scholarly journals Modeling of Melting and Resolidification in Domain of Metal Film Subjected to a Laser Pulse

2016 ◽  
Vol 16 (1) ◽  
pp. 41-44 ◽  
Author(s):  
E. Majchrzak ◽  
B. Mochnacki
Keyword(s):  
Laser Pulse ◽  
Metal Film ◽  
Initial Conditions ◽  
Control Volume ◽  
Extreme Temperature ◽  
Laser Action ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Thin Metal Film ◽  
Phase Lag

Abstract Thermal processes in domain of thin metal film subjected to a strong laser pulse are discussed. The heating of domain considered causes the melting and next (after the end of beam impact) the resolidification of metal superficial layer. The laser action (a time dependent bell-type function) is taken into account by the introduction of internal heat source in the energy equation describing the heat transfer in domain of metal film. Taking into account the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered, the mathematical model of the process is based on the dual phase lag equation supplemented by the suitable boundary-initial conditions. To model the phase transitions the artificial mushy zone is introduced. At the stage of numerical modeling the Control Volume Method is used. The examples of computations are also presented.

scholarly journals Dual Phase Lag Model of Melting Process in Domain of Metal Film Subjected to an External Heat Flux

2016 ◽  
Vol 16 (4) ◽  
pp. 85-90 ◽  
Author(s):  
B. Mochnacki ◽  
M. Ciesielski
Keyword(s):  
Mushy Zone ◽  
Metal Film ◽  
Control Volume ◽  
Extreme Temperature ◽  
Internal Heat ◽  
Melting Process ◽  
Thin Metal Film ◽  
Heating Process ◽  
Phase Lag ◽  
Dual Phase

Abstract Heating process in the domain of thin metal film subjected to a strong laser pulse are discussed. The mathematical model of the process considered is based on the dual-phase-lag equation (DPLE) which results from the generalized form of the Fourier law. This approach is, first of all, used in the case of micro-scale heat transfer problems (the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered). The external heating (a laser action) is substituted by the introduction of internal heat source to the DPLE. To model the melting process in domain of pure metal (chromium) the approach basing on the artificial mushy zone introduction is used and the main goal of investigation is the verification of influence of the artificial mushy zone ‘width’ on the results of melting modeling. At the stage of numerical modeling the author’s version of the Control Volume Method is used. In the final part of the paper the examples of computations and conclusions are presented.

scholarly journals Numerical Simulation of Thermal Processes in a Domain of Thin Metal Film Subjected to an Ultrashort Laser Pulse

Materials ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2116 ◽  
Author(s):  
Ewa Majchrzak ◽  
Bohdan Mochnacki
Keyword(s):  
Laser Pulse ◽  
Metal Film ◽  
Ultrashort Laser Pulse ◽  
Initial Conditions ◽  
Time Derivative ◽  
Thin Metal Film ◽  
Thin Metal ◽  
Thermal Processes ◽  
Phase Lag ◽  
Ultrashort Laser

A thin metal film subjected to an ultrashort laser pulse is considered. With a sufficiently high laser intensity the process of the film heating may cause metal melting and even ablation. In this work, the numerical model of the melting and resolidification processes is presented. The mathematical model is based on the dual phase lag equation in which two positive constants appear, this means the relaxation and thermalization times. The considered equation contains a second-order time derivative and higher order mixed derivative in both time and space and should be supplemented by the appropriate boundary and initial conditions. The model of the melting and resolidification is presented in two versions. The first can be called ‘the introduction of the artificial mushy zone sub-domain’, while the second ‘the two forms of the basic energy equation’. At the stage of numerical computations, the implicit scheme of the finite difference method is used. The numerical algorithm is tested for the two proposed models which are applied to the computations concerning the thermal processes occurring in the cylindrical micro-domain (chromium, gold) subjected to an ultrashort laser pulse.

scholarly journals Second-Order Dual Phase Lag Equation. Modeling of Melting and Resolidification of Thin Metal Film Subjected to a Laser Pulse

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 999 ◽  
Author(s):  
Ewa Majchrzak ◽  
Bohdan Mochnacki
Keyword(s):  
Laser Pulse ◽  
Latent Heat ◽  
Metal Film ◽  
Thin Metal Film ◽  
Second Order ◽  
Phase Changes ◽  
Thin Metal ◽  
Phase Lag ◽  
Dual Phase ◽  
Numerical Computations

