Heat Transport on Ultrashort Time and Space Scales in Nanosized Systems: Diffusive or Wave-like?

Abstract

The non-Fourier effects, such as wave-like temperature propagation and boundary temperature jumps, arise in nanosized systems due to the multiple time and space scales nature of out-of-equilibrium heat transport. The relaxation to equilibrium occurs in successive time and space scales due to couplings between different excitations, whose relaxation times have different physical meanings and may differ significantly in magnitude. The out-of-equilibrium temperature evolution is described by a hierarchy of partial differential equations of a higher order, which includes both the diffusive and wave modes of heat transport. The critical conditions of transition from wave to diffusive modes are identified. We demonstrate that the answer to the question concerning which of these modes would be detected by experimental measurements may also depend on the accuracy of the experimental setup. Comparisons between the proposed approach and other non-Fourier models, such as the Guyer–Krumhansl and Jeffreys type, are carried out. The results presented here are expected to be useful for the theoretical and experimental treatment of non-Fourier effects and particularly heat wave phenomena in complex nanosized systems and metamaterials.

Causality in non-fourier heat conduction

“…The additional term γ 2 is related to processes that preserve phonon momentum [62]. Because of the spacederivative of the heat flux, the corresponding memory function will have a spatial dependence.…”

“…Unlike Cattaneo's model, which is hyperbolic, the DPL and GK equations are parabolic. However, by including additional terms in the Taylor expansion of the delay time, there is a 'hyperbolic' version of these models [62], whose response kernels and corresponding complex thermal susceptibilities are yet to be determined.…”

“…The memory function when τ q < τ T is obtained exchanging, in equation (1), τ q by τ T , and the heat flux by the temperature gradient. The dual-phase lag model is also known as the Jeffreys equation [1,62].…”

A Thermal Analogue of the Zel’Dovich Effect

“…One critical aspect of this model, we think, is that it derives a Doppler effect even if the temperature fields considered are not found by solving a real damped wave equation, as the well known telegraph equation [10].…”

The Finite Element Method of Flow and Heat Transfer in Heterogeneous Materials

“…The two-temperature (2T) approach, [6], [7], [8] however, it has not been tested on heat pulse experiments so far but has a good background and could influence, e.g., the thermoelectric conversion processes [9], [10]. The 2T model has been successfully used for heat transport in metals under ultrashort heat pulses, [11] but they are not tested or not applicable for macroscale solids at room temperature.…”