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EXPERIMENTAL VERIFICATION OF APPROXIMATE SOLUTION OF THE INVERSE STEFAN PROBLEM OBTAINED BY APPLYING THE INVASIVE WEED OPTIMIZATION ALGORITHM

ABSTRACT
The paper proposes a procedure for solving the inverse Stefan problem consisted in reconstruction of the function describing the heat transfer coefficient on the basis of temperature measurements. Elaborated method is based on two procedures: solution of the appropriate direct Stefan problem by using the finite difference method combined with the alternating phase truncation method and minimization of some functional with the aid of invasive weed optimization algorithm. For verifying the effectiveness of investigated algorithm the experimental data obtained in the solidification of aluminum are used.
KEYWORDS
PAPER SUBMITTED: 2014-10-10
PAPER REVISED: 2015-01-21
PAPER ACCEPTED: 2015-02-02
PUBLISHED ONLINE: 2015-08-02
DOI REFERENCE: https://doi.org/10.2298/TSCI15S1S05H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S205 - S212]
REFERENCES
  1. Gupta, S.C., The Classical Stefan Problem. Basic Concepts. Modelling and Analysis, Elsevier, Amsterdam, The Netherlands, 2003
  2. Beck, J. V., et al., Inverse Heat Conduction: Ill Posed Problems, Wiley Interscience, New York, USA, 1985
  3. Nowak, I., et al., Identification of Phase Change Fronts by Bezier Spline and BEM, Int. J. Therm. Sci., 41 (2002), 6, pp. 492-499
  4. Ren, H.-S., Application of the Heat-Balance Integral to an Inverse Stefan Problem, Int. J. Therm. Sci., 46 (2007), 2, pp. 118-127
  5. Slota, D., Solving the Inverse Stefan Design Problem Using Genetic Algorithm, Inverse Probl. Sci. En., 16 (2008), 7, pp. 829-846
  6. Liu, C.-S., Solving Two Typical Inverse Stefan Problems by Using the Lie-Group Shooting Method, Int. J. Heat Mass Tran., 54 (2011), 9-10, pp. 1941-1949
  7. Slota, D., Restoring Boundary Conditions in the Solidification of Pure Metals, Comput. Struct., 89 (2011), 1-2, pp. 48-54
  8. Johansson, B., et al., A Meshless Method for an Inverse Two-Phase One-Dimensional Linear Stefan Problem, Inverse Probl. Sci. En., 21 (2013), 1, pp. 17-33
  9. Grzymkowski, R., et al., A Certain Analytical Method Used for Solving the Stefan Problem, Thermal Science, 17 (2013), 3, pp. 635-642
  10. Wituła, R., et al., Solution of the Two-Phase Stefan Problem by Using the Picard's Iterative Method, Thermal Science, 15 (2011), Suppl. 1, pp. S21-S26
  11. Hetmaniok, E., et al., Identification of the Heat Transfer Coefficient in the Inverse Stefan Problem by Using the ABC Algorithm, Arch. Foundry Eng., 12 (2012), Special issue 2, pp. 27-32
  12. Grzymkowski, R., et al., Application of the Ant Colony Optimization Algorithm in Solving the Inverse Stefan Problem, Steel Res. Int., Special edition: Metal Forming, 2012, pp. 1287-1290
  13. Hetmaniok, E., et al., Experimental Verification of Immune Recruitment Mechanism and Clonal Selection Algorithm Applied for Solving the Inverse Problems of Pure Metal Solidification, Int. Commun. Heat Mass, 47 (2013), 1, pp. 7-14
  14. Mehrabian, A. R., Lucas, C., A Novel Numerical Optimization Algorithm Inspired from Weed Colonization, Ecol. Inform., 1 (2006), 4, pp. 355-366
  15. Nikoofard, A. H., et al., Multiobjective Invasive Weed Optimization: Application to Analysis of Pareto Improvement Models in Electricity Markets, Appl. Soft Comp., 12 (2012), 1, pp. 100-112
  16. Mallahzadeh, A. R., et al., Application of the Invasive Weed Optimization Technique for Antenna Configurations, Pr. Electrom. Res., 79 (2008), 1, pp. 137-150
  17. Rogers, J. C. W., et al., The Alternating Phase Truncation Method for Numerical Solution of a Stefan Problem, SIAM J. Numer. Anal., 16 (1979), 4, pp. 563-587
  18. Hetmaniok, E., Invasive Weed Optimization Algorithm Applied for Solving the Inverse Stefan Problem, Hutnik, 81 (2014), 1, pp. 76-79
  19. Back, T., Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford University Press, Oxford, UK, 1996
  20. Dobrzanski, L. A., et al., A Novel Approach to the Design and Optimization of Aluminum Cast Component Heat Treatment Processes Using Advanced UMSA Physical Simulations, J. Achiev. Mater. Manuf. Eng., 24 (2007), 2, pp. 139-142
  21. Kasprzak, M., et al., Method and Apparatus for Universal Metallurgical Simulation and Analysis, US Patent No. US 7,354,491 B2, 2008
  22. Foley, J. D., et al., Computer Graphics - Principles and Practice, Addison-Wesley, San Diego, Cal., USA, 1990

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence