Please wait a minute...
Chin. Phys. B, 2020, Vol. 29(5): 057301    DOI: 10.1088/1674-1056/ab7d96

Influence of spherical inclusions on effective thermoelectric properties of thermoelectric composite materials

Wen-Kai Yan(闫文凯)1, Ai-Bing Zhang(张爱兵)1, Li-Jun Yi(易利军)1, Bao-Lin Wang(王保林)2, Ji Wang(王骥)1
1 Piezoelectric Device Laboratory, School of Mechanical Engineering&Mechanics, Ningbo University, Ningbo 315211, China;
2 Centre for Infrastructure Engineering, School of Engineering, Western Sydney University, Penrith, NSW 2751, Australia
Abstract  A homogenization theory is developed to predict the influence of spherical inclusions on the effective thermoelectric properties of thermoelectric composite materials based on the general principles of thermodynamics and Mori-Tanaka method. The closed-form solutions of effective Seebeck coefficient, electric conductivity, heat conductivity, and figure of merit for such thermoelectric materials are obtained by solving the nonlinear coupled transport equations of electricity and heat. It is found that the effective figure of merit of thermoelectric material containing spherical inclusions can be higher than that of each constituent in the absence of size effect and interface effect. Some interesting examples of actual thermoelectric composites with spherical inclusions, such as insulated cavities, inclusions subjected to conductive electric and heat exchange and thermoelectric inclusions, are considered, and the numerical results lead to the conclusion that considerable enhancement of the effective figure of merit is achievable by introducing inclusions. In this paper, we provide a theoretical foundation for analytically and computationally treating the thermoelectric composites with more complicated inclusion structures, and thus pointing out a new route to their design and optimization.
Keywords:  thermoelectric composites      effective properties      spherical inclusions  
Received:  01 December 2019      Revised:  15 February 2020      Accepted manuscript online: 
PACS:  73.50.Lw (Thermoelectric effects)  
  84.60.Rb (Thermoelectric, electrogasdynamic and other direct energy conversion)  
  84.60.Bk (Performance characteristics of energy conversion systems; figure of merit)  
  46.25.Cc (Theoretical studies)  
Fund: Project supported by the Ningbo Natural Science Foundation, China (Grant Nos. 2019A610151 and 2018A610081), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LY17A020001 and LY20A020002), the National Natural Science Foundation of China (Grant No. 11402063), and the K C Wong Magna Fund in Ningbo University, China.
Corresponding Authors:  Ai-Bing Zhang     E-mail:

Cite this article: 

Wen-Kai Yan(闫文凯), Ai-Bing Zhang(张爱兵), Li-Jun Yi(易利军), Bao-Lin Wang(王保林), Ji Wang(王骥) Influence of spherical inclusions on effective thermoelectric properties of thermoelectric composite materials 2020 Chin. Phys. B 29 057301

