## 1 Introduction  
Hydrogen energy is one of the most promising clean power sources due to its efficient energy conversion and low carbon emissions. It can sustain diverse resources, the environment, and sustainable development needs in the new era. In the hydrogen energy industry, proton exchange membrane fuel cells (PEMFCs) are widely used in various transportation, industry, and portable energy applications because of their high conversion efficiency, high power density, and lack of pollution [1; 2; 3; 4; 5]. Thermal management plays a vital role in the performance of the fuel cell stack. On the one hand, the electrochemical reactions in the stack generate heat. On the other hand, the fuel cell stack has thermal inertia. Multiple coupling relationships exist between the stack and the coolant [6]. Therefore, it is necessary to design an effective thermal management system to maintain the thermal balance of the fuel cell system. The thermal effect can cause operating temperature changes, affecting the proton membrane's water content, the reaction catalyst's activeness, and thus the electrochemical reaction rate. Working at an appropriate temperature is conducive to improving the stack's output performance. When the temperature is excessively high, gas-phase water inside the membrane may leave the stack, causing local drying and even degradation of the electrolyte membrane [7]. On the other hand, if the temperature is too low, the cathode flow channel may be flooded, affecting the oxygen diffusion and increasing the concentration overvoltage, thus reducing the stack's output performance. It is well known that liquids possess a much higher heat capacity than gases [8], making liquid cooling the most suitable heat exchange method for high-power automotive fuel cell stacks [9]. The liquid cooling of fuel cells requires a reasonable coolant flow field and complex thermal management system support. A combination of reliable experiments and accurate system models is needed to study thermal management systems. [PERSON] et al. [10] tested a 10 kW fuel cell system and found that the coolant temperature constantly fluctuates with thermal hysteresis, impacting the stack's performance. To optimize the PEMFC system's thermal management, multi-dimensional models are studied [11]. [PERSON] et al. [12] developed a 2D thermal model and a thermal management system to simulate the temperature distribution characteristics during stack operation. The results showed that the maximum temperature of the fuel cell is suggested as the representative operating temperature because the maximum temperature can be more conveniently measured and monitored than other possible temperatures. [PERSON] et al. [13] established a 3D simulation model including fans and radiators and a 1D model to simulate a PEMFC's cooling system. The results indicate that the 3D simulation can quickly capture fluid flow distribution. In contrast, the simulation time of the 1D thermal system is short, and it can quickly guide the matching of heat transfer components. [PERSON] et al. [14] combined experiments and a computational fluid dynamic (CFD) model to demonstrate the importance of the thermal conductivity of the fuel cell's porous layers for analyzing the thermal effects. The strong influence of the temperature profile on water transport through the cell was demonstrated. [PERSON] et al. [15] simulated serpentine and parallel flow fields with the CFD model, and the results pointed out that heat transfer rate has different effects on different coolant flow fields. [PERSON] et al. [16] proposed a 3D two-phase model to investigate the interaction between water and thermal transport processes. This reveals a coupling relationship between water and thermal management where boundary temperature concurrently affects temperature and water saturation distributions.