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An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition
In a flexible electronic heater (FEH), periodic metal wires are often encapsulated into the soft elastic substrate as heat sources. It is of great significance to develop analytic models on transient heat conduction of such an FEH in order to provide a rapid analysis and preliminary designs based on...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9611051/ https://www.ncbi.nlm.nih.gov/pubmed/36295980 http://dx.doi.org/10.3390/mi13101627 |
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author | Xu, Dian Xiong, Sijun Meng, Fanxing Wang, Bo Li, Rui |
author_facet | Xu, Dian Xiong, Sijun Meng, Fanxing Wang, Bo Li, Rui |
author_sort | Xu, Dian |
collection | PubMed |
description | In a flexible electronic heater (FEH), periodic metal wires are often encapsulated into the soft elastic substrate as heat sources. It is of great significance to develop analytic models on transient heat conduction of such an FEH in order to provide a rapid analysis and preliminary designs based on a rapid parameter analysis. In this study, an analytic model of transient heat conduction for bi-layered FEHs is proposed, which is solved by a novel symplectic superposition method (SSM). In the Laplace transform domain, the Hamiltonian system-based governing equation for transient heat conduction is introduced, and the mathematical techniques incorporating the separation of variables and symplectic eigen expansion are manipulated to yield the temperature solutions of two subproblems, which is followed by superposition for the temperature solution of the general problem. The Laplace inversion gives the eventual temperature solution in the time domain. Comprehensive time-dependent temperatures by the SSM are presented in tables and figures for benchmark use, which agree well with their counterparts by the finite element method. A parameter analysis on the influence of the thermal conductivity ratio is also studied. The exceptional merit of the SSM is on a direct rigorous derivation without any assumption/predetermination of solution forms, and thus, the method may be extended to more heat conduction problems of FEHs with more complex structures. |
format | Online Article Text |
id | pubmed-9611051 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-96110512022-10-28 An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition Xu, Dian Xiong, Sijun Meng, Fanxing Wang, Bo Li, Rui Micromachines (Basel) Article In a flexible electronic heater (FEH), periodic metal wires are often encapsulated into the soft elastic substrate as heat sources. It is of great significance to develop analytic models on transient heat conduction of such an FEH in order to provide a rapid analysis and preliminary designs based on a rapid parameter analysis. In this study, an analytic model of transient heat conduction for bi-layered FEHs is proposed, which is solved by a novel symplectic superposition method (SSM). In the Laplace transform domain, the Hamiltonian system-based governing equation for transient heat conduction is introduced, and the mathematical techniques incorporating the separation of variables and symplectic eigen expansion are manipulated to yield the temperature solutions of two subproblems, which is followed by superposition for the temperature solution of the general problem. The Laplace inversion gives the eventual temperature solution in the time domain. Comprehensive time-dependent temperatures by the SSM are presented in tables and figures for benchmark use, which agree well with their counterparts by the finite element method. A parameter analysis on the influence of the thermal conductivity ratio is also studied. The exceptional merit of the SSM is on a direct rigorous derivation without any assumption/predetermination of solution forms, and thus, the method may be extended to more heat conduction problems of FEHs with more complex structures. MDPI 2022-09-28 /pmc/articles/PMC9611051/ /pubmed/36295980 http://dx.doi.org/10.3390/mi13101627 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Xu, Dian Xiong, Sijun Meng, Fanxing Wang, Bo Li, Rui An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition |
title | An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition |
title_full | An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition |
title_fullStr | An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition |
title_full_unstemmed | An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition |
title_short | An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition |
title_sort | analytic model of transient heat conduction for bi-layered flexible electronic heaters by symplectic superposition |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9611051/ https://www.ncbi.nlm.nih.gov/pubmed/36295980 http://dx.doi.org/10.3390/mi13101627 |
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