Fundamental solutions of the equations of classical and generalized heat conduction models
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 4, pp. 404-414
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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.
Keywords:
classical heat conduction, Maxwell–Cattaneo theory, Cattaneo–Vernott–Lykov law, Green–Nagdy theory, generalized heat conduction, differential equations, integral transformations.
@article{UZKU_2023_165_4_a4,
author = {A. A. Orekhov and L. N. Rabinsky and G. V. Fedotenkov},
title = {Fundamental solutions of the equations of classical and generalized heat conduction models},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {404--414},
publisher = {mathdoc},
volume = {165},
number = {4},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2023_165_4_a4/}
}
TY - JOUR AU - A. A. Orekhov AU - L. N. Rabinsky AU - G. V. Fedotenkov TI - Fundamental solutions of the equations of classical and generalized heat conduction models JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2023 SP - 404 EP - 414 VL - 165 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2023_165_4_a4/ LA - ru ID - UZKU_2023_165_4_a4 ER -
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A. A. Orekhov; L. N. Rabinsky; G. V. Fedotenkov. Fundamental solutions of the equations of classical and generalized heat conduction models. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 4, pp. 404-414. http://geodesic.mathdoc.fr/item/UZKU_2023_165_4_a4/