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Reconstruction of the heat transfer coefficient on the grounds of experimental data

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Wybrane pełne teksty z tego czasopisma
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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 the solid and liquid phases is described by the heat conduction equation with initial and boundary conditions. The inverse Stefan problem can be applied to solve design problems in 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 experimental data. Findings: The verification of the method of reconstructing the cooling conditions during the solidification of pure metals. The solution of the problem consists of selecting the heat transfer coefficient on the boundary, so that the temperature in selected points on the boundary of the domain assumes 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, that the sought boundary condition should be linearly dependent on those parameters. Practical implications: The presented method can be easy applied 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: Verification, on the grounds of experimental data, the formerly devised method of determining the heat transfer coefficient during the solidification of pure metals.
Rocznik
Strony
63--70
Opis fizyczny
Bibliogr. 38 poz., rys., tabl.
Twórcy
autor
  • Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland, damian.slota@polsl.pl
Bibliografia
  • [1] K. Okamoto, B. Q. Li, A regularization method for the inverse design of solidification processes with natural convection, International Journal Heat and Mass Transfer 50 (2007) 4409-4423.
  • [2] C. A. Santos, A. Garcia, C. R. Frick, J. A. Spim, Evaluation of heat transfer coefficient along the secondary cooling zones in the continuous casting of steel billets, Inverse Problems in Science and Engineering 14 (2006) 687-700.
  • [3] N. L. Goldman, Inverse Stefan Problem, Kluwer, Dordrecht, 1997.
  • [4] L. Xiyuan, Determination of the unknown boundary conditions in a two-phase Stefan problem, Journal of Partial Differential Equations 8 (1995) 249-260.
  • [5] D. A. Murio, Solution of inverse heat conduction problems with phase changes by the mollification method, Computers and Mathematics with Applications 24 (1992) 45-57.
  • [6] D. A. Murio, The Mollification Method and the Numerical Solution of Ill-Posed Problems, Wiley-Interscience, New York, 1993.
  • [7] N. Zabaras, Inverse finite element techniques for the analysis of soldification processes, International Journal for Numerical Methods in Engineering 29 (1990) 1569-1587.
  • [8] N. Zabaras, S. Kang, On the solution of an ill-posed design solidification problem using minimization techniques in finite- and infinite-dimensional function space, International Journal for Numerical Methods in Engineering 36 (1993) 3973-3990.
  • [9] N. Zabaras, Y. Ruan, O. Richmond, Design of two-dimensional Stefan processes with desired freezing front motions, Numerical Heat Transfer Part B 21 (1992) 307-325.
  • [10] N. Zabaras, T. H. Nguyen, Control of the freezing interface morphology in solidification processes in the presence of natural convection, International Journal for Numerical Methods in Engineering 38 (1995) 1555-1578.
  • [11] G. Z. Yang, N. Zabaras, An adjoint method for the inverse design of solidification processes with natural convection, International Journal for Numerical Methods in Engineering 42 (1998) 1121-1144.
  • [12] V. R. Voller, Control of the solidification and melting of metals using inverse methods, Proceedings of the 5th International Conference “Modelling of Casting and Welding Processes”, M. Rappaz, M. R. Ozgu, K. W. Mahin, eds., The Minerals, Metals & Materials Society Publ., Warrendale, 1991, 515-522.
  • [13] N. Zabaras, G. Z. Yang, A functional optimization formulation and implementation of the inverse natural convection problem, Computer Methods in Applied Mechanics and Engineering 144 (1997) 245-274.
  • [14] N. Zabaras, G. Z. Yang, Inverse design of solidification processes with desired freezing front motions and heat fluxes, in: Inverse Problems in Engineering: Theory/Practice - 1998, ASME, Fairfield, 1998, 549-553.
  • [15] H.-S. Ren, Application of the heat-balance integral to an inverse Stefan problem, International Journal of Thermal Sciences 46 (2007) 118-127.
  • [16] R. Grzymkowski, D. Słota, One-phase inverse Stefan problems solved by Adomian decomposition method, Computers and Mathematics with Applications 51 (2006) 33-40.
  • [17] D. Słota, Direct and inverse one-phase Stefan problem solved by variational iteration method, Computers and Mathematics with Applications 54 (2007) 1139-1146.
