Nonlocal behavior in phonon transport

Tzou, D. Y.

doi:10.1016/j.ijheatmasstransfer.2010.09.022

Cited by 91 publications

(70 citation statements)

References 23 publications

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“…Three such approaches are the phonon hydrodynamics [5][6][7], the thermomass theory [12][13][14], and the dualphase-lag model [15,16]. All these models consider the heat carriers as a fluid, whose hydrodynamic-like equations of motion describe the heat transport.…”

Section: Heat Transport Equations Beyond the Fourier Law And Hydrodynmentioning

confidence: 99%

“…All these models consider the heat carriers as a fluid, whose hydrodynamic-like equations of motion describe the heat transport. The phonon hydrodynamics lays on the Guyer-Krumhansl transport equation [16][17][18][19][20][21][22] for the heat flux q, i.e., (1) τq…”

Section: Heat Transport Equations Beyond the Fourier Law And Hydrodynmentioning

confidence: 99%

“…(14) while the evolution of the heat flux is ruled by an equation of the type (16), then the use of a dynamical nonequilibrium temperature β [4,20,21,45], allows to obtain a nonlinear generalization of the classical Maxwell-Cattaneo-vernotte and Guyer-Krumhansl equations [5][6][7]. For instance, Eq.…”

Section: Higher-order Fluxes and Hierarchy Of Nonlinear Transport Equmentioning

confidence: 99%

See 2 more Smart Citations

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

Jou¹,

Cimmelli

2016

Communications in Applied and Industrial Mathematics

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Section: Heat Transport Equations Beyond the Fourier Law And Hydrodynmentioning

confidence: 99%

Section: Heat Transport Equations Beyond the Fourier Law And Hydrodynmentioning

confidence: 99%

Section: Higher-order Fluxes and Hierarchy Of Nonlinear Transport Equmentioning

confidence: 99%

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Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

Jou¹,

Cimmelli

2016

Communications in Applied and Industrial Mathematics

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“…In fact, it is well-known that the heat-transfer process in nanosystems significantly differs from that in macrosystems [1][2][3][4][5]. The consequent inapplicability of the classical Fourier law in practical applications to well-describe heat transport at nanoscale has led to several generalizations of it [6][7][8][9][10][11][12][13][14]. Leaving untouched the differences between all theoretical approaches one can find in literature [15], it is possible to claim that each of them provides a comprehension of heat-transfer mechanism at nanoscale which is almost satisfactory.…”

Section: Introductionmentioning

confidence: 99%

Heat-pulse propagation along nonequilibrium nanowires in thermomass theory

Sellitto

Rogolino

Carlomagno

2016

Communications in Applied and Industrial Mathematics

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We analyze the consequences of the nonlinear terms in the heat-transport equation of the thermomass theory on heat pulses propagating in a nanowire in nonequilibrium situations. As a consequence of the temperature dependence of the speeds of propagation, in temperature ranges wherein the specific heat shows negligible variations, heat pulses will shrink (or extend) spatially, and will increase (or decrease) their average temperature when propagating along a temperature gradient. A comparison with the results predicted by a different theoretical proposal on the shape of a propagating heat pulse is made, too.

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“…Experimental evidence, in fact, clearly shows that it is completely inefficient to describe accurately heat transport at the nanometer length scale [1][2][3][4][5][6][7]. Several theories have been developed to describe heat transport in nanostructured materials [8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Non-Fourier Heat Transfer with Phonons and Electrons in a Circular Thin Layer Surrounding a Hot Nanodevice

Cimmelli

Carlomagno

Sellitto

2015

Entropy

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A nonlocal model for heat transfer with phonons and electrons is applied to infer the steady-state radial temperature profile in a circular layer surrounding an inner hot component. Such a profile, following by the numerical solution of the heat equation, predicts that the temperature behaves in an anomalous way, since for radial distances from the heat source smaller than the mean-free path of phonons and electrons, it increases for increasing distances. The compatibility of this temperature behavior with the second law of thermodynamics is investigated by calculating numerically the local entropy production as a function of the radial distance. It turns out that such a production is positive and strictly decreasing with the radial distance.

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Nonlocal behavior in phonon transport

Cited by 91 publications

References 23 publications

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

Heat-pulse propagation along nonequilibrium nanowires in thermomass theory

Non-Fourier Heat Transfer with Phonons and Electrons in a Circular Thin Layer Surrounding a Hot Nanodevice

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