Heat conduction of micropolar solids sensitive to mirror reflections of three-dimensional space

E. V. Murashkin ; Yu. N. Radayev

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 4, pp. 389-403

Résumé

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 three-dimensional 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.

Détail

Keywords: heat conduction, micropolarity, mirror reflection, semi-isotropic solid.
Mots-clés : volume tensor element, heat flux pseudotensor