Identification of the heat transfer coefficient in phase change problems

• Autorzy: Słota D.
• Języki publikacji: EN

Abstrakty

EN

In this paper, an algorithm will be presented that enables solving the two-phase inverse Stefan problem, where the additional information consists of temperature measurements in selected points of the solid phase. The problem consists in the reconstruction of the function describing the heat transfer coefficient, so that the temperature in the given points of the solid phase would differ as little as possible from the predefined values. The featured examples of calculations show a very good approximation of the exact solution and stability of the algorithm.

Słowa kluczowe

EN

Inverse Stefan problem; solidification

PL

krzepnięcie; odwrotne zagadnienie Stefana

• Wydawca: Wydawnictwo Instytutu Maszyn Przepływowych PAN ; Komitet Termodynamiki i Spalania PAN
• Czasopismo: Archives of Thermodynamics
• Rocznik: 2010
• Tom: Vol. 31, no. 1
• Strony: 61--78
• Opis fizyczny: Bibliogr. 31 poz.,Rys., tab., wykr., wz.

Twórcy

autor

Słota D.

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

Bibliografia

• [1] ANG D.D., DINH A.P.N., THANH D.N.: Regularization of an inverse two-phase Stefan problem, Nonlinear Anal. 34 (1998), 719-731.
• [2] GRZYMKOWSKI R., SŁOTA D.: Numerical method for multi-phase inverse Stefan design problems, Arch. Metall. Mater. 51 (2006), 161-172.
• [3] GRZYMKOWSKI R., SŁOTA D.: One-phase inverse Stefan problems solved by Adomian decomposition method, Comput. Math. Appl. 51 (2006), 33-40.
• [4] LIU J., GUERRIER B.: A comparative study of domain embedding methods for regularized solutions of inverse Stefan problems, Int. J. Numer. Methods Engrg. 40 (1997), 3579-3600.
• [5] REN H.-S.: Application of the heat-balance integral to an inverse Stefan problem, Int. J. Therm. Sci. 46 (2007), 118-127.
• [6] SŁOTA D.: Direct and inverse one-phase Stefan problem solved by variational iteration method, Comput. Math. Appl. 54 (2007), 1139-1146.
• [7] ZABARAS N.: Inverse finite element techniques for the analysis of soldification processes, Int. J. Numer. Methods Engrg. 29 (1990), 1569-1587.
• [8] ZABARAS N., KANG S.: On the solution of an ill-posed design solidification problem using minimization techniques in finite- and infinite-dimensional function space, Int. J. Numer. Methods Engrg. 36 (1993), 3973-3990.
• [9] GRZYMKOWSKI R., SŁOTA D.: Multi-phase inverse Stefan problems solved by approximation method. In: Parallel Processing and Applied Mathematics, R. Wyrzykowski, J. Dongarra, M. Paprzycki, J. Waśniewski, (eds.), LNCS, 2328, Springer, Berlin 2002, 679-686.
• [10] BUNDAY B.D.: Basic Optimisation Method, Edward Arnolds Publ., London 1984.
• [11] NELDER J. A., MEAD R.: A simplex method for function minimization, The Comp. Journal 7 (1965), 308-313.
• [12] CHAMBERS L.: The Practical Handbook of Genetic Algorithms, Applications, Chapman & Hall/CRC, Boca Raton 2001.
• [13] MICHALEWICZ Z.: Genetic Algorithms + Data Structures = Evolution Programs, Springer, Berlin 1996.
• [14] OSYCZKA A.: Evolutionary Algorithms for Single and Multicriteria Design Optimization, Physica-Verlag, Heidelberg 2002.
• [15] BURCZYŃSKI T., DŁUGOSZ A.: Evolutionary optimization in thermoelastic problems using the boundary element method, Comput. Mech. 28 (2002), 317-324.
• [16] DIVO E., KASSAB A., RODRIGUEZ F.: Characterization of space dependent thermal conductivity with a BEM-based genetic algorithm, Numer. Heat Transf. A 37 (2000), 845-875.
• [17] KARR CH.L., YAKUSHIN I., NICOLOSI K.: Solving inverse initial-value, boundary-value problems via genetic algorithm, Eng. Appl. Artif. Intel. 13 (2000), 625-633.
• [18] MERA N.S., ELLIOTT L., INGHAM D.B.: A multi-population genetic algorithm approach for solving ill-posed problems, Comput. Mech. 33 (2004), 254-262.
• [19] WROBEL L.C., MILTIADOU P.: Genetic algorithms for inverse cathodic protection problems, Eng. Anal. Bound. Elem. 28 (2004), 267-277.
• [20] SŁOTA D.: Using genetic algorithms for the determination of an heat transfer coefficient in three-phase inverse Stefan problem, Int. Comm. Heat & Mass Transf. 35 (2008), 149-156.
• [21] SŁOTA D.: Solving the inverse Stefan design problem using genetic algorithms, Inverse Probl. Sci. Eng. 16 (2008), 829-846.
• [22] MAJCHRZAK E., MOCHNACKI B.: Application of the BEM in the thermal theory of foundry, Eng. Anal. Bound. Elem. 16 (1995), 99-121.
• [23] ROGERS J.C.W., BERGER A.E., CIMENT M.: The alternating phase truncation method for numerical solution of a Stefan problem, SIAM J. Numer. Anal. 16 (1979), 563-587.
• [24] BECK J.V., BLACKWELL B., CLAIR C.R.ST.: Inverse Heat Conduction. Ill Posed Problems, Wiley Interscience, New York 1985.
• [25] KURPISZ K., NOWAK A. J.: Inverse Thermal Problems, Computational Mech. Publ., Southampton 1995.
• [26] TIKHONOV A.N., ARSENIN V.Y.: Solution of Ill-Posed Problems, Wiley & Sons, New York 1977.
• [27] LAIT E.: Mathematical modeling of heat flow in the continuous casting of steel, Ironmaking and Stellmaking 44 (1973), 589-594.
• [28] MOCHNACKI B, SUCHY J.S.: Numerical Methods in Computations of Foundry Processes, PFTA, Krakow 1995.
• [29] SLOTA D.: Influence of choice of the crossover operator on the solution of an inverse Stefan problem by genetic algorithms. In: Artificial Intelligence and Soft Computing, A. Cader, L. Rutkowski, R. Tadeusiewicz, J. Zurada (eds.), EXIT, Warszawa 2006, 217-223.
• [30] SŁOTA D.: Influence of the mutation operator on the solution of an inverse Stefan problem by genetic algorithms, w: Computational Science - ICCS 2006, part I, V.N. Alexandrov, G. D. van Albada, P.M.A. Sloot, J. Dongarra (eds.), LNCS, 3991, Springer, Berlin 2006, 786-789.
• [31] SŁOTA D.: Influence of the selection method on the solution of an inverse Stefan problem using genetic algorithms. In: Proc. of the 10th IASTED Int. Conf. on Artifical Intelligence and Soft Computing, A.P. del Pobil (ed.), ACTA Press, Anaheim 2006, 285-290.