Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space
This article considers a variant of the heat conduction theory of thermal conductivity, in which the heat flux pseudovector has a weight of 1. The pseudoinvariants associated to the heat flux pseudovector are sensitive to mirror reflections and inversions of threedimensional space. The primary purpo...
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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 |
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| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/29 |
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| author | E. V. Murashkin Y. N. Radayev |
| author_facet | E. V. Murashkin Y. N. Radayev |
| author_sort | E. V. Murashkin |
| collection | DOAJ |
| description | This article considers a variant of the heat conduction theory of thermal conductivity, in which the heat flux pseudovector has a weight of 1. The pseudoinvariants associated to the heat flux pseudovector are sensitive to mirror reflections and inversions of threedimensional space. The primary purpose of the study was to find a heat flux vector that is algebraically equivalent to the microrotation pseudovector and to measure elementary volumes and areas using pseudoinvariants that are sensitive to mirror reflections. To represent spinor displacements, a contravariant microrotation pseudovector with a weight of +1 was selected. Thus, the heat flux and mass density were expressed as odd-weight pseudotensors. The Helmholtz free energy per unit doublet pseudoinvariant volume was employed as the thermodynamic state potential of the following functional arguments: absolute temperature, symmetric parts, and accompanying vectors for the linear asymmetric strain tensor and the wryness pseudotensor. The results obtained show that the thermal conductivity coefficient and heat capacity of elastic micropolar solids are pseudoscalars of odd weight, indicating their sensitivity to mirror reflections. |
| format | Article |
| id | doaj-art-1c062feafaf94faeadbabeb39a9f674c |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-1c062feafaf94faeadbabeb39a9f674c2025-02-02T23:06:08ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-02-01165438940310.26907/2541-7746.2023.4.389-40327Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional SpaceE. V. Murashkin0Y. N. Radayev1Ishlinsky Institute for Problems in Mechanics, Russian Academy of SciencesIshlinsky Institute for Problems in Mechanics, Russian Academy of SciencesThis article considers a variant of the heat conduction theory of thermal conductivity, in which the heat flux pseudovector has a weight of 1. The pseudoinvariants associated to the heat flux pseudovector are sensitive to mirror reflections and inversions of threedimensional space. The primary purpose of the study was to find a heat flux vector that is algebraically equivalent to the microrotation pseudovector and to measure elementary volumes and areas using pseudoinvariants that are sensitive to mirror reflections. To represent spinor displacements, a contravariant microrotation pseudovector with a weight of +1 was selected. Thus, the heat flux and mass density were expressed as odd-weight pseudotensors. The Helmholtz free energy per unit doublet pseudoinvariant volume was employed as the thermodynamic state potential of the following functional arguments: absolute temperature, symmetric parts, and accompanying vectors for the linear asymmetric strain tensor and the wryness pseudotensor. The results obtained show that the thermal conductivity coefficient and heat capacity of elastic micropolar solids are pseudoscalars of odd weight, indicating their sensitivity to mirror reflections.https://uzakufismat.elpub.ru/jour/article/view/29heatconductionmicropolarityvolumetensorelementheatfluxpseudotensormirror reflectionsemi-isotropic solid |
| spellingShingle | E. V. Murashkin Y. N. Radayev Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space Учёные записки Казанского университета: Серия Физико-математические науки heatconduction micropolarity volumetensorelement heatfluxpseudotensor mirror reflection semi-isotropic solid |
| title | Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space |
| title_full | Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space |
| title_fullStr | Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space |
| title_full_unstemmed | Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space |
| title_short | Heat Conduction of Micropolar Solids Sensitive to Mirror Reflections of Three-Dimensional Space |
| title_sort | heat conduction of micropolar solids sensitive to mirror reflections of three dimensional space |
| topic | heatconduction micropolarity volumetensorelement heatfluxpseudotensor mirror reflection semi-isotropic solid |
| url | https://uzakufismat.elpub.ru/jour/article/view/29 |
| work_keys_str_mv | AT evmurashkin heatconductionofmicropolarsolidssensitivetomirrorreflectionsofthreedimensionalspace AT ynradayev heatconductionofmicropolarsolidssensitivetomirrorreflectionsofthreedimensionalspace |