[1] Bell L E 2008 Science 321 1457
[2] Callen H B 1960 Am. J. Phys. 28 684
[3] Harman T C and Honig J M 1967 Thermoelectric and thermomagnetic effects and applications. (New York: McGraw-Hill)
[4] Mahan G D 1997 Phys. Rev. B: Solid State Phys. 51 81
[5] Gao C Y and Chen G M 2016 Compos. Sci. Technol. 124 52
[6] Rowe D M 1999 Renew. Energ. 16 1251
[7] Duan W Y, Liu J F, Zhang C and Ma Z S 2018 Chin. Phys. B 27 097204
[8] Xu K Q, Zeng H R, Yu H Z, Zhao K Y, Li G R, Song J Q, Shi X and Chen L D 2014 Chin. Phys. Lett. 31 127201
[9] Song K, Song H P and Gao C F 2018 Chin. Phys. B 27 077304
[10] Rowe D M 2005 Thermoelectric handbook: macro to nano (BocaRaton: CRC Press)
[11] Riffat S B and Ma X 2003 Appl. Therm. Eng. 23 913
[12] Zhou B, Huang Y, En Y F, Fu Z W, Chen S and Yao R H 2018 Acta Phys. Sin. 67 028101 (in Chinese)
[13] Zhu Y Q, Zhang Z H, Song S N, Xie H Q, Song Z T, Shen L L, Li L, Wu L C and Liu B 2015 Chin. Phys. Lett. 32 77302
[14] Hong M, Chen Z G and Zou J 2018 Chin. Phys. B 27 048403
[15] Tritt T M, Boettner L and Chen L 2008 MRS Bull. 33 366
[16] Dresselhaus M S, Chen G, Tang M Y, Yang R G, Lee H, Wang D Z, Ren Z F, Fleurial J P and Gogna P 2007 Adv. Mater. 19 1043
[17] Gooth J, Schiering G, Felser C and Nielsch K 2018 MRS Bull. 43 187
[18] Gnanaseelan M, Chen Y, Luo J J, Krause B, Pionteck J, Pötschke P and Qi H S 2018 Compos. Sci. Technol. 163 133
[19] Liu W S, Yan X, Chen G and Ren Z F 2012 Nano Energy 1 42
[20] Yuan G C, Chen X, Huang Y Y, Mao J X, Yu J Q, Lei X B and Zhang Q Y 2019 Acta Phys. Sin. 68 117201 (in Chinese)
[21] Wang T, Chen H Y, Qiu P F, Shi X and Chen L D 2019 Acta Phys. Sin. 68 090201 (in Chinese)
[22] Huang P, You L, Liang X, Zhang J Y and Luo J 2019 Acta Phys. Sin. 68 077201 (in Chinese)
[23] Tao Y, Qi N, Wang B, Chen Z Q and Tang X F 2018 Acta Phys. Sin. 67 197201 (in Chinese)
[24] Zhang F P, Zhang J W, Zhang J X, Yang X Y, Lu Q M and Zhang X 2017 Acta Phys. Sin. 66 247202 (in Chinese)
[25] Wang R F, Dai L, Yan Y C, Peng K L, Lu X, Zhou X Y and Wang G Y 2018 Chin. Phys. B 27 067201
[26] Liu C Y, Miao L, Wang X Y, Wu S H, Zheng Y Y, Deng Z Y, Chen Y L, Wang G W and Zhou X Y 2018 Chin. Phys. B 27 047211
[27] Qin D D, Liu Y, Meng X F, Cui B, Qi Y Y, Cai W and Sui J H 2018 Chin. Phys. B 27 048402
[28] Bergman D J and Fel L G 1999 J. Appl. Phys. 85 8205
[29] Bergman D J and Levy O 1991 J. Appl. Phys. 70 6821
[30] Yang, Y, Xie S H, Ma F Y and Li J Y 2012 J. Appl. Phys. 111 013510
[31] Yang Y, Ma F Y, Liu Y Y and Li J Y 2013 Appl. Phys. Lett. 102 053905
[32] Song K, Song H P, Li M, Schiavone and Gao C F 2019 Int. J. Heat Mass Transfer. 135 1319
[33] Song K, Song H P, Schiavone and Gao C F 2019 Acta Mech. 230 3693
[34] Zhang A B, Wang B L, Wang J, Du J K, Xie C and Jin Y A 2017 Appl. Therm. Eng. 127 1442
[35] Wang P, Wang B L, Wang K F, Hirakata H and Zhang C 2019 Int. J. Eng. Sci. 142 158
[36] Liu L P 2012 Int. J. Eng. Sci. 55 35
[37] Yang Y, Lei C H, Gao C F and Li J Y 2015 J. Mech. Phys. Solids 76 98
[38] Mori T and Tanaka K 1973 ACTA Metall. 21 571
[39] Zhang A B and Wang B L 2016 Eng. Fract. Mech. 151 11
[40] Norris A N 1989 J. Appl. Mech. 56 83
[41] Tzou D Y 1991 J. Compos. Mater. 25 1064
[42] Song K, Song H P and Gao C F 2017 Chin. Phys. B 26 498
