flow rate is helpful for water management. Chen et al. [15] developed a partially separated and partially coupled channel to improve the oxygen concentration near the outlet, which is conducive to the uniformity of water and temperature. Song et al. [16] studied low-power air-cooled stacks and reported that the maximum power of the stacks could be obtained when the air flow was 55.7 SLPM. Rahgoshay et al. [17] analysed the performance of a serpentine liquid-cooling channel and a parallel liquid-cooling channel and compared the effects of a non-liquid-cooling channel; they reported that the serpentine cooling channel had a better uniformity index of temperature. Xu et al. [18] studied the influence of a phase-change-induced flow on water transport in porous media and reported that an increase in the operating temperature promoted a phase-change-induced water transport. In addition, there are other methods of thermal management for fuel cells. For example, Peng et al. [19] balanced the cooling effect and water removal by inserting porous media at the outlet of the channel and reported that the current density increased by 18% compared to the parallel flow field.
Phase-change materials (PCMs) have been widely used in the thermal management of Li-ion batteries owing to their large latent heat of phase change [20]. Diaconu et al. [21] discussed the research progress of active and passive technology, system design, and optimization of phase-change heat storage. Hamidi et al. [22] reviewed the research related to enhancing the heat transfer of metal foam with PCM. Osman et al. [23] studied the application of PCM in building thermal management. As power sources, Li-ion batteries and fuel cells have high-temperature uniformity requirements. Composite PCMs and phase-change fluids have been widely used in the passive thermal management of Li-ion batteries [24, 25]. Zhao et al. [26] achieved thermal management via coupling PCM and heat pipes for cylindrical power batteries and reported that the cooling effect of the PCM was better than that of air cooling. Safdari et al. [27] analysed the influence of the shape of the PCM containers on the cooling performance and reported that the thermal management performances of hexagonal and circular PCM containers were similar. Wu et al. investigated the performance of a composite PCM with paraffin-coupled graphite and reported that the cooling effect was best when the mass fraction of graphite was 15–20% [28]. According to the above study on the application of PCMs to the thermal management of power batteries, PCMs exhibit excellent thermal management performances. Therefore, thermal management using PCMs should be considered for PEMFCs.
The thermal management of PEMFCs focuses on channel design and air or liquid cooling, which increases the parasitic power. PCMs have been extensively applied in the thermal management of Li-ion batteries. However, they have not been extensively used in the thermal management of PEMFCs. To achieve better thermal management of PEMFCs, passive thermal management using a PCM is proposed, and a three-dimensional (3D) and nonisothermal numerical model of a PEMFC with an ACC and a PCM cooling channel (PCC) is established. The performance of the PEMFC under different cooling channels was analysed, including the concentrations of the reactants and products, temperature distribution and uniformity, membrane conductivity, and current density. In addition, considering the high temperature near the outlet of the flow channel, the cooling effects of fillings of 1/3 PCM and 2/3 PCM near the outlet and filling of all PCM in the cooling channel were investigated. The passive thermal management of the PEMFC using a PCM imparts higher competitiveness, better temperature uniformity, and better performance than air cooling while not increasing the parasitic power.
2. Numerical Model
2.1. Physical Model
The 3D model of PEMFC proposed in this paper is illustrated in Figure 1. The geometric structure of the model consists of a PEM, cathode/anode catalytic layer (CL), cathode/anode GDL, cathode/anode channel, cathode/anode ACC or PCC, and cathode/anode bipolar plate (BP). The inlets of the channels and ACC were at the front of the model, while their outlets were at the back of the model. To reduce the calculation time, the model was simplified to a single-channel geometric model of PEMFC. Table 1 shows the geometric parameters of the model.

