**1. Introduction**

As one of the solutions to the global energy crisis and environmental problems, the proton exchange membrane fuel cell (PEMFC) has the advantages of near-zero emissions and high conversion efficiency [1–5]. However, the commercialization process of PEMFC still faces many challenges. Among them, the hydrothermal management of PEMFC also needs effective technical breakthroughs, which is the research focus of scholars today [6,7]. During the operation of a PEMFC, heat will be generated with the generation of electric energy. Fuel cells primarily generate heat from the entropic heat of reactions, the irreversibility of the electrochemical reactions, ohmic resistances and heat from the condensation of water vapors [8]. The increase in temperature in a certain range is conducive to improving the activity of the catalytic layer and accelerating the rate of the electrochemical reaction, but if the heat energy is not discharged in time, the overall temperature of the PEMFC will be too high and the local temperature distribution will be uneven, which will seriously degrade its performance [9–11].

A cooling plate is an indispensable structure of a fuel cell stack. It can reduce the temperature of the PEMFC and improve the temperature distribution in terms of nonuniformity [12,13]. Many studies have proven that a reasonably distributed flow channel can effectively improve the uniformity of temperature distribution during fuel cell operation, reduce the pressure drop of the cooling flow channel, avoid the occurrence of fluid blockage and cause the cooling liquid to circulate quickly.

**Citation:** Song, J.; Huang, Y.; Liu, Y.; Ma, Z.; Chen, L.; Li, T.; Zhang, X. Numerical Investigation and Optimization of Cooling Flow Field Design for Proton Exchange Membrane Fuel Cell. *Energies* **2022**, *15*, 2609. https://doi.org/10.3390/ en15072609

Academic Editor: Antonino S. Aricò

Received: 3 March 2022 Accepted: 30 March 2022 Published: 2 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Kurnia et al. [14] studied the heat transfer performance of parallel, serpentine, wavy, coiled and novel hybrid channels, and the coiled-base channel was discovered to be a desirable option, particularly in sensitive applications where cooling performance is crucial. Jeon [15] examined the cyclic and single cells and discovered that at high current densities, the cyclic cell's voltage was lowered due to increasing ohmic losses. The innovative serpentine channel exhibits the highest uniformity index of temperature distribution, power density and pressure drop, according to Atyabi et al. [16]. In comparison to other types, the design obtained the lowest temperature observed at the catalyst layer. The cooling field in serpentine channels had several passes and a high channel length, which allowed heat to be removed from the system but resulted in a substantial pressure drop across the system. Matian et al. [17] reported that increasing the size of the cooling channels resulted in a more uniform temperature distribution because more air could pass through the channels for a given pressure drop, allowing more thermal energy to be exchanged between the plate and cooling air. According to the research of Wilberforce et al. [18], a mixture of serpentine and parallel flow channels was intended to deliver better performance, owing to the prevalence of the serpentine channel portion, while still ensuring an overall lower pressure drop given the presence of parallel bypass channels, and the adapted serpentine designs with bypass channels presented a pressure drop 50 times lower than the classical serpentine design. Rahgoshay et al. [19] performed numerical analysis on two conventional cooling plates with serpentine and parallel flow fields, and found that modifying the rate of heat transfer has an effect on the performance of PEMFC and PEMFC with serpentine cooling flow fields compared to parallel cooling flow fields. In terms of effective physical parameters, the serpentine flow field offers greater cooling performance. According to the research of Yang et al. [20], operating temperatures have been shown to have significant effects on water distribution, and cells running at low temperatures have been shown to be more prone to severe water flooding, particularly downstream. Shian et al. [21] also discovered the essentiality of downstream water management; they investigated traditional straight channel cooling plates and innovative non-uniform flow channel designs, and the results showed that the downstream flow area improves the heat dissipation performance of the cooling plate. The results show that the optimum thermal, water, and gas management may be found in serpentine-based channel designs, and because of the substantially smaller pressure drop, the innovative hybrid parallel-serpentine-oblique-fin channel design generates the most net power. Sasmito et al. [22] evaluated numerically the performance of various gas and coolant channel designs simultaneously. Due to the existence of complex turns, Ravishankar et al. [23] presented four new designs and discovered that in comparison to serpentine, the pressure drop needed to accelerate the flow is higher in spiral and innovative designs. Castelain et al. [24] created an experimental device in order to characterize the chaotic geometries' thermal properties under consideration, and the measurements corroborated the simulated values, which indicate that for chaotic geometries, the interior convective heat transfer coefficient significantly increases when compared to the tube with no bends. Liu et al. [25] used the genetic algorithm with several objectives to optimize the operating condition, and then used the multi-objective genetic algorithm to optimize the PEMFC's channel design based on the ideal operating condition. The best channel produced through optimization was a tapered channel with heights of 0.3909 mm and 0.2042 mm at the inlet and outflow, respectively.

