Modelling of temperature field with physical characteristics dependence on temperature

Authors

  • Ірина Юріївна Михайлова National Technical University of Ukraine "Kyiv Polytechnic Institute" 6, Polytechnichna st., Kyiv, 03056, Ukraine

DOI:

https://doi.org/10.15587/2312-8372.2013.18218

Keywords:

three-dimensional unsteady nonlinear heat conduction equation, coordinate-wise splitting method

Abstract

The model of a metal plate heating by laser beam, taking into account the dependence of density, heat capacity and heat conduction of material on the temperature, is considered in the paper. For describing the temperature distribution, three-dimensional nonlinear unsteady heat conduction equation is used. For its solution the coordinate wise splitting method was used, which reduces the three dimensional problem to a sequence of one-dimensional. At each time step, a system of nonlinear algebraic equations is formed, for its solving the Newton’s method was used. The system of linear algebraic equations with a tridiagonal matrix is formed at each iтteraсtion. For reducing the dimensionality of generating systems, the method for constructing adaptive difference grids was used, in which nodes are concentrated in the areas of large solution gradients. The model can be applied to compare the results obtained with regard to the dependence of physical characteristics of material on the temperature and without it.

Author Biography

Ірина Юріївна Михайлова, National Technical University of Ukraine "Kyiv Polytechnic Institute" 6, Polytechnichna st., Kyiv, 03056

Post-graduate student of APPSD sub-Department

References

  1. Лазерні технології та комп’ютерне моделювання [Текст]: монографія / за ред. Л. Ф. Головка, С. О. Лук’яненка. – К. : Вістка, 2009. – 296 с.
  2. Головко, Л. Ф. Моделирование процесса бесконтактной лазерной деформации адаптивным методом [Текст] / Л. Ф. Головко, С. О. Лукьяненко, И. Ю. Михайлова, В. А. Третяк // Электронное моделирование. – 2011. – Вып. 3, Том 33. – С. 71-84.
  3. Михайлова, І. Ю. Моделювання двопроменевої лазерної деформації [Текст] / І. Ю. Михайлова // Східно-Європейський журнал передових технологій. – 2013 – №1/7 (61). – С. 33-38. Режим доступу : URL : http://journals.uran.ua/eejet/article/view/9322
  4. Shi, Y. Temperature gradient mechanism in laser forming of thin plates [Text] / Y. Shi, H. Shen, Z. Yao, J. Hu // Optics & Laser Technology. – 2007. – Vol. 39(4). – P. 858-863.
  5. Jin, Y. Research on the Mechanisms of Laser Forming for the Micro-Structural Element [Text] / Y. Jin, J. H. Wu, Y. J. Shi, H. Shen, Z. Q. Yao // Materials Science Forum. – 2008. – Vol. 575-578. – P. 1145-1150.
  6. Hu, Z. Experimental and numerical modeling of buckling instability of laser sheet forming [Text] / Z. Hu // International Journal of Machine Tools and Manufacture. – 2002. – Vol. 42(13). – P. 1427-1439.
  7. Shi, Y. Research on the mechanisms of laser forming for the metal plate [Text]/ Y. Shi, Z. Yaoa, H. Shena, J. Hua // International Journal of Machine Tools and Manufacture. – 2006. – Iss. 12-13. – P. 1689-1697.
  8. Liu, F. R. Finite element modeling of laser forming of aluminum matrix composites [Text]/ F.R. Liu, K.C. Chan, C.Y. Tang // Journal of Laser Applications. – 2006. – Iss. 18(1). – P. 56.
  9. Тихонов, А. Н. Уравнения математической физики [Текст] / А. Н. Тихонов, А. А. Самарский. – 5-е изд. – M.: Наука, 1977. – 735 с.
  10. Лук’яненко, С. О. Адаптивні обчислювальні методи моделювання об’єктів з розподіленими параметрами [Текст] / С. О. Лук’яненко. – К.: ІВЦ «Політехніка», 2004. – 236 с.
  11. Golovko, L. F., Lukyanenko, S. O. (2009). Laser technologies and computer modeling. Kiev. Ukraine: Vistka, 296.
  12. Golovko, L. F., Lukyanenko, S. O., Mykhailova, I. Yu., Tretyak, V. A. (2011). Modeling of the process of contactless laser deformation using adaptive method. Electronic modeling, 3, 71-84.
  13. Mykhailova, I. Yu. (2013). Dual laser deformation modeling. Eastern-European Journal of Enterprise Technologies, 61, 33-38.
  14. Shi, Y., Shen, H., Yao, Z., Hu, J. (2007). Temperature gradient mechanism in laser forming of thin plates. Optics and Laser Technology, 39, 858-863.
  15. Jin, Y., Wu, J. H., Shi, Y. J., Shen, H., Yao, Z. Q. (2008). Research on the Mechanisms of Laser Forming for the Micro-Structural Element. Materials Science Forum, 575-578, 1145-1150.
  16. Hu, Z. (2002). Experimental and numerical modeling of buckling instability of laser sheet forming. International Journal of Machine Tools and Manufacture, 42, 1427-1439.
  17. Shi, Y., Yaoa, Z., Shena, H., Hua, J. (2006). Research on the mechanisms of laser forming for the metal plate. International Journal of Machine Tools and Manufacture, 12-13, 1689-1697.
  18. Liu, F. R., Chan, K. C., Tang, C. Y. (2006). Finite element modeling of laser forming of aluminum matrix composites. Journal of Laser Applications, 18, 56.
  19. Tihonov, A. N., Samarskii, A. A. (1977). Mathematical physics equations. Ed. 5. Moscow. USSR: Nauka, 735.
  20. Lukyanenko, S. O. (2004). Adaptive computational methods of modeling objects with distributed parameters. Kiev. Ukraine: Politehnika, 236.

Downloads

Published

2013-10-28

How to Cite

Михайлова, І. Ю. (2013). Modelling of temperature field with physical characteristics dependence on temperature. Technology Audit and Production Reserves, 5(4(13), 12–15. https://doi.org/10.15587/2312-8372.2013.18218

Issue

Vol. 5 No. 4(13) (2013): MATERIALS OF SCIENTIFIC CONFERENCE. Mathematical modeling - applied aspects

Section

Mathematical Modeling - Applied Aspects

License

Copyright (c) 2016 Ірина Юріївна Михайлова

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.