Phonon hydrodynamics and phonon-boundary scattering in nanosystems

Álvarez, F. X.; Jou, David; Sellitto, A.

doi:10.1063/1.3056136

Cited by 136 publications

(184 citation statements)

References 18 publications

Supporting

Mentioning

173

Contrasting

Unclassified

Order By: Relevance

“…The choice of this geometry takes us beyond the usual one-dimensional situations, in which some of the non-local effects vanish identically. In fact, in one-dimensional heat transport in nanowires and thin layers, the non-local effects are also present through the variation of the heat flux inside the system, but their effects may be embedded in size-dependent thermal conductivity (Alvarez et al 2009(Alvarez et al , 2011Sellitto et al 2010b). Although this approach is very useful for practical applications, it slightly obscures some essential points of non-local transport.…”

Section: Non-local Heat Transport and The Steady-state Temperature Prmentioning

confidence: 99%

“…These systems have been much studied theoretically (Alvarez et al 2009(Alvarez et al , 2011 and experimentally (Asheghi et al 1997;Ju & Goodson 1999;Liu & Asheghi 2004;Saito et al 2007;Balandin et al 2008;Ghosh et al 2008;Balandin 2011). However, the thermodynamical behaviour in…”

Section: Consequences Of Non-local Terms In Silicon and Graphenementioning

confidence: 99%

“…The non-local effects influence the heat transport both in the radial (r) direction and in the transverse direction z. The latter can be taken into account, in phonon hydrodynamics, by assuming that the longitudinal heat flux has a bulk contribution q b (with a parabolic profile) and a wall contribution q w (Alvarez et al 2009(Alvarez et al , 2011. (Online version in colour.…”

Section: Consequences Of Non-local Terms In Silicon and Graphenementioning

confidence: 99%

See 2 more Smart Citations

Non-local effects in radial heat transport in silicon thin layers and graphene sheets

2011

Self Cite

View full text Add to dashboard Cite

We explore non-local effects in radially symmetric heat transport in silicon thin layers and in graphene sheets. In contrast to one-dimensional perturbations, which may be well described by means of the Fourier law with a suitable effective thermal conductivity, twodimensional radial situations may exhibit a more complicated behaviour, not reducible to an effective Fourier law. In particular, a hump in the temperature profile is predicted for radial distances shorter than the mean-free path of heat carriers. This hump is forbidden by the local-equilibrium theory, but it is allowed in more general thermodynamic theories, and therefore it may have a special interest regarding the formulation of the second law in ballistic heat transport.

show abstract

Section: Non-local Heat Transport and The Steady-state Temperature Prmentioning

confidence: 99%

Section: Consequences Of Non-local Terms In Silicon and Graphenementioning

confidence: 99%

Section: Consequences Of Non-local Terms In Silicon and Graphenementioning

confidence: 99%

See 1 more Smart Citation

Non-local effects in radial heat transport in silicon thin layers and graphene sheets

2011

Self Cite

View full text Add to dashboard Cite

show abstract

“…Then, the nonlocal term in Eq. (5) may be more important than the heat flux itself [32][33][34][35], and that equation reduces to…”

Section: Heat Transport Equations Beyond the Fourier Law And Hydrodynmentioning

confidence: 99%

“…In other words, since we regard phonons and electrons as a mixture of gases flowing through the crystal lattice [32,71], each of which is endowed with its own temperature, according with the theory of fluid mixtures with different temperatures [74][75][76], we assume that each constituent obeys the same balance laws as a single fluid. The average temperature of the mixture may introduced by the consideration that the internal energy of the mixture is the same as in the case of a single-temperature mixture [75].…”

Section: Two-temperature Thermoelectric Systemsmentioning

confidence: 99%

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

Jou¹,

Cimmelli

2016

Communications in Applied and Industrial Mathematics

View full text Add to dashboard Cite

show abstract

Heat Transport by Phonons and Electrons

Tzou¹

2014

Macro‐ to Microscale Heat Transfer

View full text Add to dashboard Cite

Efficient heat transport requires a sufficient number of collisions among energy carriers to take place. Mean free path can be thought of as the averaged distance traveled by the energy carrier per collision over a sufficient number of collisions. Mean free time, on the other hand, is the averaged time traveled by the energy carrier per collision over a sufficient number of collisions. The mean free path for the lattice is of the order of 10 1 -10 2 nm. The mean free time for electron-electron, electron-phonon (for metals), and phonon-phonon (semiconductors, dielectric crystals, and insulators) collisions is of the order of 10 0 femtoseconds, 10 0 ps, and 10 1 ps, respectively. As the physical scale of a device shrinks to the order of the mean free path of the energy carriers (microscale effect in space), or the process time shortens into the range of their mean free time (microscale effect in time), individual and yet statistically meaningful behavior of the energy carriers becomes pronounced. The resulting behavior of heat transport in microscale will be very different from macroscale heat transfer based on the averages taken over hundreds of thousands of grains (in space) and collisions (in time). Different physical bases have been used in describing different types of energy carriers in microscale heat transfer. This chapter reviews most representative phonon-electron interaction (for metals) and phonon scattering (for semiconductors, dielectric crystals, and insulators) models in microscale heat transfer to exemplify the differences resulting from the development made on different physical bases. Special effort then follows to extract the commonalities among the differences, paving the way for the generalized dual-phase-lag model that will be deployed through the rest of the book.From a microscopic point of view, the process of heat transport is governed by phonon-electron interaction in metallic films and by phonon scattering in dielectric films, insulators, and semiconductors. Conventional theories established on the macroscopic level, such as heat diffusion assuming Fourier's law, are not expected to be informative for microscale conditions because they describe macroscopic behavior averaged over many grains. This holds even more true should the transient behavior at extremely short times, say, of the order of picoseconds to femtoseconds, become major concerns. A typical example is the ultrafast 1 laser heating in thermal processing of materials. The quasiequilibrium concept implemented in Fourier's law further breaks down in this case, along with the termination of macroscopic behavior in heat transport.This chapter provides a brief summary of existing microscale heat-transfer models, including the microscopic two-step model (phonon-electron interaction model), phonon-scattering model, phonon radiative transfer model, and the thermal wave model. The first three models emphasize microscale effects in space, while the fourth, the thermal wave model, describes microscale effects in time. Rather than a detai...

show abstract

Phonon hydrodynamics and phonon-boundary scattering in nanosystems

Cited by 136 publications

References 18 publications

Non-local effects in radial heat transport in silicon thin layers and graphene sheets

Non-local effects in radial heat transport in silicon thin layers and graphene sheets

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

Heat Transport by Phonons and Electrons

Contact Info

Product

Resources

About