An enhanced Gray model for nondiffusive heat conduction solved by implicit lattice Boltzmann method

Wang, Dadong; Qu, Zhengxian; Ma, Yanbao

doi:10.1016/j.ijheatmasstransfer.2015.11.003

Cited by 7 publications

(3 citation statements)

References 41 publications

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“…Boltzmann method is also a popular method used to solve the title problem. Wang et al [26] developed an enhanced Gray model by considering the second-order terms in Taylor expansion in the phonon Boltzmann transport equation. Xu and Wang derived the DPL model using the Boltzmann method, and investigated the oscillation of the microscale heat conduction systemically [27,28].…”

Section: Introductionmentioning

confidence: 99%

Analysis and Modelling of Non-Fourier Heat Behavior Using the Wavelet Finite Element Method

et al. 2019

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Non-Fourier heat behavior is an important issue for film material. The phenomenon is usually observed in some laser induced thermal responses. In this paper, the non-Fourier heat conduction problems with temperature and thermal flux relaxations are investigated based on the wavelet finite element method and solved by the central difference scheme for one- and two-dimensional media. The Cattaneo–Vernotte model and the Dual-Phase-Lagging model are used for finite element formulation, and a new wavelet finite element solving formulation is proposed to address the memory requirement problem. Compared with the current methodologies for the Cattaneo–Vernotte model and the Dual-Phase-Lagging model, the present model is a direct one which describe the thermal behavior by one equation about temperature. Compared with the wavelet method proposed by Xiang et al., the developed method can be used for arbitrary shapes. In order to address the efficient computation problems for the Dual-Phase-Lagging model, a novel iteration updating methodology is also proposed. The proposed iteration algorithms on time avoids the use the global stiffness matrix, which allows the efficient calculation for title issue. Numerical calculations have been conducted in the manner of comparisons with the classical finite element method and spectral finite element method. The comparisons from accuracy, efficiency, flexibility, and applicability validate the developed method to be an effective and alternative tool for material thermal analysis.

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Section: Introductionmentioning

confidence: 99%

Analysis and Modelling of Non-Fourier Heat Behavior Using the Wavelet Finite Element Method

et al. 2019

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“…[6][7][8]. The BTE is difficult to solve and for this reason in numerical computations the lattice Boltzmann method (LBM) is used [9][10][11]. The LBM solves a discretized set of the Boltzmann transport equations.…”

Section: Introductionmentioning

confidence: 99%

Modelling of transient heat transport in metal films using the interval lattice Boltzmann method

Piasecka-Belkhayat

Korczak

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. In the paper a description of heat transfer in one-dimensional crystalline solids is presented. The lattice Boltzmann method based on Boltzmann transport equation is used to simulate the nanoscale heat transport in thin metal films. The coupled lattice Boltzmann equations for electrons and phonons are applied to analyze the heating process of thin metal films via laser pulse. Such approach in which the parameters appearing in the problem analyzed are treated as constant values is widely used, but in the paper the interval values of relaxation times and electron-phonon coupling factor are taken into account. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic. In the final part of the paper the results of numerical computations are shown. are still a subject of discussion [18]. The analogical problem is with the electron-phonon coupling factor. In the literature we can find a wide range of this value [19]. So it seems natural to take the interval values of relaxation times and coupling factor and this assumption is closer to the real physical conditions of the process analyzed.In the article the authors present an innovative approach of the described problem using the interval lattice Boltzmann method. Using interval numbers, the mathematical model reflects better the course of the heat flow. There was no such an approach in available literature until now. Moreover, there isn't any known commercial software using the interval LBM, although the presented method can easily be programmed.Here, the interval lattice Boltzmann method (ILBM) is presented with the approach of the directed interval arithmetic [16,20,21]. In this arithmetic a set of proper intervals is extended by improper intervals, and all arithmetic operations and functions are also extended. The main advantage of the directed interval arithmetic [20,22] upon the usual interval arithmetic [23] is that the obtained temperature intervals are much narrower and their width does not increase in time.In theory as well as in practice it is valuable to develop the interval version of the LBM. Directed interval arithmeticLet us consider a directed interval ā which can be defined as a set D of all directed pairs of real numbers defined as follows [17,20,24] where a − and a + denote the beginning and the end of the interval, respectively.

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“…Dissipation of current-generated heat is traditionally analyzed in terms of Fourier's law of diffusive heat flow. However, it is now recognized that diffusive approximation starts to break down in modern transistors whose dimensions are comparable to the phonon mean free path (MFP) [12][13][14][15]. Thus, optimizing heat dissipation at nanoscale is not equivalent to maximizing thermal conductivity [16][17][18].…”

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confidence: 99%

Transport and relaxation of current-generated nonequilibrium phonons from nonlocal electronic measurements

Chen,

Urazhdin

2021

Preprint

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We study phonons generated by current in a Pt nanowire, by measuring resistance of another nanowire separated from the first one by an insulating spacer. For thin spacers, the resistance varies almost linearly with current at cryogenic temperatures, while an additional quadratic contribution emerges for thicker spacers. These observations suggest a non-thermal distribution of currentgenerated phonons that relaxes via strongly nonlinear dynamical processes rather than few-phonon scattering. Our results provide insight into the nonequilibrium phonon dynamics at nanoscale, which may facilitate efficient heat management in electronic nanodevices.

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An enhanced Gray model for nondiffusive heat conduction solved by implicit lattice Boltzmann method

Cited by 7 publications

References 41 publications

Analysis and Modelling of Non-Fourier Heat Behavior Using the Wavelet Finite Element Method

Analysis and Modelling of Non-Fourier Heat Behavior Using the Wavelet Finite Element Method

Modelling of transient heat transport in metal films using the interval lattice Boltzmann method

Transport and relaxation of current-generated nonequilibrium phonons from nonlocal electronic measurements

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