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Power Series Iterative Approximation Solution to the Temperature Field in Thermoelectric Generators Made of a Functionally Graded Temperature-Dependent Material

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Abstract

To investigate the temperature field in and thermoelectric (TE) efficiency of TE generators made of a functionally graded temperature-dependent material, a power series iteration method is proposed for solving the weak nonlinear differential equation with variable coefficients. A homogeneous structure made of regular Bi2Te3 and a gradient structure composed of regular Bi2Te3 and nano-Bi2Te3 are investigated. The power series iteration solution of the temperature field has good convergence and high accuracy. After four iterations, the relative error of the solution can be less than 10−6. The numerical results obtained show that the maximum energy efficiency of a functionally graded structure composed of regular Bi2Te3 and nano-Bi2Te3 is larger than that of a homogeneous regular Bi2Te3 structure. To reveal that the maximum energy efficiency depends on the gradient distribution, we compare the maximum energy efficiency of TE generators made of nano-Bi2Te3, nano-PbTe, and different types of functionally graded structures made of these two materials. Results indicate that the maximum energy efficiency of certain functionally graded structures is 9.9%. The effective gradient distribution can significantly enhance the maximum TE efficiency. The method and results provide theoretical guidance for the optimization of temperature-dependent materials for TE generators using functionally graded structures.

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Funding

This work was supported by the National Natural Science Foundation of China [Grant Numbers 11572244, 11872300]; NSAF [Grant Number U1630144]; the Open Subject of State Key Laboratories of Transducer Technology [Grant Number SKT1506]; and the Youth Innovation Team of Shaanxi Universities.

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  1. School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an, 710048, China

    Xiaoshan Cao, Wei Niu, Zhiyao Cheng & Junping Shi

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  1. Xiaoshan Cao
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Cao, X., Niu, W., Cheng, Z. et al. Power Series Iterative Approximation Solution to the Temperature Field in Thermoelectric Generators Made of a Functionally Graded Temperature-Dependent Material. J. Electron. Mater. 49, 5379–5390 (2020). https://doi.org/10.1007/s11664-020-08270-z

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