Heat waves and phonon–wall collisions in nanowires

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

doi:10.1098/rspa.2010.0645

Cited by 50 publications

(36 citation statements)

References 42 publications

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“…As discussed in the Introduction, new technologies present heat transfer problems on ever reduced scales, and the phenomena we describe seem likely to be of particular relevance to such systems (where hyperbolic heat-flow effects are known to be especially pronounced), alongside biological contexts for which thermal relaxation times are relatively long [8][9][10][11][13][14][15]. Nevertheless, one of the pressing issues surrounding hyperbolic modifications to the usual Fourier law of heat conduction is to establish which kind of heat-flow model should be properly employed (the model used here is simply one more frequently encountered).…”

Section: Resultsmentioning

confidence: 99%

On oscillatory convection with the Cattaneo–Christov hyperbolic heat-flow model

Bissell

2015

Proc. R. Soc. A.

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Adoption of the hyperbolic Cattaneo-Christov heatflow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection, R c and R S respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value C T ≥ 8/27π 2 ≈ 0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number P 1 , which-in contrast to the classical stationary scenario-can impact on oscillatory modes significantly owing to the non-zero frequency of convection. Numerical investigation indicates that the behaviour found analytically for free boundaries applies in a qualitatively similar fashion for fixed boundaries, while the threshold Cattaneo number C T is computed as a function of P 1 ∈ [10 −2 , 10 +2 ] for both boundary regimes.

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Section: Resultsmentioning

confidence: 99%

On oscillatory convection with the Cattaneo–Christov hyperbolic heat-flow model

Bissell

2015

Proc. R. Soc. A.

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“…Finally, as shown in the previous section, the establishment of appropriate boundary conditions remains a delicate task. In that respect, recent work (Jou et al 2010b(Jou et al , 2011) describes interesting and original perspectives. In spite of the above limitations, application of the model to the problem of transient heat conduction in materials with thickness of the order of magnitude of the mean free path of heat carriers has led to satisfactory results.…”

Section: Final Comments and Conclusionmentioning

confidence: 99%

An extended thermodynamic model of transient heat conduction at sub-continuum scales

et al. 2011

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A thermodynamic description of transient heat conduction at small length and timescales is proposed. It is based on extended irreversible thermodynamics and the main feature of this formalism is to elevate the heat flux vector to the status of independent variable at the same level as the classical variable, the temperature. The present model assumes the coexistence of two kinds of heat carriers: diffusive and ballistic phonons. The behaviour of the diffusive phonons is governed by a Cattaneo-type equation to take into account the high-frequency phenomena generally present at nanoscales. To include non-local effects that are dominant in nanostructures, it is assumed that the ballistic carriers are obeying a Guyer-Krumhansl relation. The model is applied to the problem of transient heat conduction through a thin nanofilm. The numerical results are compared with those provided by Fourier, Cattaneo and other recent models.

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“…This remarkable result has been attributed to the dramatic decrease in the thermal conductance due to the increase phonon scattering by the rough surfaces. 25,59,[82][83][84] In the quest for efficient thermoelectric materials, we have proposed a novel approach to improve the overall figure of merit of Si nanowires. Our calculations show that covering the Si nanowires with a thin shell of Ge (or an alloy of Si and Ge) does improve the figure of merit.…”

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confidence: 99%

Review—Towards the Next Generation of Thermoelectric Materials: Tailoring Electronic and Phononic Properties of Nanomaterials

Caballero-Calero

D’Agosta

2017

ECS J. Solid State Sci. Technol.

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In this review article we present the most relevant outcomes of the joint project “Tailoring Electronic and Phononic Properties of Nanomaterials: Towards Improved Thermoelectricity (nanoTHERM)”, a Spanish research Consolider project focused on the understanding of the thermoelectric materials and the tailoring of both their electronic and phononic properties toward the optimization of the efficiency of thermoelectric devices working at low and high temperatures.

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Heat waves and phonon–wall collisions in nanowires

Cited by 50 publications

References 42 publications

On oscillatory convection with the Cattaneo–Christov hyperbolic heat-flow model

On oscillatory convection with the Cattaneo–Christov hyperbolic heat-flow model

An extended thermodynamic model of transient heat conduction at sub-continuum scales

Review—Towards the Next Generation of Thermoelectric Materials: Tailoring Electronic and Phononic Properties of Nanomaterials

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