2.2. Governing Equations and Boundary Conditions
The governing equations of the numerical model have been reported, including the continuity, momentum, energy, species transport, electron and proton transport, and electrochemical equations [29–32]. The following assumptions are employed [33, 34]: (1)The operation of the PEMFC is stable(2)The gas flow in the channel is laminar(3)All gases in the channel are considered ideal gases(4)The PEM, CL, and GDL are homogeneous and isotropic(5)The PEM does not allow gas to pass through(6)The effect of gravity is ignored
The governing equations and boundary conditions are as follows:
Continuity equation: where is the porosity of the porous zones (GDL and CL) ( for the channel zone), is the density of the reactants, is the velocity vector of the reactants, and is the mass source term. The reaction occurs in the CL. Thus, in the channel and GDL, . In the anode/cathode CL, is as follows: where denotes the Faraday constant, , , and are the molar masses of hydrogen, water, and oxygen, respectively, and and are the cathode and anode transfer current densities, respectively.
Energy equation: where is the specific heat capacity at a constant pressure, is the temperature, is the effective thermal conductivity, and is the energy source term, which is expressed as follows: where is the current density, is the Ohmic resistivity, is the reaction enthalpy, and is the cathode/anode over-potential.
Momentum equation: where is the pressure of the reactants and is the dynamic viscosity. is the momentum source term in the cathode and anode channels (). in a porous medium is as follows: where is the permeability of the porous medium.
Species transport equation: where denotes the molar fraction of species , denotes the effective diffusivity coefficient of species , and denotes the species source term. In the channel and GDL, , while in the anode/cathode CL is as follows:
The effective diffusivity coefficient of species is as follows: where is the reference diffusivity coefficient of species , is the reference temperature, and is the reference pressure.
Electron and proton transport equation: where the subscripts and denote the solid and membrane phases, respectively, is the electrical conductivity, and is the electric potential. is the current source term:
The PEM conductivity is as follows [33]: where is the water content.
Electrochemical equation:
The electrochemical reaction in the cathode/anode CL was solved using the Butler–Volmer function. where and are the reference exchange current density per unit active surface area, is the specific active surface area, is the concentration-dependent index, is the transfer coefficient, is the universal gas constant, and is the local surface over-potential: where is the cathode open-circuit voltage.
PCM model:
For a cooling channel filled with a PCM, the state of the PCM determines its thermophysical properties. The specific heat capacity () of the PCM is as follows [35]: where , , and are the heat capacities of the solid PCM and liquid PCM and latent heat of the PCM, respectively, , , and are the temperature of the PCM, the initial temperature of the phase change, and end temperature of the phase change, respectively, and is the volume fraction of the liquid PCM, which is expressed as follows:
Boundary conditions and model settings:
The reactant flow in the channel was considered fully developed. The inlet velocities were computed by the following equation [36]: where represents the stoichiometry, is the reference current density, is the species mass fraction, and is the cross-sectional area of the channel.
The outlet of the channel was set to atmospheric pressure. Nonslip conditions were employed for all channel walls. The anode BP was grounded, the potential was 0 V, the cathode BP was set to an open-circuit voltage, and the surface temperature was 293.15 K. In addition, the air flow rate in the ACC was 0.05 m/s, while the air inlet temperature of the cooling channel was 293.15 K. Table 2 lists the model parameters and boundary conditions. The physical parameters of sodium acetate trihydrate, the PCM filled in the cooling channel, are listed in Table 3, and the termination phase transition temperature of PCM is 339.18 [37].
2.3. Model Validation
To ensure the reliability of the simulation, model verification and grid-independence tests were performed using the PEMFC model. The model in this study is similar to that of Sezgin et al. [38]; therefore, a model with the same geometric parameters and operating conditions as those of Sezgin et al. was established for verification. The verification results are shown in Figure 2. The polarisation curve of the model in this study is in agreement with the polarisation curve of the model of Sezgin et al.; therefore, the calculated results are reliable. In addition, the model was verified by grid-number independence. 239219, 294064, 357771, 404347, and 451387 grids were used for the calculations. As shown in Table 4, the relative errors of the 404347 and 451387 grids were smaller than those of the previous model at 0.5 V, which were 0.240% and 0.135%, respectively. The model was subsequently calculated with a grid number of 404347.

3. Results and Discussion
3.1. Mass Transfer Analysis under PCC and ACC
The concentration and uniformity of the reactants and products have crucial influences on the performance of the PEMFC [39]. Figure 3(a) shows the molar fraction of oxygen at the interface of the cathode, GDL, and CL. The oxygen molar fraction was close to that of the inlet; however, the oxygen molar fraction of the PCC was higher than that of the ACC at the middle surface. Therefore, the PCC is conducive to oxygen transmission. Figure 3(b) shows the average value and uniformity index of the oxygen molar fraction. The uniformity index can be calculated as follows [40]: where is a local parameter such as the oxygen molar fraction, water molar fraction, and temperature. represents the average values of parameters. is the area of the interface between the GDL and CL.

