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1 Journal of Applied Mathematics and Computational Mechanics

1 2016

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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

2016

Vol. 15, nr 1

123--135

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.