Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions
An integro-differential equation describes the non-equilibrium thermal response of glass-forming substances with a dynamic (time-dependent) heat capacity to fast thermal perturbations. We found that this heat transfer problem could be solved analytically for a heat source with an arbitrary time depe...
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MDPI AG
2021-02-01
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Series: | Symmetry |
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Online Access: | https://www.mdpi.com/2073-8994/13/2/256 |
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author | Alexander A. Minakov Christoph Schick |
author_facet | Alexander A. Minakov Christoph Schick |
author_sort | Alexander A. Minakov |
collection | DOAJ |
description | An integro-differential equation describes the non-equilibrium thermal response of glass-forming substances with a dynamic (time-dependent) heat capacity to fast thermal perturbations. We found that this heat transfer problem could be solved analytically for a heat source with an arbitrary time dependence and different geometries. The method can be used to analyze the response to local thermal perturbations in glass-forming materials, as well as temperature fluctuations during subcritical crystal nucleation and decay. The results obtained can be useful for applications and a better understanding of the thermal properties of glass-forming materials, polymers, and nanocomposites. |
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institution | Directory Open Access Journal |
issn | 2073-8994 |
language | English |
last_indexed | 2024-03-09T05:49:55Z |
publishDate | 2021-02-01 |
publisher | MDPI AG |
record_format | Article |
series | Symmetry |
spelling | doaj.art-27d54c26ec43443baa7f779b086e6d842023-12-03T12:18:12ZengMDPI AGSymmetry2073-89942021-02-0113225610.3390/sym13020256Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical SolutionsAlexander A. Minakov0Christoph Schick1Prokhorov General Physics Institute of the Russian Academy of Sciences, GPI RAS, Vavilov Str. 38, 119991 Moscow, RussiaInstitute of Physics and Competence Centre CALOR, University of Rostock, Albert-Einstein-Str. 23-24, 18051 Rostock, GermanyAn integro-differential equation describes the non-equilibrium thermal response of glass-forming substances with a dynamic (time-dependent) heat capacity to fast thermal perturbations. We found that this heat transfer problem could be solved analytically for a heat source with an arbitrary time dependence and different geometries. The method can be used to analyze the response to local thermal perturbations in glass-forming materials, as well as temperature fluctuations during subcritical crystal nucleation and decay. The results obtained can be useful for applications and a better understanding of the thermal properties of glass-forming materials, polymers, and nanocomposites.https://www.mdpi.com/2073-8994/13/2/256non-equilibrium heat transfer problemtime-dependent response functionsecond-kind integro-differential equationsVolterra integral equations |
spellingShingle | Alexander A. Minakov Christoph Schick Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions Symmetry non-equilibrium heat transfer problem time-dependent response function second-kind integro-differential equations Volterra integral equations |
title | Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions |
title_full | Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions |
title_fullStr | Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions |
title_full_unstemmed | Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions |
title_short | Integro-Differential Equation for the Non-Equilibrium Thermal Response of Glass-Forming Materials: Analytical Solutions |
title_sort | integro differential equation for the non equilibrium thermal response of glass forming materials analytical solutions |
topic | non-equilibrium heat transfer problem time-dependent response function second-kind integro-differential equations Volterra integral equations |
url | https://www.mdpi.com/2073-8994/13/2/256 |
work_keys_str_mv | AT alexanderaminakov integrodifferentialequationforthenonequilibriumthermalresponseofglassformingmaterialsanalyticalsolutions AT christophschick integrodifferentialequationforthenonequilibriumthermalresponseofglassformingmaterialsanalyticalsolutions |