(a) Distribution of the oxygen molar fraction

(b) Average value and uniformity index
The average oxygen molar fraction of the PCC was 0.116, which was higher than 0.107 in the ACC. The uniformity of the oxygen molar fraction in the PCC was 0.681, which was higher than 0.573 in the ACC. Thus, the average value and uniformity index of the oxygen molar fraction of the PCC were higher than those of the ACC.
As shown in Figure 4(a), the water molar fraction at the interface of the cathode GDL and CL in the PCC was lower than that in the ACC, which was more evident near the outlet. Figure 4(b) shows the average value and uniformity index of the water molar fraction at the interface of the cathode GDL and CL. The average water molar fraction of the PCC is lower than that of the ACC, while the uniformity of the water molar fraction is larger than that of the ACC. Therefore, the PCC can improve water removal.

(a) Distribution of the water molar fraction

(b) Average value and uniformity index
To further investigate the effect of the PCC on the mass transfer of reactants and products, the diffusion coefficients of oxygen and water along the length direction at the interface of the channel and GDL and along the depth direction in the middle of the model were analysed. Figure 5(a) shows the diffusion coefficients of oxygen and water along the length direction at the interface of the cathode channel and GDL under different cooling channels. Notably, the diffusion coefficients of oxygen and water in the PCC are higher than those in the ACC. Therefore, the PCC is conducive to the transmission of oxygen along the length and can improve the effect of water removal in the channel. Figure 5(b) shows the diffusion coefficients of oxygen and water along the depth direction of the cell in the middle of the model, where the depth direction is from the top of the cathode channel to the bottom of the PEM, and the top of the flow field retains a part of the distance. The front parts of the curves represent the diffusion coefficients of oxygen and water in the channel from top to bottom, which hardly change. However, from the second half of the curves, which are in the porous zones of the GDL and CL, the diffusion coefficients of oxygen and water exhibit an obvious downward trend. The last part of the curve is in the PEM zone; the oxygen and water diffusion coefficients exhibit stable trends. In addition, the diffusion coefficients of oxygen and water along the depth direction of the cell were consistent with the diffusion coefficients of oxygen and water along the length direction of the cell at the interface of the channel and GDL under the PCC and ACC because the diffusion coefficients of oxygen and water in the PCC were higher than those in the ACC. This shows that the mass transfer in the PCC was stronger than that in the ACC, along the length of the channel and along the depth of the cell.

(a) Along the cell length direction

(b) Along the depth of the cell
3.2. Temperature and Performance Analysis under Different Cooling Channels
Figure 6(a) shows the temperature at the interface of the cathode GDL and CL under the two cooling channels. The temperature of the PCC is lower than that of the ACC at the interface of the cathode GDL and CL. The temperature of the PCC near the outlet is lower. Figure 6(b) presents the average value and uniformity index of the temperature under different cooling channels. The average temperatures of the PCC and ACC are 354.41 and 355.47 K, while their uniformity indices of temperature are 0.684 and 0.569, respectively. The PCC is superior to the ACC in terms of cooling effect and temperature uniformity.

(a) Temperature distribution

(b) Average value and uniformity index
Figure 7(a) shows the conductivity of the PEM in the two cooling channels. The conductivity of the PEM in the PCC is higher than that in the ACC, which is conducive to an increase in the electrochemical reaction rate. Figure 7(b) shows the polarisation and power density curves for the two cooling channels. The concentration loss area and polarisation curve of the PCC were higher than those of the ACC. The peak current density and peak power density of the PCC were 4.60% and 5.14% higher than those of the ACC, respectively. In summary, the PCC has a better cooling effect, a more uniform temperature, and a higher PEM conductivity; therefore, the performance of the PCC is better than that of the ACC.

(a) PEM conductivity

(b) Polarisation and power density curves
3.3. Performance Analysis of Filling of Different Contents of PCM
The temperature near the outlet of the channel was relatively high. Therefore, to improve the uniformity of the temperature of the PEMFC, the cooling performances of fillings of 1/3 and 2/3 PCM near the outlet and filling of all PCM in the cooling channel were investigated. A schematic of the model is shown in Figure 8.

