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Thermoelectric generators are being used as a successful power sources for space applications since 1960's in radioisotope-thermoelectric generators (RTGs) to supply power to space systems in deep space. RTG’s are capable of directly converting heat energy to uninterrupted electric power with no moving parts involved. The ability of thermoelectric materials to convert heat energy to electrical energy is defined by a dimensionless value known as the thermoelectric figure of merit (ZT) 1. This value quantifies the maximum thermoelectric efficiency of a thermoelectric generator (TEG) and is calculated by ZT= S2σT/κ, where S, σ, T, and κ represent Seebeck coefficient, electrical conductivity, temperature, and thermal conductivity, respectively. Among all of the thermoelectric materials, Bi2Te3 and its alloys have been reported to have high ZT values for low temperature energy harvesting and are highly suitable for powering wearables and self-powering sensors2, 3.
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Beyond zT: Is There a Limit to Thermoelectric Figure of Merit?
The concept of the dimensionless thermoelectric figure of merit zT was derived by A.F. Ioffe and has been widely used to assess the desirability of thermoelectric materials for devices. Solid state physics does not set limits on this criterion, but it can be shown that such restrictions are imposed by the laws of thermodynamics. The physical meaning of zT can be interpreted as the ratio of the virtual efficiency of a thermoelectric generator (TEG) ηo and the Carnot efficiency ηc: zT = ηo/ηc. Hence, the conclusion about the zT restriction: lim(zT) ≤ 1, which is correlated with the data on the properties of well-studied thermoelectric materials, but contradicts much new experimental data. This contradiction serves as a pretext for further study of possible constraints on zT. An additional bonus from this analysis is the possibility of the experimental determination of zT by direct measurement of temperatures, heat flux, and open circle voltage. An analysis of the expanded mathematical model of a TEG shows that the influence of the Biot criterion on the power capacity of the TEG significantly exceeds the influence of zT. That is, it is possible to compensate for the high thermal conductivity of materials due to more intense heat transfer. This approach to improving the characteristics is demonstrated by developing a TEG for the conversion of latent heat of liquid natural gas (LNG).
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- Award ID(s):
- 1722127
- PAR ID:
- 10086730
- Date Published:
- Journal Name:
- Journal of Electronic Materials
- ISSN:
- 0361-5235
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Thermoelectric active cooling uses nontraditional thermoelectric materials with high thermal conductivity, high thermoelectric power factor, and relatively low figure of merit (ZT) to transfer large heat flows from a hot object to a cold heat sink. However, prior studies have not considered the influence of external thermal resistances associated with the heat sinks or contacts, making it difficult to design active cooling thermal systems or compare the use of low-ZT and high-ZT materials. Here, we perform a non-dimensionalized analysis of thermoelectric active cooling under forced heat flow boundary conditions, including arbitrary external thermal resistances. We identify the optimal electrical currents to minimize the heat source temperature and find the crossover heat flows at which low-ZT active cooling leads to lower source temperatures than high-ZT and even ZT→+∞ thermoelectric refrigeration. These optimal parameters are insensitive to the thermal resistance between the heat source and thermoelectric materials, but depend strongly on the heat sink thermal resistance. Finally, we map the boundaries where active cooling yields lower source temperatures than thermoelectric refrigeration. For currently considered active cooling materials, active cooling with ZT < 0.1 is advantageous compared to ZT→+∞ refrigeration for dimensionless heat sink thermal conductances larger than 15 and dimensionless source powers between 1 and 100. Thus, our results motivate further investigation of system-level thermoelectric active cooling for applications in electronics thermal management.more » « less
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Abstract A large amount of energy from power plants, vehicles, oil refining, and steel or glass making process is released to the atmosphere as waste heat. The thermoelectric generator (TEG) provides a way to reutilize this portion of energy by converting temperature differences into electricity using Seebeck phenomenon. Because the figures of merit zT of the thermoelectric materials are temperature-dependent, it is not feasible to achieve high efficiency of the thermoelectric conversion using only one single thermoelectric material in a wide temperature range. To address this challenge, the authors propose a method based on topology optimization to optimize the layouts of functional graded TEGs consisting of multiple materials. The multimaterial TEG is optimized using the solid isotropic material with penalization (SIMP) method. Instead of dummy materials, both the P-type and N-type electric conductors are optimally distributed with two different practical thermoelectric materials. Specifically, Bi2Te3 and Zn4Sb3 are selected for the P-type element while Bi2Te3 and CoSb3 are employed for the N-type element. Two optimization scenarios with relatively regular domains are first considered with one optimizing on both the P-type and N-type elements simultaneously, and the other one only on single P-type element. The maximum conversion efficiency could reach 9.61% and 12.34% respectively in the temperature range from 25 °C to 400 °C. CAD models are reconstructed based on the optimization results for numerical verification. A good agreement between the performance of the CAD model and optimization result is achieved, which demonstrates the effectiveness of the proposed method.more » « less
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Abstract Over 50% of the energy from power plants, vehicles, oil refining, and steel or glass making process is released to the atmosphere as waste heat. As an attempt to deal with the growing energy crisis, the solid-state thermoelectric generator (TEG), which converts the waste heat into electricity using Seebeck phenomenon, has gained increasing popularity. Since the figures of merit of the thermoelectric materials are temperature dependent, it is not feasible to achieve high efficiency of the thermoelectric conversion using only one single thermoelectric material in a wide temperature range. To address this challenge, this paper proposes a method based on topology optimization to optimize the layouts of functional graded TEGs consisting of multiple materials. The objective of the optimization problem is to maximize the output power and conversion efficiency as well. The proposed method is implemented using the Solid Isotropic Material with Penalization (SIMP) method. The proposed method can make the most of the potential of different thermoelectric materials by distributing each material into its optimal working temperature interval. Instead of dummy materials, both the P and N-type electric conductors are optimally distributed with two different practical thermoelectric materials, namely Bi2Te3 & PbTe for P-type, and Bi2Te3 & CoSb3 for N-type respectively, with the yielding conversion efficiency around 12.5% in the temperature range Tc = 25°C and Th = 400°C. In the 2.5D computational simulation, however, the conversion efficiency shows a significant drop. This could be attributed to the mismatch of the external load and internal TEG resistance as well as the grey region from the topology optimization results as discussed in this paper.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s11664-019-06943-y
