Numerical model of thin metal film heating using the boundary element method
Ewa Majchrzak1
, Bohdan Mochnacki2
1Silesian University of Technology, Konarskiego 18a, 44-100 Gliwice.
2University of Occupational Safety Management, Bankowa 8, 40-007 Katowice.
DOI:
https://doi.org/10.7494/cmms.2017.1.0569
Abstract:
The subject of the paper is connected with the microscale heat transfer proceeding in the metal domain. In particular, the heating process of thin metal film subjected to an external heat flux is analysed. Thermal processes in the domain considered are described by the dual-phase lag equation (DPLE) supplemented by the appropriate boundary and initial conditions. At the stage of numerical modeling the variant of the boundary element method called the BEM using discretization in time is applied. So far, this method has not been used fo the hyperbolic equations describing the microscale heat transfer. In the final part the example of computations is shown.
Cite as:
Majchrzak, E., Mochnacki, B. (2017). Numerical model of thin metal film heating using the boundary element method. Computer Methods in Materials Science, 17(1), 12 – 17. https://doi.org/10.7494/cmms.2017.1.0569
Article (PDF):
Keywords:
Thin metal film heating, Dual-phase lag equation, The BEM using discretization in time, Numerical methods
References:
Al-Nimr, M.A., 1997, Heat transfer mechanisms during shortduration laser heating of thin metal films, Int. J. Termophys.,18, 5, 1257-1268.
Anisimov, S.I., Kapeliovich, T. L., Perelman, T. E., 1974, Zh.Exp. Teor. Fiz. 66, 776. Sov. Phys. JEEP, 39, 375.
Brebbia, C.A. Telles, J.C.F., Wrobel, L.C., 1984, Boundaryelements techniques, Springer-Verlag, Berlin.Cattaneo, M.C., 1958, A form of heat conduction equationwhich eliminates the paradox of instantaneous propagation,C.R. Acad. Sci. I – Math., 247, 431-433.
Chen, J.K., Beraun, J. E., 2001, Numerical study of ultrashortlaser pulse interactions with metal films, Numer. HeatTransfer. Part A, 40, 1-20.
Chen, G., Borca-Tasciuc , D., Yang, R.G., 2004, Nanoscale heatTransfer, Encyclopedia of NanoScience & Nanotechnology,7, ed. H.S.Nalwa, American Scienfic Publishers,29-459; http:/www.aspbs.com/enn.
Chou, Y., Yang, R.J., 2009, Two-dimensional dual-phase-lagthermal behavior in single-/multi-layer structures usingCESE method, Int. J. Heat Mass Trans., 52, 1-2, 239–249.
Curran, D.A.S., Cross, M., Levis, B.A., 1980, Solution of parabolicdifferential equations by the boundary elementmethod using discretization in time, Appl. Math. Model.4, 398-400.
Dai, W., Nassar, R., 2001, A compact finite difference schemefor solving a one-dimensional heat transport equation atthe microscale. J. Comput. Appl. Math., 132, 431-441.
Grigoropoulos, C.P., Chimmalgi, A., Hwang, D.J., 2007, Nanostructuringusing pulsed laser radiation, in: Laser Ablationand its Applications, Springer Series in Optical Sciences,129, 473-504.
Ho, J.R., Kuo, C.P., Jiaung, W. S., 2003, Study of heat transferin multilayered structure within the framework of dualphase-lag heat conduction model using lattice Boltzmannmethod, Int. J. Heat Mass Tran., 46, 1, 55–69.
Majchrzak, E., 2010, Numerical solution of dual phase lagmodel of bioheat transfer using the general boundary elementmethod, CMES : Comp. Model. Eng. Sci., 69, 1,43-60.
Majchrzak, E., Mochnacki, B., Suchy, J.S., 2009a, Finite differencemodel of short-pulse laser interactions with thinmetal film, Comput. Meth. Mater. Sci., 9, 2, 316-322.
Majchrzak, E., Mochnacki, B., 2014, Sensitivity analysis oftransient temperature field in microdomains with respectto the dual-phase-lag model parameters. Int. J. MultiscaleCom. 12, 1, 65-77.
Majchrzak, E., Mochnacki B., Suchy J.S. 2009b, Numericalsimulation of thermal processes proceeding in a multilayeredfilm subjected to ultrafast laser heating, J. Theor.Appl. Mech., 47, 2, 383-397.
Majchrzak E., Mochnacki, B., Greer, A.L., Suchy, J.S., 2009c,Numerical modeling of short pulse laser interactionswith multi-layered thin metal films, CMES: ComputerModel. Eng. Sci., 41, 2, 131-146.
Majchrzak, E., Turchan, L., 2015, The general boundary elementmethod for 3D dual-phase lag model of bioheat transfer,Eng. Anal. Bound. Elem., 50, 76-82.
Mochnacki, B., Paruch, M., 2013, Estimation of relaxation andthermalization times in microscale heat transfer model,J. Theor. Appl. Mech., 51, 4, 837-845.
Özișik, N., Tzou, D.Y., 1994, On the wave theory in heat conduction,J. Heat Transf., 116, 526-535.
Ramadan, K., Tyfour, W.R. Al-Nimr, M.A., 2009, On the analysisof short-pulse laser heating of metals using the dualphase lag heat conduction model, J. Heat Transf., 131,11, 111301.
Smith, A.N., Norris, P.M., 2003, Microscale heat transfer, Chapter18 in: Heat Transfer Handbook, John Willey&Sons,New York.
Szopa, R., 1999, Modeling of solidification using the combinedvariant of the BEM, Metallurgy 54, Publ. of Sil. Univ. ofTechn., Gliwice (in Polish).
Tamma, K.K., Zhou, X., 1998, Macroscale and microscalethermal transport and thermo-mechanical interactions:Some noteworthy perspectives, J. Therm. Stresses, 21,405-449.
Tang, D.W., Araki, N., 1999, Wavy, wavelike, diffusive thermalresponses of finite rigid slabs to high-speed heating oflaser-pulses, Int. J. Heat Mass Transfer, 42, 855-860.
Tzou, D.Y., 1997, Macro- to microscale heat transfer: the laggingbehavior, Taylor & Francis, Washington DC.Zhang, Z. N., 2007, Nano/microscale heat transfer, McGraw-Hill, New York.