{"title":"广义热传递方程的热力学框架","authors":"Yangyu Guo, Moran Wang","doi":"10.1515/caim-2016-0012","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, a generalized heat transport equation including relaxational, nonlocal and nonlinear effects is provided, which contains diverse previous phenomenological models as particular cases. The aim of the present work is to establish an extended irreversible thermodynamic framework, with generalized expressions of entropy and entropy flux. Nonlinear thermodynamic force-flux relation is proposed as an extension of the usual linear one, giving rise to the nonlinear terms in the heat transport equation and ensuring compatibility with the second law. Several previous results are recovered in the linear case, and some additional results related to nonlinear terms are also obtained.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"7 1","pages":"167 - 176"},"PeriodicalIF":0.3000,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/caim-2016-0012","citationCount":"4","resultStr":"{\"title\":\"Thermodynamic framework for a generalized heat transport equation\",\"authors\":\"Yangyu Guo, Moran Wang\",\"doi\":\"10.1515/caim-2016-0012\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper, a generalized heat transport equation including relaxational, nonlocal and nonlinear effects is provided, which contains diverse previous phenomenological models as particular cases. The aim of the present work is to establish an extended irreversible thermodynamic framework, with generalized expressions of entropy and entropy flux. Nonlinear thermodynamic force-flux relation is proposed as an extension of the usual linear one, giving rise to the nonlinear terms in the heat transport equation and ensuring compatibility with the second law. Several previous results are recovered in the linear case, and some additional results related to nonlinear terms are also obtained.\",\"PeriodicalId\":37903,\"journal\":{\"name\":\"Communications in Applied and Industrial Mathematics\",\"volume\":\"7 1\",\"pages\":\"167 - 176\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2016-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/caim-2016-0012\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/caim-2016-0012\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/caim-2016-0012","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Thermodynamic framework for a generalized heat transport equation
Abstract In this paper, a generalized heat transport equation including relaxational, nonlocal and nonlinear effects is provided, which contains diverse previous phenomenological models as particular cases. The aim of the present work is to establish an extended irreversible thermodynamic framework, with generalized expressions of entropy and entropy flux. Nonlinear thermodynamic force-flux relation is proposed as an extension of the usual linear one, giving rise to the nonlinear terms in the heat transport equation and ensuring compatibility with the second law. Several previous results are recovered in the linear case, and some additional results related to nonlinear terms are also obtained.
期刊介绍：
Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.
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