4.7 Article

Analysis of three-dimensional ellipsoidal inclusions in thermoelectric solids

Journal

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
Volume 142, Issue -, Pages 158-169

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijengsci.2019.06.005

Keywords

Thermoelectric materials; Three-dimensional ellipsoidal inclusion; Green's function method; Effective material properties

Funding

  1. Research Innovation Fund of Shenzhen City of China [JCYJ20170811160538023, JCYJ20170413104256729]
  2. National Natural Science Foundation of China [11672084, 11602072, 11502101, 11372086]
  3. China Scholarship Council [201806120352]

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Thermoelectric (TE) materials as energy functional semiconductors can directly convert heat into electrical power. Due to the brittle nature of semiconductors, voids or inclusions are easy to be produced in the TE materials. This paper studies the three-dimensional ellipsoidal inclusion problem in thermoelectric materials. By introducing two auxiliary functions, we successfully simplify the non-linear coupled governing equations into linear uncoupled equations and the linearization is validated by two practical cases. Based on the Green's function method, the analytical solutions of this problem are derived. We find that the thermoelectric field inside the ellipsoidal inclusion is always uniform when subjected to far-field uniform loads. Furthermore, we derive the effective material properties of the matrix-inclusion system in closed-form. We find that it is possible to enhance the thermoelectric properties as well as the figure of merit by inserting specific inclusions. Moreover, among the different shapes of inclusions, the elliptical cylinder fiber that lies along the loading direction has the most significant improvements to the material properties. This paper is the first that derives the analytical solutions of three-dimensional inclusion problems in TE materials. (C) 2019 Elsevier Ltd. All rights reserved.

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