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

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## 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.

[1] Mochnacki, B. & Majchrzak, E. (2010). Numerical modeling of casting solidification using generalized finite difference method. Materials Science Forum. 638-642, 2676-2681.

[2] Mochnacki, B. (2012). Definition of alloy substitute thermal capacity using the simple macrosegregation models. Archives of Foundry Engineering. 19(4), 113-116.

[3] Mochnacki, B. (2011). Computational simulations and applications. Numerical modeling of solidification process (Chapter 24), Ed. Jianping Zhu, INTECH, 513-542.

[4] Majchrzak, E. & Mochnacki, B. (2016). Modeling of melting and resolidification in domain of metal film subjected to a laser pulse. Archives of Foundry Engineering. 16(1), 41-44.

[5] Szopa, R. (2015). Numerical modeling of pure metal solidification using the one domain approach. Journal of Applied Mathematics and Computational Mechanics. 14(3), 28-34.

[6] Bondarenko, V.I., Bilousov, V.V., Nedopekin, F.V. & Shalapko, J.I. (2015). The mathematical model of hydrodynamics and heat and mass transfer at formation of steel ingots and castings. Archives of Foundry Engineering. 15(1), 13-16.

[7] Ivanova, A.A. (2012). Calculation of phase change boundary position in continuous casting. Archives of Foundry Engineering. 13(4), 57-62.

[8] Mochnacki, B., Majchrzak, E. (2016). Chapter 86: Numerical modeling of biological tissue freezing process using the Dual-Phase-Lag Equation, Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, Proceedings of the 3rd Polish Congress of Mechanics (PCM) and 21st International Conference on Computer Methods in Mechanics (CMM), CRC Press, 413-418.

[9] Majchrzak, E. & Dziatkiewicz, J. (2012). Numerical modeling of melting process of thin metal film subjected to the short laser pulse. Archives of Foundry Engineering. 12(4), 105-108.

[10] Kumar, S. & Katiyar, V.K. (2010). Mathematical modeling of freezing and thawing process in tissues: a porous media approach. Int. J. Appl. Mechanics. 2(3), 617-633.

[11] Chen, J.K. & Beraun, J.E. (2001). Numerical study of ultrashort laser pulse interactions with metal films. Numerical Heat Transfer. Part A, 40, 1-20.

[12] Chen, G., Borca-Tascius, D. & Yang, R.G. (2004). Nanoscale heat Transfer, Encyclopedia of NanoScience & Nanotechnology. 7, 429-459.

[13] Zhang, Z.N. (2007). Nano/microscale heat transfer. McGraw-Hill, New York.

[14] Mochnacki, B. & Ciesielski, M. (2015). Micro-scale heat transfer. Algorithm basing on the Control Volume Method and the identification of relaxation and thermalization times using the search method. Computer Methods in Materials Science. 15(2), 353-361.

[15] Mochnacki, B. & Ciesielski, M. (2007). Application of Thiessen polygons in control volume model of solidification. Journal of Achievements of Materials and Manufacturing Engineering. 23(2), 75-78.

[16] Tang, D.W. & Araki, N. (1999). Wavy, wavelike, diffusive thermal responses of finite rigid slabs to high-speed heating of laser pulses. International Journal of Heat and Mass Transfer. 42, 855-860.

# Archives of Foundry Engineering

## The Journal of Polish Academy of Sciences

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CiteScore 2016: 0.42

SCImago Journal Rank (SJR) 2016: 0.192
Source Normalized Impact per Paper (SNIP) 2016: 0.316

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