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Modelling of transient heat transport in two-layered crystalline solid films using the interval lattice Boltzmann method

Belkhayat-Piasecka A., Korczak A.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 4

57--65

EN

In the paper, the numerical modelling of heat transfer in one-dimensional crystalline solid films is considered. A generalized two-layer problem is described by the Boltzmann transport equations transformed in the phonon energy density equations supplemented by the adequate boundary-initial conditions. Such an approach in which the parameters appearing in the problem analysed are treated as the constant values is widely used, but in this paper the interval values of relaxation time and the boundary condition for silicon and diamond 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 presented.

2

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

Piasecka-Belkhayat A., Korczak A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 3

599--606

EN

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.

3

Numerical modelling of the transient heat transport in 2D silicon thin film using the interval lattice Boltzmann method

Piasecka-Belkhayat A., Korczak A.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 2

95--103

EN

In the paper the description of numerical analysis of the heat transfer process proceeding in a two-dimensional silicon thin film is presented. It is assumed that some parameters like relaxation time and boundary temperatures appearing in the mathematical model of the analyzed problem are given as intervals. The discussed problem has been solved using the interval form of the lattice Boltzmann method applying the rules of the directed interval arithmetics. In the final part of the paper, the results of numerical computations are shown.

4

Modelling of transient heat transport in crystalline solids using the interval lattice Bolzmann method (two-dimesnsional model)

Piasecka-Belkhayat A., Korczak A.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2014

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nr 1

69--71

EN

In the paper the two-dimensional numerical modelling of heat transfer in crystalline solids is considered. In the mathematical description the relaxation time and the boundary conditions are given as interval numbers. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic.

PL

W artykule zaprezentowano dwuwymiarowy model numeryczny przepływu ciepła w ciele krystalicznym. W opisie matematycznym czas relaksacji i warunki brzegowe są zdefiniowane jako liczby przedziałowe. Sformułowane zagadnienie rozwiązano za pomocą interwałowej metody siatek Boltzmanna stosując skierowaną arytmetykę interwałową.

5

Application of the interval lattice boltzmann method for a numerical modelling of thin metal films irradiation by ultra short laser pulses

Piasecka-Belkhayat A., Korczak A.

Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska

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2014

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nr 4

85--88

EN

In the paper the one-dimensional numerical modelling of heat transfer in thin metal films irradiated by ultra short laser pulses is considered. In the mathematical description the relaxation times and the boundary conditions for phonons and electrons are given as interval numbers. The problem formulated has been solved by means of the interval lattice Boltzmann method using the rules of directed interval arithmetic. The examples of numerical computations are presented in the final part of the paper.

PL

W artykule zaprezentowano jednowymiarowy model numeryczny przepływu ciepła w cienkich warstwach metalowych poddanych. naświetlaniu laserem pulsacyjnym. W opisie matematycznym czasy relaksacji oraz warunki brzegowe dla fononów i elektronów są zdefiniowane jako liczby przedziałowe. Sformułowane zagadnienie rozwiązano za pomocą interwałowej metody siatek Boltzmanna stosując skierowaną arytmetykę interwałową. W końcowej części artykułu przedstawione są przykłady obliczeń numerycznych.

6

The interval lattice Boltzmann method for transient heat transport

Piasecka Belkhayat A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2009

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Vol. 8, nr 1

155-160

EN

In this paper an application of the interval lattice Boltzmann method for solving one-dimensional problems is presented. The Boltzmann transport equation transformed in the phonon energy density equation is considered. Such approach in which the parameters appearing in the problem analyzed are treated as the constant values is widely used. Here, the model with interval value of relaxation time is analyzed. In the final part of the paper, results of numerical computations are shown.