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

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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
839—852
Opis fizyczny
Bibliogr. 30 poz., rys., tab.
Twórcy
  • Czestochowa University of Technology, Institute of Computer and Information Sciences, Częstochowa, Poland
Bibliografia
  • 1. Belkhayat-Piasecka A., Korczak A., 2016, Modeling of transient heat transport in metal films using the interval lattice Boltzmann method, Bulletin of the Polish Academy of Sciences – Technical Sciences, 64, 3, 599-505
  • 2. Cattaneo C., 1958, A form of heat conduction equation which eliminates the paradox of instantaneous propagation, Compte Rendus, 27, 431-433
  • 3. Chen G., Borca-Tasciuc D., Yang R.G., 2004, Nanoscale heat transfer, [In:] Encyclopedia of Nanoscience and Nanotechnology, Nalwa H.S. (Edit.), Vol. X, 1-30, http://www.aspbs.com/enn.html
  • 4. 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
  • 5. Chen W.H., Cheng H.C., Hsu Y.C., 2007, Mechanical properties of carbon nanotubes using molecular dynamics simulations with the inlayer van der Waals interactions, CMES: Computer Modeling in Engineering and Sciences, 20, 2, 123-145
  • 6. Ciesielski M., Duda M., Mochnacki B., 2016, Comparison of bio-heat transfer numerical models based on the Pennes and Cattaneo-Vernotte equations, Journal of Applied Mathematics and Computational Mechanics, 15, 4, 33-38
  • 7. Ciesielski M., Mochnacki B., 2014, Application of the control volume method using the Voronoi polygons for numerical modeling of bio-heat transfer processes, Journal of Theoretical and Applied Mechanics, 52, 4, 927-935
  • 8. Dai W., Nassar R., 2000, A domain decomposition method for solving three-dimensional heat transport equations in a double-layered thin film with microscale thickness. Numerical Heat Transfer, Part A, 38, 243-255
  • 9. Dziatkiewicz J., Kuś W., Majchrzak E., Burczyński T., Turchan L., 2014, Bioinspired identification of parameters in microscale heat transfer, International Journal for Multiscale Computational Engineering, 12, 1, 79-89
  • 10. Escobar R.A., Ghai S.S., Jhon M.S., Amon C.H., 2006, Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling, International Journal of Heat and Mass Transfer, 49, 97-107
  • 11. Kaba I.K., Dai W., 2005, A stable three-level finite difference scheme for solving the parabolic two-step model in a 3D micro-sphere heated by ultrashort-pulsed lasers, Journal of Computational and Applied Mathematics, 181, 125-147
  • 12. Lin Z., Zhigilei L.V., 2008, Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium, Physical Review, B, 77, 075133-1-075133-17
  • 13. Liu D.S., Tsai C.Y., 2009, Estimation of thermo-elasto-plastic properties of thin-film mechanical properties using MD nanoindentation simulations and an inverse FEM/ANN computational scheme, CMES: Computer Modeling in Engineering and Sciences, 39, 1, 29-47
  • 14. Majchrzak E., 2012, Parabolic and hyperbolic two-temperature models of microscopic heat transfer. Comparison of numerical solutions, Materials Science Forum, 706-709, 1454-1459
  • 15. Majchrzak E., Dziatkiewicz J., 2015, Analysis of ultashort laser pulse interactions with metal films using a two-temperature model, Journal of Applied Mathematics and Computational Mechanics, 14, 2, 31-39
  • 16. Majchrzak E., Mochnacki B., 2014, Sensitivity analysis of transient temperature field in microdomains with respect to the dual phase lag model parameters, International Journal for Multiscale Computational Engineering, 12, 1, 65-77
  • 17. Majchrzak E., Mochnacki B., Greer A.L., Suchy J.S., 2009a, Numerical modeling of short pulse laser interactions with multi-layered thin metal films, CMES: Computer Modeling in Engineering and Sciences, 41, 2, 131-146
  • 18. Majchrzak E., Mochnacki B., Suchy J.S., 2009b, Numerical simulation of thermal processes proceeding in a multi-layered film subjected to ultrafast laser heating, Journal of Theoretical and Applied Mechanics, 47, 2, 383-396
  • 19. Majchrzak E., Turchan L., 2016, Modeling of phase changes in the metal micro-domains subjected to ultrafast laser heating using dual-phase lag equation, Materialwissenschaft und Werkstofftechnik, 47, 5/6, 409-418
  • 20. Mitra K., Kumar S., Vedavarz A., Moallemi M.K., 1995, Experimental evidence of hyperbolic heat conduction in processed meat, ASME Journal of Heat Transfer, 17, 568-573
  • 21. Mochnacki B., Ciesielski M., 2012, Numerical model of thermal processes in domain of thin film subjected to a cyclic external heat flux, Materials Science Forum, 706-709, 1460-1465
  • 22. 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
  • 23. Mochnacki B., Paruch M., 2013, Estimation of relaxation and thermalization times in microscale heat transfer, Journal of Theoretical and Applied Mechanics, 51, 4, 837-845
  • 24. Orlande H.R.B., Ozis¸ik M.N., Tzou D.Y., 1995, Inverse analysis for estimating the electronphonon coupling factor in thin metal films, Journal of Applied Physics, 78, 3, 1843-1849
  • 25. Smith A.N., Norris P.M., 2003, Microscale Heat Transfer, Chapter 18 in: Heat Transfer Handbook, John Wiley & Sons
  • 26. 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
  • 27. Theodosiou T.C., Saravanos D.A., 2007, Molecular mechanics based finite element for carbon nanotube modeling, CMES: Computer Modeling in Engineering and Sciences, 19, 121-134
  • 28. Tian W., Yang R., 2008, Phonon transport and thermal conductivity percolation in random nanoparticle composites, CMES: Computer Modeling in Engineering and Sciences, 24, 123-142
  • 29. Tzou D.Y., 2015, Macro- to Microscale Heat Transfer: The Lagging Behavior, John Wiley & Sons, Ltd.
  • 30. Zhang Z.M., 2007, Nano/microscale Heat Transfer, McGraw-Hill, New York
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b5f275e8-c837-4b23-9f62-1d05332d1982
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