The process of partial melting and resolidification of a thin metal film subjected to a high-power laser beam is considered. The mathematical model of the process is based on the second-order dual phase lag equation (DPLE). Until now, this equation has not been used for the modeling of phase changes associated with heating and cooling of thin metal films and the considerations regarding this issue are the most important part of the article. In the basic energy equation, the internal heat sources associated with the laser action and the evolution of phase change latent heat are taken into account. Thermal processes in the domain of pure metal (chromium) are analyzed and it is assumed that the evolution of latent heat occurs at a certain interval of temperature to which the solidification point was conventionally extended. This approach allows one to introduce the continuous function corresponding to the volumetric fraction of solid or liquid state at the neighborhood of the point considered, which significantly simplifies the phase changes modeling. At the stage of numerical computations, the authorial program based on the implicit scheme of the finite difference method (FDM) was used. In the final part of the paper, the examples of numerical computations (including the results of simulations for different laser intensities and different characteristic times of laser pulse) are presented and the conclusions are formulated.

Application of Interval Arithmetic in Numerical Modeling of Microscale Heat Transfer

2016 ◽  
Vol 366 ◽  
pp. 1-9
Author(s):  
Bohdan Mochnacki ◽  
Alicja Piasecka-Belkhayat
Keyword(s):  
Numerical Solution ◽  
Interval Arithmetic ◽  
Hyperbolic Equations ◽  
Initial Conditions ◽  
Thin Metal Film ◽  
Phase Lag ◽  
Interval Numbers ◽  
Thermophysical Parameters ◽  
Microscale Heat Transfer ◽  
The Mathematical Model

Thermal processes in the domain of a thin metal film which are subjected to a laser pulse are considered. The mathematical model based on the dual phase lag equation (DPLE) results from the generalized form of the Fourier law. The governing equation is supplemented by appropriate boundary and initial conditions. The numerical model of metal heating is constructed using the explicit scheme of the finite difference method for hyperbolic equations. The thermophysical parameters of the material (gold) are treated as interval numbers and at the stage of the FDM algorithm construction the rules of interval arithmetic are applied. In this way the numerical solution is obtained in the fuzzy form. Such an approach gives interesting practical information about the course of the process because the values of thermophysical parameters collected in the literature often differ significantly. In the final part of the paper an example for a numerical solution is presented.

scholarly journals Разрушение пленки золота при моделировании процесса лазерной биопечати

2021 ◽  
Vol 47 (12) ◽  
pp. 10
Author(s):  
В.С. Жигарьков ◽  
Н.В. Минаев ◽  
В.И. Юсупов
Keyword(s):  
Laser Pulse ◽  
Metal Film ◽  
Gold Film ◽  
Glass Plate ◽  
Thin Metal Film ◽  
Nanosecond Laser Pulse ◽  
Nanosecond Laser ◽  
Acceptor Substrate ◽  
Gel Layer ◽  
Partial Destruction

Laser printing with gel microdroplets is a promising method for biotechnology and medicine. During printing, a nanosecond laser pulse is absorbed in a thin metal film of a donor substrate with a covered gel layer, which leads to its heating, partial destruction of the film, and transfer of a gel microdroplet to the acceptor substrate. In this work, the dynamics of destruction of a film with a thickness of 50 nm is studied. It is shown that when threshold is exceeded, the gold film peels off from the glass plate. A further increase in the laser fluence occurs to the formation of a orifice in the film. The results obtained are of interest for improving the technology of laser bioprinting.

Modeling of Laser-Soft Tissue Interactions Using the Dual-Phase Lag Equation: Sensitivity Analysis with Respect to Selected Tissue Parameters

2017 ◽  
Vol 379 ◽  
pp. 108-123
Author(s):  
Ewa Majchrzak ◽  
Marek Jasiński ◽  
Łukasz Turchan
Keyword(s):  
Sensitivity Analysis ◽  
Soft Tissue ◽  
Laser Irradiation ◽  
Soft Tissues ◽  
Initial Conditions ◽  
Internal Heat ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Coupled Equations

