Design specifications, material properties, and thermal conditions for the TEG device.
Abstract
Power generation using thermoelectric generator technology is becoming increasingly attractive solution due to the ongoing substantial improvements in material engineering, system optimization, and novel manufacturing technologies with recent advances in nanotechnology. The design and fabrication of novel thermoelectric materials is challenging because they require co-optimization of complex properties to efficiently convert thermal energy to electricity in what is known as the Seebeck effect. Computational chemistry and machine learning offer a solution toward finding optimal thermoelectric semiconductor alloys with higher figure of merit values. In this chapter, fundamental aspects and advances in thermoelectric materials for power generation are presented and discussed. A thorough modeling and numerical simulation for a case study of a TEG device application are also presented and discussed in this chapter.
Keywords
- thermoelectric power generation
- novel thermoelectric material
- figure of merit
- nanomaterial
- clean power technology
- computational chemistry
- machine learning
- artificial intelligence
- Seebeck effect
1. Introduction
Due to the increasing demands and attractions toward the use of alternative and green power generation, thermoelectric (TE) technology is considered to be promising one for its inherent merits and advantages over other alternative technologies. Thermoelectrics is the direct conversion of thermal energy (heat) due to temperature difference into electrical energy using solid-state Seebeck effect in semiconductors that would contribute to mitigating the worldwide energy crisis, and reduce air pollution and GHG emissions. The key distinct merits of using thermoelectric power generator (TEGs): they are compact and safe devices; they are flexible power sources and convenient for remote applications; they are eco-friendly; they are capable of operating at high temperatures; they are very reliable; they have no mechanical moving parts and therefore noise-free in operation with significantly less maintenance requirements [1]. The major shortcoming of the thermoelectric power generator (TEG) is its relatively low conversion and thermal efficiency. This has been a major cause in restricting their use in electrical power generation to certain specialized fields. However, the ongoing substantial improvements in TE material engineering, system optimization, and novel manufacturing technologies with recent advances in nanotechnology and machine learning/artificial intelligence (AI) bring TEG to a different level of renewed significance. Over the past couple of decades, TEG applications included industrial instruments, medical and aerospace, military, and applications for mobile and remote power supply [2, 3, 4]. More recently, industrial applications involving TEG technology are becoming more attractive, especially if the waste heat associated with these applications is dissipated to the environment and available at no cost, which could be used as heat source for operating TEG and producing power at larger amounts possible [2]. In these applications, large quantities of waste heat energy are discharged into the earth’s environment much of it at temperatures which are typically too low to recover using conventional electrical power generators. In general, the cost of a TEG mainly consists of the device cost and operating cost. Ismail and Ahmed [1] and Ismail [5] presented various interesting waste-heat industrial related applications where TEGs were successfully used. Luo et al. [6] presented recent advances in modeling and simulation of thermoelectric power generation. They performed a comprehensive review of theoretical models with a specific focus on the different modeling approaches and different application scenarios. In particular, the basic principles of theoretical models of the TEG were presented in their paper, including the thermal resistance model, thermal-electric numerical model, and analogy model. They also reviewed in detail the theoretical models of the TEG system, including the thermal resistance-based analytical model, computational fluid dynamics models, and fluid-thermal-electric multiphysics field coupled numerical model. In their work, the methods to improve the accuracy of theoretical models were also discussed.
In this chapter, some fundamental and material related aspects of TEG are introduced and discussed. A thorough modeling and numerical simulation for a case study of a TEG device application are also presented and discussed in this chapter.
2. Evolution of thermoelectric materials: from nanostructures to wearable applications
Over the past couple of decades, there has been extensive research carried out related to advances in thermoelectric materials for various applications. In general, effective TE materials should have a low thermal conductivity but a high electrical conductivity. Most widely used TE semiconductor materials are based on Bismuth Telluride (Bi2Te3), Lead Telluride (PbTe), and Si-Ge alloys. The large amount of research in thermoelectric materials has focused on optimizing the nanostructure of the thermoelectric materials to specifically improve the thermoelectric properties (e.g., increasing the Seebeck coefficient and reducing the thermal conductivity) of the TEG device. For example, Weiling and Shantung [7] reported that because the electrical conductivity and thermal conductivity correlate with the charge carriers, new methods of material synthesis must be applied to conciliate the contradiction between high electrical conductivity and low thermal conductivity. Research has been focused mainly on improving the material’s figure-of-merit
Moreover, it is desirable to fabricate TE modules which can conform easily to a heat source surface which would improve the thermal contact to heat sources of arbitrary geometry. Therefore, recent research has also been focused on developing novel flexible- and cylindrical-based shapes of TEG devices. For example, Yadav et al. [11] proposed and demonstrated the use of flexible and cost-effective TEG based on thin film thermoelectric on flexible fiber substrates. Min and Rowe [12] have also recently developed a novel tube-shape thermoelectric module for power generation. Most recently, Soleimani et al. [13] reported that wearable TEG devices are becoming attractive power supply for relatively low-power electronic devices. They indicated from their research that to maximize the higher power output from these devices, the focus should be on improving TE material, such as using promising electrically conductive and flexible hybrid organic and inorganic TE material, and the configuration and arrangement of thermoelements in the TEG device. In these applications, the thermal energy sources of the human body are used to power these wearable devices. Soleimani et al. [13] provided extensive research of recent studies on wearable TEG devices. Most recently, Zhu et al. [14] indicated the challenges and outlooks toward future development of wearable TEG devices and their potential applications. Lemine et al. [15] reported a comprehensive review research highlighting the promising and future-generation TEG devices based on thin film technologies with highly flexible, transparent, non-toxic, plentiful, and light-density
