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Neutral coated inhomogeneities of various shapes in nonlinear thermoelectricity

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Abstract

We study the thermoelectric field in a nonlinear thermoelectric matrix containing a coated inhomogeneity. The inhomogeneity can be either an electrically and thermally insulated hole or an electrically and thermally conducting body. We prove that when two simple conditions on the thermoelectric parameters of the composite and the directions of applied fields are met, the coated hole or coated conductor will not disturb the prescribed thermoelectric field of uniform electric current density and energy flux in the matrix and can thus be considered as neutral. The two boundaries of the coating can still be determined using Milton and Serkov’s formulae. Explicit expressions of the two analytic functions characterizing the thermoelectric field in the coating are obtained. Although the considered thermoelectric problem is nonlinearly coupled, the conditions leading to neutrality of the coated hole or coated conductor are strikingly simple.

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Acknowledgements

The authors are greatly indebted to a reviewer for the very helpful comments and suggestions. This work is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN-2017-03716115112).

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China

    Xu Wang

  2. Department of Mechanical Engineering, 10-203 Donadeo Innovation Centre for Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Peter Schiavone

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  1. Xu Wang
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  2. Peter Schiavone
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Correspondence to Xu Wang or Peter Schiavone.

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Wang, X., Schiavone, P. Neutral coated inhomogeneities of various shapes in nonlinear thermoelectricity. Acta Mech 233, 3719–3724 (2022). https://doi.org/10.1007/s00707-022-03305-4

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