{"title":"A unified mixed hp-finite element framework for modeling laser pulse heating processes in the refined thermodynamics","authors":"Balázs Tóth","doi":"10.1016/j.ijheatmasstransfer.2024.126456","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, new multi-field variational formulations are derived for solving the following thermodynamic models: (i) ballistic-conductive system, (ii) the Guyer–Krumhansl heat conduction model and (iii) the Maxwell–Cattaneo–Vernotte model as some models of the extended irreversible thermodynamic, handling the temperature, the heat flux and the current density of heat flux as independent field variables. Based on these variational approaches as mathematical background, a family of mixed <span><math><mrow><mi>h</mi><mi>p</mi></mrow></math></span>-version finite element methods, which is capable of reliably and efficiently modeling the temperature responses, is designed. The solutions provided by the constructed <span><math><mrow><mi>h</mi><mi>p</mi></mrow></math></span>-FE framework are illustrated for the following two heat pulse experiments as benchmark problems: (1) sinusoid laser pulse heating process and (2) rectangular (step-like) laser pulse train. It is shown that stable, oscillation-free temperature response functions can be obtained not only for the ballistic-conductive system and the Maxwell–Cattaneo–Vernotte model but also for the under-diffuse and the over-diffuse parameter settings of the Guyer–Krumhansl heat conduction model.</div></div>","PeriodicalId":336,"journal":{"name":"International Journal of Heat and Mass Transfer","volume":"238 ","pages":"Article 126456"},"PeriodicalIF":5.0000,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Heat and Mass Transfer","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0017931024012845","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, new multi-field variational formulations are derived for solving the following thermodynamic models: (i) ballistic-conductive system, (ii) the Guyer–Krumhansl heat conduction model and (iii) the Maxwell–Cattaneo–Vernotte model as some models of the extended irreversible thermodynamic, handling the temperature, the heat flux and the current density of heat flux as independent field variables. Based on these variational approaches as mathematical background, a family of mixed -version finite element methods, which is capable of reliably and efficiently modeling the temperature responses, is designed. The solutions provided by the constructed -FE framework are illustrated for the following two heat pulse experiments as benchmark problems: (1) sinusoid laser pulse heating process and (2) rectangular (step-like) laser pulse train. It is shown that stable, oscillation-free temperature response functions can be obtained not only for the ballistic-conductive system and the Maxwell–Cattaneo–Vernotte model but also for the under-diffuse and the over-diffuse parameter settings of the Guyer–Krumhansl heat conduction model.
期刊介绍:
International Journal of Heat and Mass Transfer is the vehicle for the exchange of basic ideas in heat and mass transfer between research workers and engineers throughout the world. It focuses on both analytical and experimental research, with an emphasis on contributions which increase the basic understanding of transfer processes and their application to engineering problems.
Topics include:
-New methods of measuring and/or correlating transport-property data
-Energy engineering
-Environmental applications of heat and/or mass transfer