Hydrodynamic Phonon Transport Perpendicular to Diffuse-Gray Boundaries

Yang, Runqing; Yue, Shidong; Liao, Bolin

doi:10.1080/15567265.2018.1551449

Cited by 18 publications

(21 citation statements)

References 42 publications

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“…Because the N scattering conserves momentum and causes no thermal resistance [22,45,46]. In other words, in both hydrodynamic and ballistic limits, the heat flux (or momentum) is conserved in the interior domain [23,24,60], which is different from that in the diffusive limit. Although Eq.…”

Section: Theoretical Analysis Of Heat Vortexes In the Ballisticmentioning

confidence: 99%

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Shang

Zhang

Guo

et al. 2020

Sci Rep

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In this work, the heat vortexes in two-dimensional porous or ribbon structures are investigated based on the phonon Boltzmann transport equation (BTE) under the Callaway model. First, the separate thermal effects of normal (N) scattering and resistive (R) scattering are investigated with frequency-independent assumptions. And then the heat vortexes in graphene are studied as a specific example. It is found that the heat vortexes can appear in both ballistic (rare R/N scattering) and hydrodynamic (N scattering dominates) regimes but disappear in the diffusive (R scattering dominates) regime. As long as there is not sufficient R scattering, the heat vortexes can appear in present simulations.

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Section: Theoretical Analysis Of Heat Vortexes In the Ballisticmentioning

confidence: 99%

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Shang

Zhang

Guo

et al. 2020

Sci Rep

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“…It remains a difficult task to include the spectral phonon properties into the lattice Boltzmann model. A semi-analytical solution of the PBE under Callaway's model has been obtained by using the integral formulation for steady-state hydrodynamic phonon transport in simple geometrical structures [17,24]. Yet it is not realistic to obtain analytical solutions of the PBE as an integro-differential equation for more general geometries.…”

Section: Introductionmentioning

confidence: 99%

Direct simulation of second sound in graphene by solving the phonon Boltzmann equation via a multiscale scheme

et al. 2019

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The direct simulation of the dynamics of second sound in graphitic materials remains a challenging task due to lack of methodology for solving the phonon Boltzmann equation in such a stiff hydrodynamic regime. In this work, we aim to tackle this challenge by developing a multiscale numerical scheme for the transient phonon Boltzmann equation under Callaway's dual relaxation model which captures well the collective phonon kinetics. Comparing to traditional numerical methods, the present multiscale scheme is efficient, accurate and stable in all transport regimes attributed to avoiding the use of time and spatial steps smaller than the relaxation time and mean free path of phonons. The formation, propagation and composition of ballistic pulses and second sound in graphene ribbon in two classical paradigms for experimental detection are investigated via the multiscale scheme. The second sound is declared to be mainly contributed by ZA phonon modes, whereas the ballistic pulses are mainly contributed by LA and TA phonon modes. The influence of temperature, isotope abundance and ribbon size on the second sound propagation is also explored. The speed of second sound in the observation window is found to be at most 20 percentages smaller than the theoretical value in hydrodynamic limit due to the finite umklapp, isotope and edge resistive scattering. The present study will contribute to not only the solution methodology of phonon Boltzmann equation, but also the physics of transient hydrodynamic phonon transport as guidance for future experimental detection.

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“…Callaway's dual relaxation model [21] represents a good approximation to the full scattering term in the phonon Boltzmann equation [10,22] and has been widely adopted in analyzing heat transport in the hydrodynamic regime by analytical or semi-analytical methods [5,[23][24][25][26][27][28][29]. The direct solution of the phonon Boltzmann equation under Callaway's model has been advanced recently by a few numerical schemes including both deterministic methods [30,31] and stochastic ones [32,33].…”

Section: Introductionmentioning

confidence: 99%

“…Within the computational framework, we investigate the hydrodynamic heat transport in graphite ribbon with finite length and width. The in-plane [19,26,30,36] (or crossplane [28,32]) heat transports along infinitely long (or wide) graphitic ribbons were widely studied previously [3]. A very important hydrodynamic phenomenon, the phonon Knudsen minimum, has been predicted in infinitely long graphene ribbons [30] and graphite ribbons [26].…”

Section: Introductionmentioning

confidence: 99%

“…The end effect is indeed relevant to the size dependence of the cross-plane thermal conductivity. In comparison with the well-established super-ballistic scaling with the width of in-plane thermal conductivity [19,26,37,38], the size scaling in the cross-plane case remains less clear despite a few notable efforts [28,32]. We will quantify the size scaling of both in-plane and crossplane thermal conductivities in the same footprint based on the direct numerical solution and a hydrodynamic approach, which helps to understand the end effect on phonon Knudsen minimum.…”

Section: Introductionmentioning

confidence: 99%

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Size effect on phonon hydrodynamics in graphite microstructures and nanostructures

et al. 2021

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The understanding of hydrodynamic heat transport in finite-sized graphitic materials remains elusive due to the lack of an efficient methodology. In this paper, we develop a computational framework enabling an accurate description of heat transport in anisotropic graphite ribbons by a kinetic theory approach with full quantum mechanical first-principles input. A unified analysis of the size scaling of the thermal conductivity in the longitudinal and transverse directions of the system is made within the computational framework complemented with a macroscopic hydrodynamic approach. As a result, we demonstrate a strong end effect on the phonon Knudsen minimum, as a hallmark of the transition from ballistic to hydrodynamic heat transports, along a rectangular graphite ribbon with finite length and width. The phonon Knudsen minimum is found to take place only when the ribbon length is ∼5-10 times the upper limit of the width range in the hydrodynamic regime. This paper contributes to a unique methodology with high efficiency and a deeper understanding of the size effect on phonon hydrodynamics, which would open opportunities for its theoretical and experimental investigation in graphitic micro-and nanostructures.

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Hydrodynamic Phonon Transport Perpendicular to Diffuse-Gray Boundaries

Cited by 18 publications

References 42 publications

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Heat vortex in hydrodynamic phonon transport of two-dimensional materials

Direct simulation of second sound in graphene by solving the phonon Boltzmann equation via a multiscale scheme

Size effect on phonon hydrodynamics in graphite microstructures and nanostructures

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