Thermal processes occurring in soft tissues are subjected to laser irradiation are analyzed. The transient bioheat transfer is described by the generalized dual-phase lag model. This model consists of two coupled equations concerning the tissue and blood temperatures supplemented by the appropriate boundary and initial conditions. The efficiency of the internal heat source connected to the laser irradiation results from the solution of the diffusion equation. This approach is acceptable when the scattering dominates over the absorption for wavelengths between 650 and 1300 nm, and just such a situation occurs in the case of soft tissues. Sensitivity analysis with respect to the parameters occurring in the mathematical model is done using the direct approach (differentiation of the basic equations and the boundary-initial conditions with respect to the parameter considered), especially the absorption coefficient and scattering coefficient of the soft tissue are considered. At the stage of numerical modeling the basic problem and additional problems connected with the sensitivity functions are solved using the finite difference method. In the final part the conclusions and examples of computations are presented.

scholarly journals The elastic wave motions for a photothermal medium of a dual-phase-lag model with an internal heat source and gravitational field

2016 ◽  
Vol 94 (4) ◽  
pp. 400-409 ◽  
Author(s):  
Kh. Lotfy
Keyword(s):  
Heat Source ◽  
Thermal Loading ◽  
Harmonic Wave ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Transfer Model ◽  
Phase Lag ◽  
Dual Phase ◽  
Horizontal Distance ◽  
Lag Model

In this work, the dual-phase-lag (DPL) heat transfer model is introduced to study the problem of an isotropic generalized thermoelastic medium with an internal heat source that is moving with a constant speed. Thermal loading at the free surface of a semi-infinite semiconconducting medium coupled plasma waves with the effect of mechanical force during a photothermal process to study the effect of a gravity field. Harmonic wave analysis is used to obtain exact expressions for the considered variables, also the carrier density coefficients were obtained analytically. The variations of the considered variables through the horizontal distance are illustrated graphically under the effects of several parameters based on the DPL model. The results are discussed and depicted graphically.

Influence of the rotation on a generalized magneto-thermoelastic medium for three-phase-lag model

2015 ◽  
Vol 11 (2) ◽  
pp. 297-318 ◽  
Author(s):  
Samia M Said
Keyword(s):  
Magnetic Field ◽  
Heat Source ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Thermoelastic Problem ◽  
Phase Lag ◽  
Content Type ◽  
Three Phase ◽  
Lag Model ◽  
Generalized Thermoelastic

Purpose – The purpose of this paper is to investigate the effect of rotation and a magnetic field on the wave propagation in a generalized thermoelastic problem for a medium with an internal heat source that is moving with a constant speed. Design/methodology/approach – The formulation is applied to a generalized thermoelastic problem based on the three-phase-lag model and Green-Naghdi theory without energy dissipation. The medium is a homogeneous isotropic thermoelastic in the half-space. Findings – The exact expressions of the displacement components, temperature, and stress components are obtained by using normal mode analysis. Originality/value – Comparisons are made with the results predicted by the two models in the absence and presence of a magnetic field as well as a rotation. A comparison also is made with the results predicted by the two models for two different values of an internal heat source.

Thermal Evolution of Hot Spots in Thermally Nonlinear Carbon Graphite Sliders

1989 ◽  
Vol 111 (4) ◽  
pp. 591-596 ◽  
Author(s):  
Young Gill Yune ◽  
M. D. Bryant
Keyword(s):  
Heat Source ◽  
Fast Moving ◽  
Thermal Evolution ◽  
Hot Spot ◽  
Frictional Heating ◽  
Extreme Temperature ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Source Distribution ◽  
Graphite Block

Frictional heating of a thermal mound (or hot spot) present on the interface between a carbon graphite block sliding against a fast moving conductor is simulated. Heating of this mound due to frictional power dissipation is modeled as a collection of internal heat sources uniformly distributed within a very shallow volume (or layer) located directly beneath the sliding contact interface. The thermal mound, assumed to be motionless on and originating from the carbon graphite block, possesses the extreme temperature dependent thermal conductivity and heat capacity common to carbon graphite materials. Evolution of thermal mound temperatures from cold to hot is studied as a function of the intensity of the internal heat source distribution and the thickness of the heat source layer. For a fast moving conducting body sliding against the graphite block, it is shown that (a) an optimal heat source layer thickness exists, whereby temperatures maximize for this thickness and (b) for a sufficiently high heat source intensity, thermal instability of the mound is possible.

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