Figure 9(a) shows the temperature at the interface of the cathode GDL and CL filled with different PCM contents. The temperature of the filling of 1/3 PCM was highest, particularly near the outlet; the temperatures of the filling of 2/3 PCM and the filling of all PCM were significantly lower. Notably, the temperature of the filling of 2/3 PCM near the inlet was slightly higher than that of the filling of all PCM, but their temperatures near the outlet were almost the same. Figure 9(b) shows the average temperature and temperature uniformity index for different PCM contents. The temperature uniformity index of the filling of 2/3 PCM was the highest, followed by that of the filling of all PCM. The temperature uniformity index of the filling of 1/3 PCM was the worst. The average temperature of the filling of 2/3 PCM was only slightly higher than that of the filling of all PCM; however, its temperature uniformity was higher than that of the filling of all PCM. Finally, the polarisation and power density curves for different PCM contents were analysed, as shown in Figure 9(c). The polarisation curve of the filling of 1/3 PCM is lower than that of the fillings of 2/3 PCM and all PCM. The polarisation curve of the filling of 2/3 PCM is slightly higher than that of the filling of all PCM. The peak current density and peak power density are increased by 2.67% and 2.94%, respectively.

(a) Temperature at the interface between the cathode GDL and CL

(b) Average value and uniformity index of temperature

(c) Polarisation and power density curves
4. Conclusions
In this study, a passive thermal management method using a PCM for PEMFCs was proposed, a 3D and nonisothermal numerical model was established, and the performances of the PEMFC under the PCC and ACC were analysed. In addition, the cooling performances of fillings of 1/3 PCM, 2/3 PCM, and all PCM near the outlet of the cooling channel were analysed. Based on the above investigation, the following conclusions were obtained: (1)Compared to that at the ACC, the oxygen molar fraction at the interface of the cathode GDL and CL was higher and more uniform, and the water molar fraction at the interface of the cathode GDL and CL was lower and more uniform in the PCC. The diffusion coefficients of oxygen and water on the surface of the channel along the length of the cell and in the middle of the model along the depth of the cell were higher in the PCC than in the ACC(2)In terms of the GDL and CL interface temperatures of the cathode, the PCC had a lower temperature and better temperature uniformity than the ACC. The PEM conductivity of the PCC was higher than that of the ACC. The peak current density and peak power density of the PCC were increased by 4.60% and 5.14%, respectively, compared to those of the ACC, which showed a better performance for the PCC than that for the ACC(3)The filling with 2/3 PCM near the outlet of the cooling channel was better than the filling with all PCM in terms of temperature uniformity. The peak current density and peak power density of the filling with 2/3 PCM in the cooling channel were 2.67% and 2.94% higher than those of the filling with all PCM, respectively, whereas the filling with 1/3 PCM exhibited poor performance
In the future, passive thermal management using PCMs can be studied on stacks. The effect of the PCC on the internal temperature of the PEMFC and the transport of reactants and products, as well as the causative factors, needs to be further studied.
Nomenclature
: | molar fraction of species (mol·m-3) |
: | velocity vector (m·s-1) |
: | source term |
: | diffusion coefficient (m2·s-1) |
: | current density (A·m-2) |
: | enthalpy change (kJ·kg-1) |
CL: | catalyst layer |
: | effective thermal conductivity (W·m-1·K-1) |
: | Ohmic resistance (Ω) |
: | latent heat (kJ·kg-1) |
: | porosity |
: | density (kg·m-3) |
: | electric potential (V) |
: | transfer coefficient |
: | local surface over-potential (V) |
: | volume fraction of liquid phase |
: | constant-pressure heat capacity (J·kg-1·K-1) |
: | open-circuit voltage (V) |
PEMFC: | proton exchange membrane fuel cell |
: | universal gas constant |
GDL: | gas diffusion layer |
: | temperature (K) |
: | absolute permeability (m2) |
: | Faraday’s constant (96487 C·mol−1) |
: | current density (A·m-2) |
: | specific active surface area (m2). |
: | concentration dependence |
: | stoichiometry |
: | conductivity (S·m-1) |
: | dynamic viscosity (Pa·s) |
: | water content. |
: | cathode |
: | anode |
: | solid phase |
: | channel |
: | mass fraction |
PCC: | PCM cooling channel |
: | membrane phase |
: | effective |
: | reference value |
: | liquid phase |
ACC: | air cooling channel. |
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no competing financial interests or personal relationships that may have influenced the work reported in this study.
Acknowledgments
This study was supported by the Natural Science Foundation of Hebei Province (No. E2019203527).