Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models
This article presents the mathematical formulations of transient heat conduction problems corresponding to the models of classical heat conduction using the Fourier law and generalized heat conduction based on the Cattaneo–Vernotta–Lykov law (Maxwell–Cattaneo model), as well as the generalized Green...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2024-02-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/31 |
| _version_ | 1797205453004865536 |
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| author | A. A. Orekhov L. N. Rabinskiy G. V. Fedotenkov |
| author_facet | A. A. Orekhov L. N. Rabinskiy G. V. Fedotenkov |
| author_sort | A. A. Orekhov |
| collection | DOAJ |
| description | This article presents the mathematical formulations of transient heat conduction problems corresponding to the models of classical heat conduction using the Fourier law and generalized heat conduction based on the Cattaneo–Vernotta–Lykov law (Maxwell–Cattaneo model), as well as the generalized Green–Nagdy type II and III models. The Fourier transforms in spatial coordinates and the Laplace transforms in time were used to obtain the fundamental solutions of the equations of the Maxwell–Cattaneo and Green–Nagdy type II and III models of classical and generalized heat conduction. The results were displayed graphically and analyzed. Differences between the considered heat conduction models were shown, and suggestions for their practical application were given. |
| first_indexed | 2024-03-07T23:47:30Z |
| format | Article |
| id | doaj.art-b980a39b3f2a43eb96bbb0835ad94e7b |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-24T08:51:21Z |
| publishDate | 2024-02-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-b980a39b3f2a43eb96bbb0835ad94e7b2024-04-16T11:42:17ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982024-02-01165440441410.26907/2541-7746.2023.4.404-41429Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction ModelsA. A. Orekhov0L. N. Rabinskiy1G. V. Fedotenkov2Moscow Aviation InstituteMoscow Aviation InstituteMoscow Aviation InstituteThis article presents the mathematical formulations of transient heat conduction problems corresponding to the models of classical heat conduction using the Fourier law and generalized heat conduction based on the Cattaneo–Vernotta–Lykov law (Maxwell–Cattaneo model), as well as the generalized Green–Nagdy type II and III models. The Fourier transforms in spatial coordinates and the Laplace transforms in time were used to obtain the fundamental solutions of the equations of the Maxwell–Cattaneo and Green–Nagdy type II and III models of classical and generalized heat conduction. The results were displayed graphically and analyzed. Differences between the considered heat conduction models were shown, and suggestions for their practical application were given.https://uzakufismat.elpub.ru/jour/article/view/31classical heat conductionmaxwell–cattaneo theorycattaneo–vernott– lykov lawgreen–nagdy theorygeneralized heat conductiondifferential equationsintegral transformations |
| spellingShingle | A. A. Orekhov L. N. Rabinskiy G. V. Fedotenkov Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models Учёные записки Казанского университета. Серия Физико-математические науки classical heat conduction maxwell–cattaneo theory cattaneo–vernott– lykov law green–nagdy theory generalized heat conduction differential equations integral transformations |
| title | Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models |
| title_full | Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models |
| title_fullStr | Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models |
| title_full_unstemmed | Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models |
| title_short | Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models |
| title_sort | fundamental solutions of the equations of classical and generalized heat conduction models |
| topic | classical heat conduction maxwell–cattaneo theory cattaneo–vernott– lykov law green–nagdy theory generalized heat conduction differential equations integral transformations |
| url | https://uzakufismat.elpub.ru/jour/article/view/31 |
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