Analysis of ultrashort laser pulse interactions with metal films using a two-temperature model

Majchrzak, Ewa; Dziatkiewicz, J.

doi:10.17512/jamcm.2015.2.04

Cited by 13 publications

(17 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(Figures 8, 9, 10). These significantly different from the previously assumed values of the delay times result from the considerations presented in the works [11,12] in which τ q and τ T are dependent mainly on the porosity of the tissue. Delays determined in this way are shorter than the most frequently reported in the literature (e.g.…”

Section: Results Of Computationscontrasting

confidence: 79%

Numerical model of biological tissue heating using the models of bio–heat transfer with delays

Majchrzak

Mochnacki

2019

E3S Web Conf.

Self Cite

View full text Add to dashboard Cite

The numerical model of thermal processes in domain of biological tissue subjected to an external heat source is discussed. The model presented is based on the second order dual–phase–lag equation (DPLE) in which the relaxation time and thermalization time thermalization time (τq and τT) are tak n into account. In this paper the homogeneous, cylindrical skin tissue domain is considered. The most important aim of the research is to compare the results obtained using the classical model (the first-orderDPLE) with the numerical solution resulting from the higher order form of this equation. At the stage of numerical computations the Finite Difference Method (FDM) is applied. In the final part of the paper the examples of computations are shown.

show abstract

Section: Results Of Computationscontrasting

confidence: 79%

Numerical model of biological tissue heating using the models of bio–heat transfer with delays

Majchrzak

Mochnacki

2019

E3S Web Conf.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Boltzmann transport equations for the coupled model (1D problem) with two kinds of carriers: electrons (e) and phonons (ph) can be written in the following form [26] Modelling of transient heat transport in metal films using the interval lattice Boltzmann method 2 (8) y the During the heating of thin metal films via laser pulse the electrons are energized and they subsequently transfer the energy to phonons via coupling between them. The Boltzmann transport equations for the coupled model (1D problem) with two kinds of carriers: electrons (e) and phonons (ph) can be written in the following form [26] 0 e e e e e e e f f f f g t…”

Section: Formulation Of the Problem Before Stylingmentioning

confidence: 99%

“…This kind of phenomena can be described by the Boltzmann transport equation (BTE) [2][3][4][5] but the other approaches can be also applied, e.g. [6][7][8]. The BTE is difficult to solve and for this reason in numerical computations the lattice Boltzmann method (LBM) is used [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

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

View full text Add to dashboard Cite

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.

show abstract

“…In this group, the microscopic two-temperature parabolic or hyperbolic models (belonging to a group of continuum models) should be mentioned (Chen and Beraun, 2001; Kaba and Dai, 2005;Lin and Zhigilei, 2008;Majchrzak, 2012;Majchrzak and Dziatkiewicz, 2015). The two-step parabolic and hyperbolic models involve two energy equations determining the thermal processes in the electron gas and the metal lattice.…”

Section: Introductionmentioning

confidence: 99%

Application of the Alternating Direction Implicit Method for numerical solution of the dual-phase lag equation

Ciesielski

2017

jtam

View full text Add to dashboard Cite

The problem discussed in the paper concerns the numerical modeling of thermal processes proceeding in micro-scale described using the Dual Phase Lag Model (DPLM) in which the relaxation and thermalization time appear. The cylindrical domain of a thin metal film subjected to a strong laser pulse beam is considered. The laser action is taken into account by the introduction of an internal heat source in the energy equation. At the stage of numerical modeling, the Control Volume Method is used and adapted to resolve the hyperbolic partial differential equation. In particular, the Alternating Direction Implicit (ADI) method for DPLM is presented and discussed. The examples of computations are also presented.

show abstract

Analysis of ultrashort laser pulse interactions with metal films using a two-temperature model

Cited by 13 publications

References 5 publications

Numerical model of biological tissue heating using the models of bio–heat transfer with delays

Numerical model of biological tissue heating using the models of bio–heat transfer with delays

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

Application of the Alternating Direction Implicit Method for numerical solution of the dual-phase lag equation

Contact Info

Product

Resources

About