Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

Xu WANG, P. SCHIAVONE

doi:10.1007/s10483-022-2924-7

Applied Mathematics and Mechanics >

2022 , Vol. 43 >Issue 11: 1691 - 1700

DOI: https://doi.org/10.1007/s10483-022-2924-7

Articles

Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

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1. School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, China;
2. Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Center for Engineering, Edmonton T6G 1H9, Canada

Received date: 2022-06-04

Revised date: 2022-08-16

Online published: 2022-10-29

Supported by

The Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (No. RGPIN-2017-03716115112)

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Abstract

We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux. A conformal mapping function for the coating and matrix is introduced, which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image plane. Using analytic continuation, we derive a general solution in terms of two auxiliary functions. The general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix interface. Once the two auxiliary functions have been obtained in the elementary-form, the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly determined. The design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple condition. Finally, the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.

Key words： thermoelectric material; nonlinear coupling; coated hole of arbitrary shape; complex variable method; analytic solution; neutral coated hole

Cite this article

Xu WANG, P. SCHIAVONE . Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material[J]. Applied Mathematics and Mechanics, 2022 , 43(11) : 1691 -1700 . DOI: 10.1007/s10483-022-2924-7

References

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