Innovative heat dissipation methods combined with a traditional cooling flow field are also being studied. Wen et al. [26] cut six pieces of heat conducting pyrolytic graphite into a channel shape, bound them to six central cathode airway plates and added forced convection; the results showed that this significantly reduced the volume, the temperature control system's weight and cooling capacity. Lin et al. [27] carried out a numerical analysis of a PEMFC stack with water cooling to determine the impact of configurations and cathode operating parameters on stack power density and efficiency of the system. The orthogonal analysis method has been shown to be reliable in obtaining the best with a confidence level nearing 95%, a mixture of setups and cathode operating conditions

was discovered. Using graphite plates, Yin et al. [28] developed a new kW-scale aircooled PEMFC stack. The experimental results confirmed that the stack with a channel on the edge performs better than the standard stack without edge channels. Because of the improved internal water balance, the counter-cross flow operation is better for stack performance than the co-cross flow operation. To improve the thermal management of a 10-cell air-cooled PEMFC stack. As heat spreaders, Zhao et al. [29] used five vapor chambers. The findings suggest that a high effective thermal conductivity can improve heat transfer and even out the temperature in the stack. Afshari et al. [30] compared the cooling performance of four different design methods, parallel flow field, serpentine flow field and metal foam porous medium flow field, among the models tested, a model with a porous metal foam flow field is the right alternative for decreasing the surface temperature difference, highest surface temperature, and average surface temperature. According to the simulation, Zhang et al. [31] investigated a novel method of cooling for a PEMFC stack; low membrane hydration is also caused by a higher temperature in the stack and, as a result, cell performance is limited, and the current density distribution is not uniform. The current cooling technique may be improved by boosting the heat transfer co-efficient between the stack and the coolant to minimize local overheating and improve the cell performance, according to the findings. To eliminate the need for a bulky humidifier and to lighten the cooling load of PEMFCs. Hwang et al. [32] used an external-mixing air-assist atomizer to build a cathode humidification and evaporative cooling system, and discovered that the humidification impact increased stack performance while the evaporative cooling effect decreased coolant temperature at the stack output. Saeedan et al. [33] proposed using water-CuO nanofluid as the coolant fluid and filling the flow field in the cooling plates with metal foam. The results showed that at low Reynolds numbers, the role of nanoparticles in improving temperature uniformity is more prominent. Furthermore, metal foam can lower the maximum temperature in the cooling channel by approximately 16.5 K and uniformize the temperature distribution, while the pressure drop increases only slightly. Asghari et al. [34] investigated the design of a cooling flow field as well as a thermal management sub-system of a 5 kW PEMFC system. The numerical simulation results show that a higher flow rate of coolant results in a more uniform temperature distribution, whereas a lower flow rate results in less pressure drop and parasitic losses. Ghasemi et al. [35] designed and simulated six cooling flow field designs. The results show that the spiral cooling flow field has the most uniform temperature distribution, but the pressure drop is large.

According to the literature created by predecessors, the design of a PEMFC cooling flow field shows a diversified trend, but there are still few field designs, especially for hightemperature PEMFCs, and most designs are lacking in innovation. This paper presents five innovative PEMFC cooling flow field designs, and analyzes the heat dissipation performance of the cooling plate by comparing the temperature and temperature uniformity, maximum temperature, pressure drop and cooling liquid velocity between the traditional serpentine cooling flow field and each new flow field. In addition, the operating conditions are optimized according to the numerical analysis.
