Przedziałowa metoda elementów brzegowych dla zadań dyfuzji w obszarach dwuwarstwowych

In the paper, the description of an unsteady heat transfer for one- dimensional problem proceeding in a two-layered domain is presented. It is assumed that all thermophysical parameters appearing in the mathematical description of the problem analysed are given as directed interval values. The problem discussed has been solved using the 1st scheme of the interval boundary element method. The interval Gauss elimination method has been applied to solve the obtained interval system of equations. In the final part of the paper, results of numerical computations are shown.W pracy przedstawiono opis nieustalonego przepływu ciepła dla zadań jednowymiarowych w obszarach dwuwarstwowych. Założono, że wszystkie parametry termofizyczne pojawiające się w opisie matematycznym analizowanego zadania są wartościami przedziałowymi skierowanymi. Omawiane zagadnienie zostało rozwiązane za pomocą pierwszego schematu przedziałowej metody elementów brzegowych. Do rozwiązania otrzymanego interwałowego układu równań zastosowano przedziałową metodę eliminacji Gaussa. W końcowej części pracy pokazano wyniki obliczeń numerycznych

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

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

Modeling of thermal processes proceeding in a 1D domain of crystalline solids using the lattice Boltzmann method with an interval source function

The interval lattice Boltzmann method (ILBM) with an uncertainly defined internal heat source function is used to simulate heat transfer in a thin silicone film. The solution to the interval Boltzmann transport equations has been obtained taking into account the rules of directed interval arithmetics. A similar analysis has been done using the sensitivity model where the Boltzmann transport equations and boundary-initial conditions have been differentiated with respect to the no-interval heat source value. The knowledge of the sensitivity function distribution and the application of the Taylor formula allow one to find the border solutions of the problem analyzed, which (to some extent) correspond to the solution obtained under the assumption of the uncertainly defined source function. In the final part of the paper, numerical computations obtained for both methods are presented

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

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

Modelowanie przepływu ciepła w dwuwymiarowym ciele krystalicznym za pomocą interwałowej metody siatek Bolzmanna

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.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

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

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

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

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

Zastosowanie interwałowej metody siatek boltzmanna do numerycznego modelowania procesu naświetlania laserem pulsacyjnym cienkich warstw metalowych

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.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