Analytical solution of hyperbolic heat conduction equation in relation to laser short-pulse heating

Yilbaş, Bekir Sami; Al-Dweik, Ahmad Y.; Mansour, Sulyman

doi:10.1016/j.physb.2011.01.068

Cited by 26 publications

(16 citation statements)

References 13 publications

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“…where Q is the power density deposited by the external source function associated with the laser irradiation [29][30][31] and G is the electron-phonon coupling factor which characterizes the energy exchange between electrons and phonons [12,19].…”

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

“…T is the phonon's initial temperature. Taking into account equations (30,31), the set of four interval partial differential equations is obtained  is the time step needed for a phonon and electron to travel from one lattice site to the neighboring lattice site. In the paper the equality of In the LBM method, it is necessary to set the grid in such a way that the result is independent of the grid size.…”

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

“…T is the phonon's initial temperature. Taking into account equations (30,31), the set of four interval partial differential equations is obtained In the LBM method, it is necessary to set the grid in such a way that the result is independent of the grid size. Generally, this can be achieved with a lattice spacing shorter than the phonon mean free path.…”

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

“…Generally, this can be achieved with a lattice spacing shorter than the phonon mean free path. The equations (22) and (23) should be supplemented by the boundary conditions [28], for example of the 2 nd type on the left boundary and the 1 st type on the right boundary as follows is the phonon's initial temperatu Taking into account equations (30,31), the set of fo interval partial differential equations is obtained In the LBM method, it is necessary to set the grid in such a way that the result is independent of the grid size. Generally, this can be achieved with a lattice spacing shorter than the phonon mean free path.…”

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

“…T is the phonon's initial temperature. Taking into account equations (30,31), the set of four interval partial differential equations is obtained …”

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

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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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Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

“…T is the phonon's initial temperature. Taking into account equations (30,31), the set of four interval partial differential equations is obtained …”

Section: Interval Lattice Boltzmann Methodsmentioning

confidence: 99%

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