文献类型：期刊文献

中文题名：Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

作者：Xu WANG[1];P.SCHIAVONE[2]

机构：[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

年份：2022

卷号：43

期号：11

起止页码：1691

中文期刊名：Applied Mathematics and Mechanics(English Edition)

外文期刊名：应用数学和力学（英文版）

收录：Scopus;CSCD:【CSCD2021_2022】；PubMed;

基金：supported by the Discovery Grant from the Natural Sciences and Engineering Research Council of Canada(No.RGPIN-2017-03716115112)。

语种：英文

中文关键词：thermoelectric material;nonlinear coupling;coated hole of arbitrary shape;complex variable method;analytic solution;neutral coated hole

摘要：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.