**3. Results and Discussion**

Table 1 lists the input parameters to compute the output thermal power and mass flow rates of the current PEMFC model. The latter are then used as input data for TEG module simulations, to investigate the recovery performance along with the flow behavior and spatial temperature distribution in the TEG unit.


**Table 1.** Input parameters for PEMFC numerical modeling [40,41].

#### *3.1. Model Validation*

The aim of the current developed PEM fuel cell model was to predict the output temperature and the mass flow rate of the water in the cooling channels, which enters the TEG heat exchanger. In this regard, to validate the output results of the PEMFC model, the I-V characteristic curves of the model should be compared with the verified results in the literature at both low and high current densities. Once the validation is performed, the model is suitable to predict the needed output values. The PEMFC model predictions were tested with both experimental and simulation results by Ticianelli et al. [42] and Mohammedi et al. [43], respectively. It is noteworthy to mention that the input model parameter values for the present verification were not those listed in Table 1, but correspond to the values reported in Mohammedi et al. [43] to allow for direct comparison. Figure 9a shows good agreement between both models and the experimental results up to at least 600 mA/cm2, for conditions corresponding to a fuel utilization of 0.75, a mass flow rate of 6 × 10−<sup>7</sup> kg s−1, and surface specific flow of 6.67 × 10−<sup>7</sup> kg.s<sup>−</sup>1.m<sup>−</sup><sup>2</sup> with a molar fraction of 0.5/0.5 H2/H2O at the anode side while having the mass flow rate of 5 × 10−<sup>6</sup> kg.s<sup>−</sup>1.w and surface specific flow of 5.56 × 10−<sup>7</sup> kg.s<sup>−</sup>1.m<sup>−</sup><sup>2</sup> with a species molar fraction of 0.1785/0.15/0.6715 O2/H2O/N2 at the cathode side. Figure 9a presents the validation results compared to the experiments by Ticianelli et al. [42] and simulations by Mohammedi et al. [43].

**Figure 9.** Validation results of the developed PEMFC model at low current densities: (**a**) model comparison with the experimental data of Ticianelli et al. [42] and simulations of Mohammedi et al. [43]; (**b**) model comparison with the 500 W BCS stack using the experimental data of Xue et al. [44], Correa et al. [45], and simulation data of Sharifi-Asl et al. [46].

Furthermore, the current model was also validated with three different sets of experimental and numerical data at low current densities. Figure 9b compares the output of the current PEM fuel cell model with the 500 W BCS stack manufactured by BCS technologies [44]. The number of cells for the 500 W BCS stack [44] was 32, with an active area of 64 cm<sup>2</sup> operating at 333 K. It should be noted that in this stack, the resistance to the electron flow was 0.0003 Ω, while the limiting current density was 0.469 A.cm<sup>−</sup>2. Accounting for the high current densities, Figure 10 illustrates the I-V characteristic curve of the current model with the output performance of the single-cell Ballard Mark V PEM fuel cell [44] at the operating temperature of 343 K. In this case, the limiting current density was 1.5 A.cm<sup>−</sup>2, the active area of the cell was 50.6 cm2, and the resistance to the electron flow was 0.0003 Ω.

**Figure 10.** Validation results of the developed model at high current densities with the Ballard Mark V PEM fuel cell given by Xue et al. [44].

The heat transfer verification of the TEG model consisted of the comparison of pressure drops computed by Fernández-Yañez et al. [28] (see Table 2), which was a follow-up of the investigation in ref. [47]. The published dataset included nine stationary modes of a light-duty diesel engine at different torques. In that article, simulations were performed to obtain the corresponding temperature and pressure drop of the exhaust gases of the diesel engine. The present TEG model verification used a subset of four of the modes reported in [26] (A, I, G and D), which means four different input temperatures and mass flow rates. The agreement shown in Table 2 indicates that the present model pressure drop predictions were in line with the mixed numerical and experimental study by Fernández-Yañez et al. [28].

**Table 2.** Validation of the simulation data obtained by the present TEG model and that by Fernández-Yañez et al. [28].


In every CFD analysis, the values of the output results should be independent from the size of the cells in the mesh structure. In this regard, a grid independency analysis is needed to prove the suitability of the simulation model for the TEG unit. As the validation of this unit (see Table 2) was conducted with the given data by Fernández-Yañez et al. [28], the grid independency of the TEG thermal model was also performed using the temperature corresponding to engine mode D. Figure 11 shows that grid independency of the temperature simulated at 475 K was reached starting around 4.2 × 10<sup>6</sup> cells. In this condition, the average surface area of the cells was 1.57 × 10−<sup>3</sup> m2, the minimum edge length was 1 × 10−<sup>3</sup> m, and the maximum cell edge size was 0.1132 m, with highest skewness of 0.9. Figure 12 shows the mesh structure of the developed model, only when the number of cells is lowest (1 × 106), for illustration reasons.

**Figure 11.** Grid independency study of the three-dimensional CFD model of the TEG unit considering the temperature in the engine mode D given by Table 2 as the verification value.

**Figure 12.** The mesh structure of the computational domain for the simulation of the TEG unit.
