Analysis of Entropy Generation Due to Heat and Mass Transfer in Porous Electrode of PEFC
Authors: Nishida Kosuke 
Published: December 2024

During operation of polymer electrolyte fuel cells (PEFCs), the complicated multi-physics phenomena including heat and mass transfer, ionic and electronic transport and electrochemical reaction simultaneously occur in porous electrodes. It has been well known that the kinetic-theory based oxygen reduction reaction (ORR) and two-phase transport within cathode electrodes cause the severe overpotentials and performance degradation. In the previous studies, the energy loss in fuel cells and electrochemical devices has been experimentally investigated by using electrochemical impedance spectroscopy (EIS) and classified into the activation, ohmic and concentration polarization. EIS technique is a powerful method to analyze the sources of their performance loss, however, it cannot locally identify the key factors and transport processes causing the loss. To further enhance the power density and efficiency of PEFCs, it’s necessary to discriminate the critical phenomena influencing on the performance degradation using an alternative approach and design the better electrode/channel structure for reducing the energy loss. Several researchers attempted to apply the analysis of entropy generation to the elucidation of performance loss mechanisms in fuel cells and electrochemical devices [1-3]. Entropy is a physical property representing the thermodynamic irreversibility. The entropy generation analysis enables to identify the dominant phenomena inducing the overpotential in such devices and contributes to design the optimum structure minimizing the energy dissipation. Kjelstrup and Røsjorde [1] numerically estimated the local entropy production in various layers of a one-dimensional PEFC and found that the dissipation of energy due to charge transport in the electrolyte membrane is more important than the that of diffusion in the electrode. The author introduced the entropy generation analysis into the two-phase flow simulation for the cathode diffusion media of a PEFC and succeeded to locally estimate the entropy production rate due to oxygen diffusion within the porous electrode in the past work [3]. This study further analyzed the distributions of entropy production rate due to the heat transfer, diffusion and electrochemical reaction in the cathode porous electrode in more detail using the conventional two-phase flow PEFC model and extracted the significant process affecting the cathode overpotential. The author also investigated the effect of land/channel geometry on the local entropy generations of these phenomena in the electrode and discussed how to design its structure reducing the entropy generation.
Fig. 1 shows the numerical results of the two-phase flow simulation and the entropy generation analysis in the cathode electrode. The two-phase flow model used in this study was developed by Natarajan and Nguyen [4]. (a), (b) and (c) denote the through-plane distribution of temperature across the cell and the profiles of oxygen concentration and water saturation in the cathode gas diffusion layer (GDL), respectively. (d), (e) and (f) are the distributions of entropy production rate due to heat flux, oxygen diffusion and ORR in the electrode. The fuel cell was operated for 50 s at the temperature of 80 oC and the current density of 1.0 A/cm2. It was noted that the entropy generation due to the electrochemical reaction gives a larger effect on the cathode overpotential than that of diffusion and heat transfer. That is very well known. The entropy production rate of ORR at the catalyst layer under the channel is larger than that under the land because the sufficient oxygen supply progresses the reaction more actively. Furthermore, the land/channel geometry has an influence on the entropy generation of diffusion and heat transfer in the cathode electrode. The entropy production rates due to oxygen diffusion and heat flux become remarkably high under the boundary between the channel and land owing to the large gradients of its concentration and temperature. To reduce the entropy generation in the porous electrode with the land/channel configuration, it’s necessary to design the cell structure uniformizing the reaction distribution and alleviating the gradients of current, concentration and temperature.
References:
[1] S. Kjelstrup, et al., J. Phys. Chem. B, 109, 9020 (2005).
[2] P. Charoen-amornkitt, et al., Int. J. Heat Mass Transf., 202, 123725 (2023).
[3] K. Nishida, ECS Trans., 112, 43 (2023).
[4] D. Natarajan and T.V. Nguyen, J. Electrochem. Soc., 148(12), A1324 (2001).

Figure 1