Macro and Macro/Micro Models of Solidification - Numerical Aspects of Process Simulation


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The solidification models basing on the Fourier equation with the additional term controlling the kinetics of phase transition are discussed. The different approaches to this term definition lead to the different solidification models, in particular the macro and the macro/micro ones can be taken into account. In the case of macro description the equation in which the parameter called a substitute thermal capacity is considered, while in the case of macro/micro approach the linear or exponential models of crystallization can be introduced. The solution of the problem can be found using the numerical methods. In this paper the boundary element method using discretization in time is applied, the examples of numerical simulations are also shown.



Materials Science Forum (Volumes 539-543)

Main Theme:

Edited by:

T. Chandra, K. Tsuzaki, M. Militzer , C. Ravindran




R. Szopa "Macro and Macro/Micro Models of Solidification - Numerical Aspects of Process Simulation", Materials Science Forum, Vols. 539-543, pp. 2564-2569, 2007

Online since:

March 2007





[1] B. Mochnacki and J.S. Suchy: Numerical methods in computations of foundry processes (Polish Foundrymen's Technical Association, Cracow 1995).

[2] E. Majchrzak and B. Mochnacki: Engineering Anal. with Boundary Elements, 16, (1995) p.5.

[3] B. Mochnacki and R. Szopa: Journal of Theoretical and Applied Mechanics, 2, 36, (1998) p.469.

[4] R. Szopa: Modelling od Solidification and Crystallization using the Combined Variant of the BEM (Publ. of the Sil. Univ. of Techn., Metallurgy, 54, Gliwice, 1999).

[5] E. Majchrzak: Engineering Analysis with Boundary Elements, 1, (1993) p.95.

[6] E. Fraś, W. Kapturkiewicz and H.F. Lopez: AFS Transactions, 92-48, (1993) p.583.

[7] W. Kapturkiewicz: Modelling of Cast Iron Crystallization, (AKAPIT, Cracow, 2003).

[8] S. Chang, D.M. Stefanescu, D. Shangguan: Metallurgical Transactions A, 23A (1992) p.1333. Acknowledgement This research is a part of the Project No 3 T08B 004 28 sponsored by KBN.

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