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

Sellitto, A.; Jou, David; Bafaluy, J.

doi:10.1098/rspa.2011.0584

Cited by 33 publications

(23 citation statements)

References 31 publications

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“…Besides, the molecular dynamics [14] and MC [15] simulations were also employed to investigate the effective thermal conductivity. Sellitto et al [16] investigated the steady-state radical heat transport in silicon thin layers based on phonon hydrodynamics and found that two-dimensional radial situations cannot be reducible to Fourier law with the effective thermal conductivity. As for experiments, Liu & Asheghi [17,18] obtained the in-plane effective thermal conductivity of silicon films by introducing a steady-state uniform internal heat source and measuring the average temperature increase.…”

Section: Introductionmentioning

confidence: 99%

“…Great efforts have focused on the reduction of in-plane effective thermal conductivity in the nanofilms [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and tried to characterize the thermal transport with phonon-boundary scattering by the modification of effective thermal conductivity [24][25][26]. Analytical effective thermal conductivity models were derived based on the steady-state phonon Boltzmann transport equation [9,10], extended irreversible thermodynamics [11] and phonon hydrodynamics [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Transient in-plane thermal transport in nanofilms with internal heating

Younan¹,

Cao²

2016

Proc. R. Soc. A.

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Wide applications of nanofilms in electronics necessitate an in-depth understanding of nanoscale thermal transport, which significantly deviates from Fourier's law. Great efforts have focused on the effective thermal conductivity under temperature difference, while it is still ambiguous whether the diffusion equation with an effective thermal conductivity can accurately characterize the nanoscale thermal transport with internal heating. In this work, transient in-plane thermal transport in nanofilms with internal heating is studied via Monte Carlo (MC) simulations in comparison to the heat diffusion model and mechanism analyses using Fourier transform. Phonon-boundary scattering leads to larger temperature rise and slower thermal response rate when compared with the heat diffusion model based on Fourier's law. The MC simulations are also compared with the diffusion model with effective thermal conductivity. In the first case of continuous internal heating, the diffusion model with effective thermal conductivity under-predicts the temperature rise by the MC simulations at the initial heating stage, while the deviation between them gradually decreases and vanishes with time. By contrast, for the one-pulse internal heating case, the diffusion model with effective thermal conductivity under-predicts both the peak temperature rise and the cooling rate, so the deviation can always exist.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transient in-plane thermal transport in nanofilms with internal heating

Younan¹,

Cao²

2016

Proc. R. Soc. A.

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“…The behavior shown in Figure 3 is anomalous, since the temperature profile in the layer is not everywhere decreasing with the radial distance, as it would be expected from the classical Fourier law [23]. Since in the present problem, the only heat source is the hot device at r * ≡ 1, that behavior (arising from the model Equation (7)) points out that in the circular layer, there are regions wherein the heat is flowing from colder points to hotter ones.…”

Section: Thermodynamic Compatibilitymentioning

confidence: 90%

“…The presence of that hump (see Figure 3) suggests that there are some areas wherein the heat flows from colder points to the hotter ones. This result completely disregards that arising from the classical Fourier law [23], which predicts that heat can only flow from the hotter zones to the colder ones. However, to check whether the theoretical predictions arising from Equation (2) are physically admissible, or not, we have analyzed the temperature hump in view of the second law of thermodynamics.…”

Section: Discussionmentioning

confidence: 99%

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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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Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

Sarkar

2020

Z Angew Math Mech

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This is an attempt to design a dynamic model of nonlocal heat conduction in a nonlocal elastic bounded rod. This model is drafted using the Lord-Shulman theory of generalized thermoelasticity due to the involvement of one relaxation time to the heat conduction equation and the equation of motion. This model is then employed to discuss the thermal behavior of the rod when subjected to a moving heat source. Both ends of the rod are assumed to be rigidly fixed and thermally insulated. Analytical solutions for the distribution of temperature, displacement and thermal stresses are obtained using integral transform in the Laplace transform technique is used to obtain the analytical solutions for the field variables such as temperature, displacement and stress. The inverse Laplace transform based on the Zakian method is used to invert the results in the space-time domain. Specific attention is paid to study the effect of thermal nonlocal parameter and the velocity of the moving heat source on the distribution of the field variables. K E Y W O R D SLaplace transform, LS model, nonlocal heat conduction, thermal nonlocal parameter, Zakian algorithm

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

Cited by 33 publications

References 31 publications

Transient in-plane thermal transport in nanofilms with internal heating

Transient in-plane thermal transport in nanofilms with internal heating

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

Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

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