Analytical and numerical modelling of ballistic heat conduction observed in heat pulse experiments

Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a thermo-mechanical model in which the generalized heat equatio...

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Bibliographic Details
Published in:arXiv.org 2020-04
Main Authors: Balassa, Gábor, Rogolino, Patrizia, Rieth, Ágnes, Kovács, Róbert
Format: Article
Language:English
Subjects:
Boundary conditions
Conduction heating
Conductive heat transfer
Exact solutions
Heat pulses
Mathematical models
Propagation modes
Thermal expansion
Thermodynamics
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Summary:Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a thermo-mechanical model in which the generalized heat equation - the so-called Maxwell-Cattaneo-Vernotte equation - is coupled to thermal expansion. At the same time, the other one uses internal variables. For the first one, we developed a numerical solution and tested on the heat pulse experiment performed by McNelly et al.~on NaF samples. For the second one, we found an analytical solution that emphasizes the role of boundary conditions. This analytical method is used to validate the earlier developed numerical code.
ISSN:2331-8422