3. Accelerating the discovery of TE materials using computational chemistry and machine learning
The design of novel thermoelectric materials is challenging because they require co-optimization of complex properties to efficiently convert thermal energy to electricity in what is known as the
where
Local density approximation (LDA) is one of the simplest functionals that were implemented for DFT calculations. It neglects spatial variations of the electron density across the system and only considers local correlation effects by treating charge density as a uniform gas of electrons, which offers a reasonable accuracy for some applications [18]. To incorporate non-local correlations, generalized gradient approximation (GGA) improves on LDA by considering not only the electron density at a given point but also considers the gradient of the electron density across the space. This provides a more accurate model accounting for electron density variations that are important in many systems. There has been a growing interest in developing more accurate functionals such as hybrid functionals and machine learning (ML)-based functionals capture complex correlations beyond the scope of LDA and GGA [19]. One of the most popular functionals used for screening of thermoelectric materials using DFT is PBE-GGA [20] and van der Waals-corrected functionals DFT-D2 [21]. However, despite selecting a suitable functionals, there are still inherit challenges that stem from the nature of DFT calculations, which do not account for temperature effects. Additionally, the lack of standardization of functionals prevents the direct comparison and transfer of results in the literature. This in turn widens the gap between computational predictions and experimental validations. Choubisa et al. [22] addressed both issues listed above regarding computational cost and accuracy of predictions by utilizing an error-correction learning (ECL) based on a neural network to model the error correction function from experimental data. This approach is implemented in two basic steps: (1) The model learns from prior experimental or computational datasets and then (2) it utilizes new experiments to provide feedback and refine the model to improve its accuracy. The second step allows the model to implicitly account for disparities in synthesis methods, material morphology, and defects, which vary from one lab setting to another and are normally not captured by DFT calculations. This improved model is then used to screen the material space, particularly Materials Project [23], a large open computational dataset of materials, with the purpose of discovering new promising chemistries. The authors focused their search on low-temperature thermoelectric materials <300°C. Notably, a new chemical family based on PbSe:SnSb (lead selenide:tin antimony) of thermoelectric materials was identified using this approach. The best composition exhibited double the power factor of a standard PbSe (lead selenide). This study encourages the development of new hybrid strategies guided by computational and experimental results, as well as machine learning models to shorten the cycle of developing thermoelectric materials.
4. The principle of a thermoelectric generator (TEG)
Figure 1 shows how a thermoelectric generator (TEG) works. A temperature difference is established between two junctions, namely, the hot junction and the cold junction, of two dissimilar materials made of metals or semiconductors. Due to this temperature difference, a voltage is generated using the Seebeck effect. This effect is fundamentally used in applications of thermocouples for temperature measurements. TEG devices can operate as electrical power generators using this effect. In a basic TEG thermocouple, heat transfers at a rate
Figure 2 shows a schematic diagram of a simple TEG device with its arrangement of components [1]. The TEG device is composed of two ceramic plates (substrates) that serve as a foundation, providing mechanical integrity, and electrical insulation for
The junctions connecting the thermoelements between the hot and cold plates are interconnected using highly conducting metal (e.g., copper) strips as shown in Figure 2. The power output for most of the commercially available TEGs ranges from microwatts to multi-kilowatts [2] (Rowe, 1999).
5. Modelling and numerical simulation: case study of the performance of a TEG device
In Figure 1, the heat transfer at the hot junction,
where
Substituting Eqs. (3)–(5) in Eq. (2), yields
In Eq. (6), α is the Seebeck coefficient,
where
The performance of thermoelectric materials can be expressed by figure of merit,
The relationship of
Maximizing
The power generated at the electrical load
where
Eq. (16) can be rewritten using Eqs. (6) and (15) as
Using the first law of thermodynamics of the closed system, the heat transfer at the low-temperature side (cold junction),
In Figure 1, the potential difference (or voltage
where,
Eq. (19) can also be written in terms of the open circuit voltage,
Also,
Equating Eqs. (21) and (22) and solving for the electric current, yield
For a thermodynamic heat engine, the maximum thermal efficiency is limited by the second law of thermodynamics given by Carnot efficiency:
Introducing the dimensionless parameters, θ, ξ, and β given by
where the average temperature,
Substituting Eq. (23) into Eq. (17) with Eqs. (12), (24)-(26), yields
The product
Substituting Eqs. (27) and (31) into Eq. (30), gives the thermal efficiency of the TE device in terms of dimensionless parameters, θ, ξ, and β, as
Normally, in designing and operating TEGs for various power generation applications, it would be very useful to maximize their performance. To determine the maximum power generation and conversion efficiency of the TEG module, the following set of equations is developed.