[1] Enhanced thermoelectric properties in two-dimensional monolayer Si2BN by adsorbing halogen atoms
Cheng-Wei Wu(吴成伟), Changqing Xiang(向长青), Hengyu Yang(杨恒玉), Wu-Xing Zhou(周五星), Guofeng Xie(谢国锋), Baoli Ou(欧宝立), and Dan Wu(伍丹). Chin. Phys. B, 2021, 30(3): 037304.
[2] Significant role of nanoscale Bi-rich phase in optimizing thermoelectric performance of Mg3Sb2
Yang Wang(王杨), Xin Zhang(张忻), Yan-Qin Liu(刘燕琴), Jiu-Xing Zhang(张久兴), Ming Yue(岳明). Chin. Phys. B, 2020, 29(6): 067201.
[3] Enhanced spin-dependent thermopower in a double-quantum-dot sandwiched between two-dimensional electron gases
Feng Chi(迟锋), Zhen-Guo Fu(付振国), Liming Liu(刘黎明), Ping Zhang(张平). Chin. Phys. B, 2019, 28(10): 107305.
[4] The magneto-thermoelectric effect of graphene with intra-valley scattering
Wenye Duan(段文晔), Junfeng Liu(刘军丰), Chao Zhang(张潮), Zhongshui Ma(马中水). Chin. Phys. B, 2018, 27(9): 097204.
[5] Improving compatibility between thermoelectric components through current refraction
K Song(宋坤), H P Song(宋豪鹏), C F Gao(高存法). Chin. Phys. B, 2018, 27(7): 077304.
[6] Multinary diamond-like chalcogenides for promising thermoelectric application
Dan Zhang(张旦), Hong-Chang Bai(白洪昌), Zhi-Liang Li(李志亮), Jiang-Long Wang(王江龙), Guang-Sheng Fu(傅广生), Shu-Fang Wang(王淑芳). Chin. Phys. B, 2018, 27(4): 047206.
[7] Enhanced thermoelectric performance through homogenously dispersed MnTe nanoparticles in p-type Bi0.52Sb1.48Te3 nanocomposites
Tian-Qi Lu(陆天奇), Peng-Fei Nan(南鹏飞), Si-Long Song(宋思龙), Xin-Yue Zhu(朱欣悦), Huai-Zhou Zhao(赵怀周), Yuan Deng(邓元). Chin. Phys. B, 2018, 27(4): 047207.
[8] Effect of Nb doping on microstructures and thermoelectric properties of SrTiO3 ceramics
Da-Quan Liu(刘达权), Yu-Wei Zhang(张玉伟), Hui-Jun Kang(康慧君), Jin-Ling Li(李金玲), Xiong Yang(杨雄), Tong-Min Wang(王同敏). Chin. Phys. B, 2018, 27(4): 047205.
[9] An overview of thermoelectric films: Fabrication techniques, classification, and regulation methods
Jing-jing Feng(冯静静), Wei Zhu(祝薇), Yuan Deng(邓元). Chin. Phys. B, 2018, 27(4): 047210.
[10] Enhanced thermoelectric performance in p-type Mg3Sb2 via lithium doping
Hao Wang(王浩), Jin Chen(陈进), Tianqi Lu(陆天奇), Kunjie Zhu(朱坤杰), Shan Li(李珊), Jun Liu(刘军), Huaizhou Zhao(赵怀周). Chin. Phys. B, 2018, 27(4): 047212.
[11] Strategies for optimizing the thermoelectricity of PbTe alloys
Jinze Zhai(翟近泽), Teng Wang(王腾), Hongchao Wang(王洪超), Wenbin Su(苏文斌), Xue Wang(王雪), Tingting Chen(陈婷婷), Chunlei Wang(王春雷). Chin. Phys. B, 2018, 27(4): 047306.
[12] Band engineering and precipitation enhance thermoelectric performance of SnTe with Zn-doping
Zhiyu Chen(陈志禹), Ruifeng Wang(王瑞峰), Guoyu Wang(王国玉), Xiaoyuan Zhou(周小元), Zhengshang Wang(王正上), Cong Yin(尹聪), Qing Hu(胡庆), Binqiang Zhou(周斌强), Jun Tang(唐军), Ran Ang(昂然). Chin. Phys. B, 2018, 27(4): 047202.
[13] Thermal conductivity of nanowires
Zhongwei Zhang(张忠卫), Jie Chen(陈杰). Chin. Phys. B, 2018, 27(3): 035101.
[14] Macro-performance of multilayered thermoelectric medium
Kun Song(宋坤), Hao-Peng Song(宋豪鹏), Cun-Fa Gao(高存法). Chin. Phys. B, 2017, 26(12): 127307.
[15] Photon-mediated spin-polarized current in a quantum dot under thermal bias
Feng Chi(迟锋), Liming Liu(刘黎明), Lianliang Sun(孙连亮). Chin. Phys. B, 2017, 26(3): 037304.
No Suggested Reading articles found!