*3.2. PEMFC Modeling*

In this study, the mass flow rates and temperature of the exhaust water from the PEMFC's coolant channel were used as inputs for the TEG unit simulations. Figure 13a,b shows the computed characteristic curves of the PEM fuel cell with the input parameters listed in Table 1. The open circuit voltage at low current density decreased because of fuel crossover. Activation losses caused the pronounced non-linear decrease in voltage at low current density. Ohmic losses resulted in a close to linear dependence until the onset of mass transport limitations became dominant at high current densities and fuel conversion.

The effects of selected model parameters relevant to thermal and water management were further evaluated using published data, as a further verification after the I-V curve comparison in Section 3.1. The one-dimensional numerical study by Falcão et al. [48], which was compared to experimental data [49,50] and a three-dimensional model [51], evaluated differences in water content and local transport properties, depending upon the membrane thickness using a one-dimensional model. Their evaluation considering four thicknesses (0.0051 cm, 0.0127 cm, 0.0178 cm, 0.003 cm) concluded that low thicknesses result in lower ionic resistance and voltage loss, hence better cell performance. However, the fabrication of MEA with thin membranes is a challenge, and other factors such as mechanical integrity of the membrane and manufacturing cost should be considered. Figure 13c illustrates the variations in water content and effective conductivity computed for different membrane thicknesses, showing qualitative agreement.

The purpose of the present agglomerate PEMFC model was to calculate the output thermal power. It should be noted that all types of heat transport and transfer by conduction, radiation, and convection were at play in the electrodes. The sources of heat in the polarized CLs were ohmic losses induced by charge transport, entropy changes, and activation overpotentials due to electrochemical reactions. The effectiveness factor (Equation (19)) is a metric for the assessment of the cell performance. An effectiveness factor equal to one corresponds to the

limiting case where all the catalyst surface area is active under polarization. It can be determined for both cathode and anode sides after calculation of the Thiele modulus (Equation (20)), which is the ratio of the reaction rate on the catalyst surface to the reaction rate without any transport losses. Figure 14 illustrates the changes in the effectiveness factor and the flux density of hydrogen upon variations in current density. Figure 14b shows that transport losses increase with increasing current, leading to an effectiveness factor approaching zero. Figure 14a indicates that hydrogen crossover increases drastically at current densities higher than 0.8 A/cm2, which is detrimental for the cell's performance and is known to increase the degradation. A current density of 0.8 A/cm2 was, therefore, the selected operation point for the coupling with the TEG module. The corresponding simulated electrical power and efficiency were 3.34 kW and 39%.

**Figure 14.** Simulated CL behavior as a function of current density: (**a**) surface-specific flux of H2; (**b**) effectiveness factors on the cathode and anode sides.

### *3.3. TEG Simulation*

As mentioned, the TEG unit will not have a direct impact on the performance of the PEMFC unit, although the integrated system of the PEMFC-TEG will have higher output power in comparison to the standalone PEMFC. The simulated output flow of water from the PEMFC's coolant channel (3 kg/s at 330.5 K, at 0.8 A/cm2) is used as the hot-side water exchanger inlet condition for the analysis of the TEG unit for waste heat recovery. Prescribed boundary conditions are the pressure outlet of the TEG unit and a temperature of 30 ◦C at all exterior walls of the PEMFC and TEG coolant domains, except those in contact with the TEG modules. A uniform convection heat transfer coefficient of 15 <sup>W</sup> m2K is assumed. The cold side coolant exchanger (see Figure 6) is fed with 1.37 kg/s of water at 30 ◦C. The reason for the mentioned flow rates of water in the TEG heat exchange module is to validate the results with the given data by Fernández-Yañez et al. [28]. Ahn and Choe [52] had already suggested the minimum mass flow rate of 0.8 kg/s for the PEM fuel cell in the coolant channel. The inlet temperature at the hot side of the water exchanger has been calculated using the agglomerate model for the PEMFC while the inlet temperature at the cold side of the water exchanger is based on the study developed by Liso et al. [53]. The high resolution Rhie-Chow [54,55] scheme with a convergence criterion of 10−<sup>5</sup> is applied for the coupling between pressure and velocity. Additionally, the 40 elements forming the TEG unit are assumed to be thermally and electrically insulated from each other.

Recovering the output flow of the PEMFC by the TEG unit, Figure 15 shows the corresponding contours of temperature, voltage, and power density in the TEG unit both on the water and coolant exchanger sides. The cooling effect of cold water on the flow of water from the PEMFC entering the water exchanger of the TEG unit is as expected in Figure 15. The regions with higher temperature in Figure 15b also result from back flow pressure on the edges, leading the water to flow around a circle. In the water exchanger, the presence of a boundary layer on the sides of the heat exchanger causes lower temperature

compared to the other parts of the heat exchanger. Consequently, the temperature on the side of the coolant exchanger is comparatively lower as well.

