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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.

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Numerical modelling of the transient heat transport in a thin gold film using the fuzzy lattice Boltzmann method with α-cuts

Belkhayat-Piasecka A., Korczak A.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 1

123--135

EN

In this paper a description of heat transfer in one-dimensional crystalline solids is presented. The fuzzy lattice Boltzmann method based on the Boltzmann transport equation is used to simulate the nanoscale heat transport in thin metal films. The fuzzy coupled lattice Boltzmann equations for electrons and phonons are applied to analyze the heating process of thin metal films via a laser pulse. Such an approach in which the parameters appearing in the problem analyzed are treated as constant values is widely used. Here, the model with fuzzy values of relaxation times and an electron-phonon coupling factor is taken into account. The problem formulated has been solved by means of the fuzzy lattice Boltzmann method using the α-cuts and the rules of directed interval arithmetic. The application of α-cuts allows one to avoid complicated arithmetical perations in the fuzzy numbers set. In the final part of the paper the results of numerical computations are shown.

3

Application of the interval methods for solving linear thermal diffusion problems

Belkhayat-Piasecka A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2005

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Vol. 4, nr 1

204-210

EN

The example of two-dimensional non-steady state heat flow using the interval arithmetic and the 1st scheme of the boundary element method is presented. This example is a typical linear task, where the boundary of the homogeneous domain is an interval. In the final part of the paper, results of numerical computations are shown with the different boundary conditions.