Phonon wave propagation in ballistic-diffusive regime

Abstract

Wide applications of ultra-short pulse laser technique in micromachining and thermophysical properties' measurements make the study on ultrafast transient thermal transport necessarily essential. When the characteristic time is comparable to the phonon relaxation time, phonons propagate in ballistic-diffusive regime and thermal wave occurs. Here, ultrafast transient phonon transport is systematically investigated based on the Monte Carlo (MC) simulations, the Cattaneo-Vernotte (C-V) model, and the phonon Boltzmann transport equation (BTE). It is found that remarkable differences exist between the C-V model and the MC simulations when describing the evolution of the thermal wave excited by the ultra-short heat pulse. The C-V model predicts a non-dispersive dissipative thermal wave, while the MC simulation with Lambert emission predicts a dispersive dissipative thermal wave. Besides, different phonon emissions can significantly influence the evolution of the thermal wave in the MC simulations. A modified C-V model with a time-and position-dependent effective thermal conductivity is derived based on the phonon BTE to characterize the evolution of the transport regime from ballistic to diffusive. The integrations on moments of the distribution function cause the loss of the information of the phonon distribution in wave vector space, making the macroscopic quantities incomplete when describing the ballistic transport processes and corresponding boundary conditions. Possible boundary conditions for the phonon BTE in practice are also discussed on different heating methods. V C 2016 AIP Publishing LLC.

Anisotropic Relaxation of Idealized Hot Spots in Crystalline 1,3,5-Triamino-2,4,6-trinitrobenzene (TATB)

“…Because the heat equation is parabolic, it does not account for a finite induction time and assumes that heat signals travel infinitely fast. , A finite induction time would also be consistent with the fact that the slab atomic kinetic energies are approximately Maxwell-Boltzmann distributed. While we do not pursue such studies here, fitting the simulated response to the hyperbolic Cattaneo heat equation would be a reasonable first step for further investigation.…”

A comparative numerical study of a semi-infinite heat conductor subject to double strip heating under non-Fourier models

“…The same feature holds true if we compare the original hyperbolic DPL and the hyperbolic MCV model. We refer the reader's attention to the work [55] wherein a comparison between the velocities of thermal wave computed from the Monte Carlo simulations and the MCV model, for ultra-short laser pulse heating, was carried out. It is salient that the macroscopic MCV model underestimates the thermal wave speed in the ultrafast transient processes, where it predicts a speed equal √ 3/3 of (or less than) the Monte Carlo simulations speed using different phonon emissions (Lambert emission and directional emission), cf .…”

Influence of the composition gradient on the propagation of heat pulses in functionally graded nanomaterials

“…However, in nanodimensional systems, as well as in several nonequilibrium situations (as for example, in miniaturized systems submitted to high-frequency perturbations which are comparable to the reciprocal of the internal relaxation times), both numerical simulations, and experimental observations point out that the limit of validity of FL is clearly exceeded [4,[14][15][16][17][18][19]; therefore, current frontiers in nanotechnology and materials' science require heat-transport equations which go both beyond FL, and beyond the local-equilibrium theory [15,19,20]. Those equations can be obtained, for instance, by solving the linearized Boltzmann equation [21][22][23], considering the time-lag effect [24,25], flux-history effect [26,27] or ballistic phonon transport [28,29], analysing the equivalence principle of energy and mass [14,30,31], or other generalized thermodynamic formalisms [15,19,32].…”