Abstract
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.
Highlights
In this paper, the application of the dual-phase lag equation (DPLE—see: Section 2) [1,2,3,4] for numerical modeling of the problems related to the microscale heat transfer are discussed
The numerical solution of the second-order DPLE using the implicit scheme of the finite difference method (FDM) is reported by Chiriţă [8]
The solution obtained for the artificial mushy zone model corresponds to ∆T = 3 K, while the thermal conductivity and volumetric specific heat of this sub-domain are equal to the arithmetic means of the liquid and solid parameters
Summary
The application of the dual-phase lag equation (DPLE—see: Section 2) [1,2,3,4] for numerical modeling of the problems related to the microscale heat transfer are discussed. The analytical solution of the dual phase lag bio-heat transfer equation using the finite integral transform is reported by Kumar and Srivastava [17], while the analysis of thermal damage to the laser irradiated tissue is done by. Depending on the laser intensity and characteristic time of laser pulse in the considered domain, the heating and cooling processes are observed and the process of melting and resolidification can take place In such a case the basic algorithm should be supplemented with the procedures of phase transformations modeling.
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