The maximum efficiency of the TE device can be determined using
Which leads to
Using Eq. (34) in Eq. (32), yields
Substituting Eq. (23) in Eq. (15) and using Eq. (26), gives
The maximum power output of the TE device can be determined using
This leads to the condition of maximum power of the TEG device,
That is,
In this case, we have
Eq. (39) can then be rewritten as
Also, the maximum power output can be expressed in terms of
where,
The maximum current can be determined by setting
The maximum voltage is the open circuit voltage, using Eq (21) (or Eq. (22))
The maximum power efficiency is given by
For a TE device with
Numerical simulations:
A TEG module is to be designed with its performance analytically and numerically evaluated to deliver a total electrical power of 1 kW using a waste heat source from hot exhaust gas at 811 K produced from an IC engine. The cold heat is rejected at a temperature of 436 K. The design specifications, material properties, and thermal conditions of the
Determine the maximum thermal efficiency, the efficiency at maximum power output, the number of thermocouples required for the TEG device, and other performance parameters.
Perform numerical simulations to determine the effect of lowering the cold temperature (heat sink temperature) on the key performance parameters of the TEG device.
8 mm | |
8 mm | |
0.6 cm2 | |
0.0140 W/cm K | |
0.0120 W/cm K | |
0.00101 Ω cm | |
0.00095 Ω cm | |
−170 × 10−6 V/K | |
190 × 10−6 V/K | |
436 K | |
811 K |
TEG device performance parameters were calculated using MS Excel program. The numerical results are shown in Table 2. For this case, 593 thermocouples are required to construct the TEG device to deliver 1 kW of electrical power. The maximum thermal efficiency and the efficiency at maximum power output of the TEG device were found to be 13.1% and 12.5%, respectively.
Parameter | Value | Equation # used |
---|---|---|
360 × 10−6 V/K | Eq. (11) | |
0.538 | Eq. (27) | |
0.629 cm2 | Eq. (14) | |
0.002555 Ω | Eqs. (7) and (8) | |
5.0927 × 10−5 ΩW/K | Eq. (13) | |
0.002545 K−1 | Eq. (12) | |
623 K | Eq. (29) | |
1.586 | Eq. (26) | |
1.6081 | Eq. (34) | |
0.004109 Ω | Eq. (25) | |
1.6082 | Eq. (25) | |
0.462 | Eq. (28) | |
0.1309 | Eq. (35) | |
2.0624 | Eq. (31) | |
20.26 A | Eq. (23) | |
1.6866 W | Eq. (15) | |
0.1309 | Eq. (30) | |
12.8846 W | Eq. (16) | |
11.1980 W | Eq. (18) | |
0.135 V | ||
52.84 A | Eq. (44) | |
0.135 V | Eq. (45) | |
26.42 A | Eq. (40) | |
0.0675 V | Eq. (43) | |
1.7833 W | Eq. (42) | |
0.1246 | Eq. (46) | |
1000 W | Given | |
593 thermocouples | Eq. (48) | |
7641 W | Eq. (47) | |
6641 W | Eq. (18) |
The numerical simulations were carried out using the simple computer program and the numerical results are shown in Table 3. It is interesting to see the detrimental effect of lowering the heat sink temperature of the TEG device on the various efficiency values of the device. Also, the number of multi-thermocouple required in constructing the TEG device decreased significantly with decreasing the heat sink temperature of the device. For example, by operating the device at the cold temperature of room temperature of 25°C, there are 317 thermocouples (i.e.,
163 | 150 | 125 | 100 | 75 | 50 | 25 (room temp) | |
46.2 | 47.8 | 50.9 | 54.0 | 57.1 | 60.2 | 63.3 | |
13.1 | 13.6 | 14.5 | 15.4 | 16.3 | 17.3 | 18.2 | |
12.5 | 12.9 | 13.8 | 14.7 | 15.6 | 16.5 | 17.5 | |
593 | 554 | 489 | 435 | 389 | 350 | 317 |
6. Conclusion
In this chapter, some fundamental and material related aspects of thermoelectric materials are introduced and discussed. A thorough modeling and numerical simulation for a hypothetical case of a TEG device are also presented and discussed in this chapter. The numerical simulation was carried out for a hypothetical practical case of a TEG made of PbTe semiconductors alloy. It was found that the heat sink cold temperature has a detrimental effect on the thermal and conversion efficiencies of the TEG device. More particularly, the efficiency at the maximum power output of the TEG device increased from 12.5% to 17.5% (i.e., by 5% increase) only by means of lowering the heat sink temperature to room temperature. In addition, the cost of the TEG device and its maintenance cost requirements were significantly reduced by lowering the operating cold temperature of the device for this case study.
Acronyms
density function theory
greenhouse gases
generalized gradient approximation
local density approximation
machine learning
thermoelectric
thermoelectric generator
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