Causality in non-fourier heat conduction

Abstract

We present a study of the causal response of non-Fourier heat conduction by introducing a dispersive generalized thermal susceptibility and show it obeys Kramers-Kronig relations. In particular, we discuss the Cattaneo-Vernotte and the dual-phase lag models. The constitutive equations are written as a linear response theory and determine the conditions for which the dual-phase lag model does not satisfy Kramers-Kronig relations. An alternative model is presented to describe non-Fourier transport using the similarity with the causal response of viscoelastic materials to avoid this unphysical issue.

Complex band structure of thermal wave crystals: The plane-wave method

“…Thermal Wave Crystals (TWCs), which were first proposed by A-Li Chen et al in 2018, have attracted a lot of interest for the existence of band gaps when heat flow is of oscillatory nature [1]. The fact that TWCs exhibit band gaps for their oscillatory behavior motivated the development of numerous studies aimed at exploring their properties and potential applications [2][3][4][5][6]. For instance, the presence of band gaps within a TWC structure has the potential to reduce heat propagation by means of interference [1].…”

Transient effects in the coupling of thermal radiation and non-Fourier heat transport at the nano-scale

“…Other proposals have been discussed in the literature to introduce a lagging behavior in Fourier's law, such as the dual-phase-lag model where two delay times are introduced, one related to the response of the system to the temperature gradient and one related to the heat flux. [30][31][32] One example of a material that exhibits non-Fourier behavior is a thin film of metal, such as gold or silver, which can have a much higher thermal conductivity than the surrounding air or substrate. 25 When a laser pulse is focused on such a material, the temperature of the metal can rapidly increase, leading to non-equilibrium behavior described by a non-Fourier model that takes into account memory effects and non-local response.…”