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Microsystem Technologies
Published in: Microsystem Technologies 12/2018

02-05-2018 | Technical Paper

Unified GN model of electro-thermoelasticity theories with fractional order of heat transfer

Authors: Magdy A. Ezzat, Alaa A. El-Bary

Published in: Microsystem Technologies | Issue 12/2018

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Abstract

A unified mathematical model of electro-thermoelasticity has been constructed in the context of a new consideration of heat conduction law with fractional order derivative. Some essential theories follow as limit cases. The governing coupled equations are applied to several concrete problems: (a) time-dependent thermal shock problem; (b) a problem for a half-space subjected to an arbitrary heating and (c) a layer media problem. Laplace transforms are used to derive the solution in the Laplace transform domain. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusion about the new theory has been constructed. The predictions of the theory are discussed and compared with dynamic classical coupled theory, Lord–Shulman, Green–Naghdi (GN) and fractional coupled thermoelasticity theories. The result provides a motivation to investigate conducting fractional thermoelectric materials as a new class of applicable materials.
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Metadata
Title
Unified GN model of electro-thermoelasticity theories with fractional order of heat transfer
Authors
Magdy A. Ezzat
Alaa A. El-Bary
Publication date
02-05-2018
Publisher
Springer Berlin Heidelberg
Published in
Microsystem Technologies / Issue 12/2018
Print ISSN: 0946-7076
Electronic ISSN: 1432-1858
DOI
https://doi.org/10.1007/s00542-018-3917-z

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