  • [18] R. Grzymkowski, D. Słota, Numerical calculations of the heat-transfer coefficient during solidification of alloys, Moving Boundaries VI, Wit Press, Southampton, 2001, 41-50.
  • [19] R. Grzymkowski, D. Słota, Multi-phase inverse Stefan problems solved by approximation method, Lecture Notes in Computer Science 2328 (2002) 679-686.
  • [20] R. Grzymkowski, D. Słota, Numerical method for multi-phase inverse Stefan design problems, Archives of Metallurgy and Materials 51 (2006) 161-172.
  • [21] A. Imani, A. A. Ranjbar, M. Esmkhani, Simultaneous estimation of temperature-dependent thermal conductivity and heat capacity based on modified genetic algorithm, Inverse Problems in Science and Engineering 14 (2006) 767-783.
  • [22] D. Słota, Three-phase inverse design Stefan problem, Lecture Notes in Computer Science 4487 (2007) 184-191.
  • [23] D. Słota, Solving the inverse Stefan design problem using genetic algorithms, Inverse Problems in Science and Engineering 16 (2008) 829-846.
  • [24] 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.
  • [25] D. Słota, Identification of the cooling condition in 2-D and 3-D continuous casting processes, Numerical Heat Transfer B 55 (2009) 155-176.
  • [26] L. A. Dobrzański, R. Maniara, J. Sokołowski, W. Kasprzak, Applications of artificial intelligence methods for modelling of solidus temperature for hypoeutectic Al-Si-Cu alloys, International Journal of Computational Materials Science and Surface Engineering 1 (2007) 214-255.
  • [27] M. Sundar, A. K. Nath, D. K. Bandyopadhyay, S. P. Chaudhuri, P. K. Dey, D. Misra, Numerical simulation of melting and solidification in laser welding of mild steel, International Journal of Computational Materials Science and Surface Engineering 1 (2007) 717-733.
  • [28] M. R. Amin, A. Mahajan, Modeling of turbulent heat transfer during the solidification process of continuous castings, Journal of Materials Processing Technology 174 (2006) 155-166.
  • [29] Cz. Baron, D. Bartocha, J. Gawroński, Thermal simulation of formation composite layer on model casting process, International Journal of Computational Materials Science and Surface Engineering 1 (2007) 163-180.
  • [30] A. Farzadi, S. Serajzadeh, A. H. Kokabi, Modelling of transport phenomena in gas tungsten arc welding, Archives of Materials Science and Engineering 28/7 (2007) 417-420.
  • [31] E. Majchrzak, M. Dziewoński, G. Kałuża, Identification of cast steel latent heat by means of gradient method, International Journal of Computational Materials Science and Surface Engineering 1 (2007) 555-570.
  • [32] Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1996.
  • [33] A. Osyczka, Evolutionary Algorithms for Single and Multicriteria Design Optimization, Physica-Verlag, Heidelberg, 2002.
  • [34] E. Majchrzak, B. Mochnacki, Application of the BEM in the thermal theory of foundry, Engineering Analysis with Boundary Elements 16 (1995) 99-121.
  • [35] L. A. Dobrzański, R. Maniara, J. H. Sokolowski, The effect of cast Al-Si-Cu alloy solidification rate on alloy thermal characteristics, Journal of Achievements in Materials and Manufacturing Engineering 17 (2006) 217-220.
  • [36] L. A. Dobrzański, R. Maniara, J. H. Sokolowski, W. Kasprzak, Effect of cooling rate on the solidification behaviour of AC AlSi7Cu2 alloy, International Journal of Materials and Product Technology 191 (2007) 317-320.
  • [37] L. A. Dobrzański, W. Kasprzak, M. Kasprzak, J. H. Sokolowski, A novel approach to the design and optimization of aluminum cast component heat treatment processes using advanced UMSA physical simulations, Journal of Achievements in Materials and Manufacturing Engineering 24/2 (2007) 139-142.
  • [38] M. Kasprzak, J. H. Sokolowski, W. T. Kierkus, W. Kasprzak, Method and apparatus for universal metallurgical simulation and analysis, US Patent, No. 7,354,491 B2, 2008.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BOS2-0020-0038
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