Determination of the boundary conditions in two-dimensional solidification of pure metals

• Autorzy: Słota D.
• Języki publikacji: EN

Abstrakty

EN

Purpose: Solidification of pure metal can be modelled by a two-phase Stefan problem, in which the distribution of temperature in solid and liquid phases is described by a heat conduction equation with initial and boundary conditions. The inverse Stefan problem can be applied to solve design problems in continuous casting process. Design/methodology/approach: In numerical calculations the alternating phase truncation method, the Tikhonov regularization and the genetic algorithm were used. The featured examples of calculations show a very good approximation of the exact solution and the stability of the procedure. Findings: The paper presents the determination method of cooling conditions in two-dimensional solidification of pure metals. The solution of the problem consisted of selecting a heat transfer coefficient on boundary, so that the temperature in selected points of the boundary of the domain would assumed the given values. Research limitations/implications: The method requires that it must be possible to describe the sought boundary condition by means of a finite number of parameters. It is not necessary, however, that the sought boundary condition should be linearly dependent on those parameters. Practical implications: The presented method can be applied without any problem to solve design problems of different types, e. g. for the design of continuous casting installations (incl. the selection of the length of secondary cooling zones, the number of jets installed in individual zones, etc.). Originality/value: The paper presents the new method of selection of the heat transfer coefficient in two-dimensional inverse Stefan problem, so that the temperature in selected points of the boundary of the domain would assumed the given values.

Słowa kluczowe

EN

artificial intelligence methods; solidification; inverse Stefan problems

PL

sztuczna inteligencja; krzepnięcie

• Wydawca: International OCSCO World Press
• Czasopismo: Journal of Achievements in Materials and Manufacturing Engineering
• Rocznik: 2008
• Tom: Vol. 28, nr 1
• Strony: 59--62
• Opis fizyczny: Bibliogr. 15 poz., tab.

Twórcy

autor

Słota D.

• Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland,

Bibliografia

• [1] P. Jochum, The numerical solution of the inverse Stefan problem, Numerische Mathematik 34 (1980) 411-429.
• [2] J. Liu, B. Guerrier, A comparative study of domain embedding methods for regularized solutions of inverse Stefan problems, International Journal for Numerical Methods in Engineering 40 (1997) 3579-3600.
• [3] R. Grzymkowski, D. Słota, One-phase inverse Stefan problems solved by Adomian decomposition method, Computers and Mathematics with Applications 51 (2006) 33-40.
• [4] D. Colton, The inverse Stefan problem for the heat equation in two space variables, Mathematika 21 (1074) 282-286.
• [5] N. Zabaras, Y. Ruan, O. Richmond, Design of two-dimensional Stefan processes with desired freezing front motions, Numerical Heat Transfer B 21 (1992) 307-325.
• [6] N. Zabaras, K. Yuan, Dynamic programming approach to the inverse Stefan design problem, Numerical Heat Transfer B 26 (1994) 97-104.
• [7] S. Kang, N. Zabaras, Control of freezing interface motion in two-dimensional solidification processes using the adjoint method, International Journal for Numerical Methods in Engineering 38 (1995) 63-80.
• [8] R. Grzymkowski, D. Słota, Optimization method for one-and two-dimensional inverse Stefan problems, Proceedings of the 3rd International Conference on Inverse Problems in Engineering, New York, 1999, EXP06 1-11.
• [9] R. Grzymkowski, D. Słota, Approximation method for inverse Stefan problems, Proceedings of the 16th IMACS World Congress, Lausanne, 2000, 1-4.
• [10] A. Osyczka, Evolutionary Algorithms for Single and Multicriteria Design Optimization, Physica-Verlag, Heidelberg, 2002.
• [11] Z. Michalewicz, Genetic Algorithms+Data Structures=Evolution Programs, Springer-Verlag, Berlin, 1996.
• [12] D. Słota, Solving the inverse Stefan design problem using genetic algorithms, Inverse Problems in Science and Engineering, (in print).
• [13] D. Słota, Using genetic algorithms for the determination of an heat transfer coefficient in three-phase inverse Stefan problem, International Communications in Heat and Mass Transfer 35 (2008) 149-156.
• [14] E. Majchrzak, B. Mochnacki, Application of the BEM in the thermal theory of foundry, Engineering Analysis with Boundary Elements 16 (1995) 99-121.
• [15] K. Kurpisz, A. J. Nowak, Inverse Thermal Problems, Computational Mechanics Publications, Southampton, 1995.