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Numerical simulation of freezing process using the BEM

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Warianty tytułu
Konferencja
Polish Conference on Computer methods in mechanics ; (14 ; 26-28.05.1999 ; Rzeszów, Poland
Języki publikacji
EN
Abstrakty
EN
The boundary element method is applied for numerical simulation of the freezing process proceeding in biological tissue under the influence of cylindrical cryoprobe. From the mathematical point of view the problem discussed belongs to the group of moving boundaries ones for which the mushy zone sub-region (intermediate phase) is considered. In this paper the mathematical model of the process is formulated using the fixed domain approach and a parameter called the substitute thermal capacity determines the evolution of latent heat. On a stage of numerical computations the generalized variant of the alternating phase truncation method (APTM) is applied and the basic mathematical model is rebuilt by the introduction of the enthalpy function. The boundary element method together with APTM leads to the simple and effective numerical algorithm because the difficulties connected with the non-linear problem modelling can be omitted. In the final part of the paper the results of computations are shown.
Rocznik
Strony
667--676
Opis fizyczny
Bibliogr. 11 poz., rys., wykr.
Twórcy
autor
  • Silesian University of Technology [Politechnika Śląska], ul. Konarskiego 18a, 44-100 Gliwice, Poland
  • Silesian University of Technology [Politechnika Śląska], ul. Konarskiego 18a, 44-100 Gliwice, Poland
Bibliografia
  • [1] C. A. Brebbia, J. C. F. Telles, L. C. Wrobel. Boundary Element Techniques. Springer-Verlag, Berlin—New York, 1984.
  • [2] H. Budman, A. Shitzer, J. Dayan. Analysis of the inverse problem of freezing and thawing of a binary solution during cryosurgical processes. Journal of Biomechanical Engineering, 117: 193-202, 1995.
  • [3] G. Comini, L. Del Giudice. Thermal aspects of cryosurgery. Journal of Heat Transfer, Transactions of the ASME, 543-549, 1976.
  • [4] M. Dziewoński. Modelling of biological tissue freezing process. Doctoral thesis. Silesian University of Technology, Gliwice, 2000 (in print)
  • [5] S. R. Idelsohn, M. A. Storti, L. A. Crivelli. Numerical methods in phase change problems. Archives of Computational Methods in Engineering, 1: 49-74, 1994.
  • [6] E. Majchrzak, E. Ladyga. Numerical analysis of freezing of a binary solution during cryosurgical process using the boundary element method. In: R. Van Keer and C.A. Brebbia, eds., Moving Boundaries IV, Computational Modelling of Free and Moving Boundary Problems, 37-46, Computational Mechanics Publications, Southampton, Boston, 1997.
  • [7] E. Majchrzak, B. Mochnacki. The BEM application for numerical solution of non-steady and nonlinear thermal diffusion problems. Computer Assisted Mechanics and Engineering Sciences. 3: 327-346, 1996.
  • [8] B. Mochnacki, E. Majchrzak, A. Kapusta. Numerical model of heat transfer process in solidifying and cooling steel ingot. In: C. A. Brebbia et al., eds., Computational Modelling of Free and Moving Boundary Problems, 177-189, Computational Mechanics Publications, Walter de Gruyer, Southampton, 1991.
  • [9] B. Mochnacki, J. S. Suchy. Numerical Methods in Computations of Foundry Processes. PFTA, Cracow, 1995.
  • [10] J. Rogers, A. Berger, M. Ciment. The alternating phase truncation method for a Stefan problem. SIAM Journal of Numerical Analysis, 16: 562-587, 1979.
  • [11] J. Spanier, K. B. Oldham. An Atlas of Functions. Hemisphere Publishing Corporation, Springer-Verlag, 1987.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0005-0042
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