**Figure 15.** The contours simulated by the TEG unit model: (**a**) temperature on the hot side of the TEG that is in contact with the water flow from the PEMFC's; (**b**) temperature on the cool side of the TEG fed with cooling water at 30 ◦C; (**c**) voltage distribution in the TEG; (**d**) spatial distribution of electrical power in the TEG considering the surface are of 117 cm2 for each module of the TEG unit.

The voltage of the TEG units computed by Equation (27) is dependent upon the solid hot water exchanger side temperature, leading as expected to a potential distribution such as shown in Figure 15c. The maximum voltage is 1.36 V, which is much lower than values around 8 V in ref. [28]. The reason is the higher hot source temperature in the light-duty diesel engines due to higher exhaust heat. The cold-side temperature varies by approximately 2 ◦C, showing that the assumption of constant cold-side temperature in Equations (27)–(29) was acceptable for the present study, even though it does not allow the analysis of the effects of flow patterns in Figure 15b on the output electrical power. Figure 15d shows the contour of produced electrical power in footprint mesh cell of the TEG unit. It indicates that the maximum local power in the module is 3.61 ×10−<sup>3</sup> W/cm2, compared to the total power of 37.7 W and the averaged power density of 0.00806 W/cm2. The corresponding value of the TEG surface-specific power density for the whole unit was also 3.41 W/cm2.

Other parameters to be considered were the PEMFC's current density, which was set at 0.8 A/cm2 in this study, and the PEMFC water cooling flux. Under the corresponding thermal conditions, the visual inspection of the temperature profile indicated that the TEG modules produce up to roughly twice less electrical power than the central ones. Moreover, the temperature difference between the cold and hot side is almost constant along the central lines in Figure 15a. This suggests that higher efficiency recovery may be achieved with a larger, yet more expensive heat exchanger module and/or improved heat exchanger designs. PEMFC operation at higher current density produces more excess heat. In the case where the stack temperature is kept at 353 K (80 ◦C) and the coolant water flow is kept constant, the temperature of the latter will increase, compared to 330 K (57 ◦C) in Figure 15a at the inlet. Therefore, the TEG output electrical power is expected to increase. Herein, the beneficial effect on TEG performance may well compensate for the heat exchanger limitations and lead to higher recovery efficiencies. Alternatively, the recovery efficiency in the present case of 0.8 A/cm2 can be increased by decreasing the PEMFC cooling water flow, which was not the case in the current study, as the coolant flow of PEMFC was in a separate water loop of the PEMFC's stack, and the water mass flow rate was assumed to be constant. As expected, the TEG module and PEMFC must be designed and operated in synergy for viable recovery efficiencies over a sufficiently large window of operation conditions for automotive applications.

#### **4. Conclusions**

This study investigated the relevance of TEG technology to recover the waste heat from the PEMFC. It was inspired by the idea of producing electricity from the exhaust heat of light-duty diesel engines by TEG. Herein, an agglomerate one-dimensional PEMFC model was developed to estimate the maximum output heat from the fuel cell stack. The validation of the I-V characteristic curves of the current model with six different series of experimental and simulation data proved the suitability of the developed model. Under the considered PEMFC operating conditions and assumptions, the simulated output water temperature and flow rate from the PEMFC's coolant channel were 330.5 K and 3 kg/s, respectively. The CFD thermal simulations with cooling water at 30 ◦C combined with post-processing based on empirical relationships for the local TEG electrical performance resulted in a modest total output electrical power of 37.7 W. The voltage was in the range of 1.25 V and showed non-uniformity (0.77–1.36 V), suggesting potential for improvement of the TEG heat exchanger design, as well as of the PEMFC operating conditions for waste heat recovery. The figures were, therefore, modest. Although this study presented the integration of the TEG unit as a cooling method for a medium-scale size of the PEMFC, further research can be performed for future studies:


• The materials in the TEG modules and their figures of merit play a crucial role in the performance of the TEG unit and the waste heat recovery. This study assumed Bi2Te3 as the base material of the TEG modules, while many other alternatives can be analyzed and evaluated to reach the highest waste heat recovery.

**Author Contributions:** Conceptualization, H.P.; Formal analysis, H.P.; Methodology, H.S.; Project administration, J.V.h.; Resources, H.P.; Software, H.P. and H.S.; Supervision, J.V.h.; Validation, H.P. and H.S.; Visualization, H.S.; Writing—original draft, H.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No. 754354.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors would like to thank Arata Nakajo for the constructive comments to improve the quality of the current article. The CFD analysis of this study was carried out with the commercial software ANSYS CFX 19.2 developed by ANSYS Inc.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

