**1. Introduction**

Concentrated efforts have been made to reduce the usage of fossil fuels after ascertaining their adverse contributions to climate change and pollution [1]. The automotive industry still largely relies on internal combustion engines fueled by diesel [2]. However, fuel cells and batteries are becoming viable alternatives to diminish and also control the localization of pollutant emissions [3]. Herein, proton exchange membrane fuel cells (PEMFCs) are a prominent technology for the automotive industry that electrochemically converts hydrogen and oxygen into water, electricity, and heat [4].

In different industries, there exist considerable amounts of heat that can be recovered [5]. Figure 1 illustrates the share of waste heat energy in United Kingdom. Approximately half of the hydrogen utilized by the low-temperature PEMFC changes to electricity, while the rest mainly converts to heat, which should be removed to keep the operational temperature range around 65 ◦C to 85 ◦C [6]. This temperature range stems from constraints related to the electrolyte membrane, usually made of Nafion [7]. Operation at temperatures above or below leads to drying of the membrane or flooding, respectively [8]. The heat produced by PEMFCs can be removed through natural convection, water evaporation, or extra reactants, but mainly through the cooling system [9]. Thermal and water management, that is, the combined control of the spatial distribution of temperature and humidity in the stack, is required to guarantee high performance and durability for PEMFCs [10]. In this regard, a precise and accurate model is needed to characterize the performance of the PEMFC.

**Citation:** Pourrahmani, H.; Shakeri, H.; Van herle, J. Thermoelectric Generator as the Waste Heat Recovery Unit of Proton Exchange Membrane Fuel Cell: A Numerical Study. *Energies* **2022**, *15*, 3018. https://doi.org/10.3390/ en15093018

Academic Editors: Bahman Shabani and Mahesh Suryawanshi

Received: 15 March 2022 Accepted: 18 April 2022 Published: 20 April 2022

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**Figure 1.** The percentage share of waste heat energy by different industries in United Kingdom [11].

Both experimental and numerical models are used to evaluate the output power density and voltage of the cell, hence the corresponding amount of waste heat [12]. The electrochemical performance of the catalyst layer (CL) can be simulated with varying levels of detail and accuracy in modeled phenomena and discretization, from zero to threedimensional [13]. The corresponding physics encompasses electrochemistry coupled with multiphase liquid, gas, and solid phase transport in the reticulated porous and Pt-loaded carbon networks [14]. Among the proposed modeling approaches for the CL [15], the socalled agglomerate model proved to be precise, at the cost of higher complexity compared to the porous electrode, interface, and microscopic models.

The agglomerate model provides an improved representation of the CL by averaged microstructural parameters, in particular the electrocatalyst and carbon agglomerates covered by a thin layer of membrane. The reaction rate is further assumed to be homogeneous. Porous electrode models also consider the presence of porous agglomerates of ionomercovered carbon particles in the CL. They, however, represent the system at the scale of the catalyst layer, while the agglomerate model accounts explicitly for the diffusion of products and reactants throughout the electrolyte film, which surrounds the electrocatalyst and carbon supports [16]. Simpler microscopic and single-pore models consider cylindrical Teflon-coated pores for gas diffusion, whereas interface models treat the CL as interface conditions between the gas diffusion layer (GDL) and membrane. In addition to the selection of the right model for the PEMFC, the most suitable strategy should be selected to recover the wasted heat and improve the thermal management [17–19].

Based on the size of the PEMFC stack, different cooling methods, such as air, passive, liquid, and phase-change cooling, can be used. The studies by Kwan [20–22] and Shen [23,24] explored thermoelectric generators (TEGs) implemented on the walls of the bipolar plates (BPs) to recover and convert the waste heat directly into electricity in small-scale applications. The performance is currently very modest: in the design developed by Kwan et al. [21], each kg of TEG material is expected to produce 0.15 W of electricity under optimized conditions.

TEGs generate electricity when subjected to a temperature gradient, and they are used in different applications such as temperature sensors, wearable energy harvesters, or for waste heat recovery [25]. Based on the trend described by He et al. [26] on the increase in the figure of merit for different materials, Shen et al. [24] evaluated the corresponding efficiency of different TEG units with different materials, i.e., considering different figures of merit, by changes in hot-side temperature. Figure 2 shows a similar trend for efficiency based on the results of Shen et al. [24] and Jouhara et al. [27] in 2016 concerning changes in the hot-side temperature and materials of TEG units in the constant cold-side temperature of 300 K. It should be noted that the data mentioned in Figure 2 were the highest possible values that could be obtained with recent TEG materials in 2016. For example, in a similar

temperature range, the efficiency of Bi2Te3 varied between 2% and 9% in 2010, based on the values reported by Shen et al. [24].

**Figure 2.** Changes in the efficiency of TEG materials considering the variation in TEG material and hot-side temperature in the constant cold-side temperature of 300 K.

Fernández-Yañez et al. [28] and Zorbas et al. [29] considered conventional TEG modules to recover the waste heat from the output exhaust gas of light-duty diesel engines. Bi2Te3 modules of 2.5 cm × 2.5 cm in size were installed at different positions on the exhaust pipe of a 96 kW engine car (1995 cm3). The power and recovery efficiency for the TEG unit in the range of 300 W and 5.5% were achieved, respectively, with a cold-side temperature of 30 ◦C and at part-load engine conditions. Projections by Zorbas et al. [29] about potential progress in TEG technology suggest that a reduction in fuel consumption by approximately 20% may be reached in the future, compared to 5% with current technology [29]. From an economic standpoint, the cost of the technology considered by Zorbas et al. [29], with an estimated 5% reduction in fuel consumption using TEG technology, was in the range of 500 EUR for a 96 kW engine implementation with amortization expected within 2 to 3 years. Although there have been suggestions for using the thermoelectric generators for waste heat recovery at small scales, TEGs have not been used on a medium-scale level accounting for liquid cooling methods.

The main novelty of the current study was to investigate the performance of TEG modules for the recovery of waste heat from the PEMFC coolant channels using the liquid cooling method with medium-scale stacks of PEMFCs (see Figure 3). The expected recovery performance was assessed assuming standard TEG material performance in terms of temperature levels. An agglomerate PEMFC model and three-dimensional thermal modeling of the TEG-based recovery module were then used to simulate the performance of the current standard material technology and component geometries. The PEMFC model was validated at low and high current densities using the I-V characteristic curve. Furthermore, a 3-D CFD thermal model of the TEG unit was developed, and pressure drops compared with numerical data by Fernández-Yañez et al. [28]. Empirical relationships were used for calculations by post-processing of TEG performance corresponding to the thermal conditions. The waste heat from the PEMFC was computed by a modeling approach with agglomerate formalism for the CL. The recovery performance and corresponding spatial distribution of temperature along the TEG heat exchangers were simulated and discussed.

**Figure 3.** Different cooling methods based on the size of the PEMFC stack.
