Discrete heat conduction equation: dispersion analysis and continuous limits

Sobolev, S.L.

Автор: Sobolev S.L.
Журнал: SSRN Electronic Journal
Год издания: 2023
Издательство: Elsevier B.V.
Местоположение издательства: Netherlands
Аннотация: The dispersion relation in ω-k space has been derived and analyzed for discrete heat conduction equation (DE), which is inherently nonlocal both in time and space and can be used to describe non-Fourier heat transport occurring on ultrashort time and length scales. An important distinction between the DE and the continuum description is that the frequencies and wave numbers available to a harmonic analysis are limited, whereas in the continuum description there are no such limitations. Analytical expressions for the attenuation distance, group and phase velocity have been obtained as functions of wave frequency. In the continuum limit, depending on the basic invariant of the continualization procedure, the DE reduces to either classical Fourier parabolic equation (PE) or hyperbolic heat conduction equation (HE). It has been shown that in the low frequency limit the spectra of the PE and HE tend to the spectrum of the DE, whereas at moderate and high frequencies the spectra differ substantially. This implies that the continuum-based approaches, including both the PE and HE, unable to describe the high-frequency and shortwavelength processes and the DE is preferable. This work provides a relatively simple analytical tool to interpret the transient wave-like behavior of the temperature field in metamaterials on ultrashort space and time scales
Добавил в систему: Соболев Сергей Леонидович

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Discrete heat conduction equation: dispersion analysis and continuous limitsстатья

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