S-functions in mathematical modeling of high-speed thermal processes for doubly connected domains

Authors

  • Анатолій Павлович Слесаренко The A.N. Podgorny Institute for Mechanical Engineering Problems of the NAS of Ukraine. 2/10 Dm. Pozharsky St., Kharkiv, 61046, Ukraine, Ukraine
  • Юлія Олегівна Кобринович The A.N. Podgorny Institute for Mechanical Engineering Problems of the NAS of Ukraine. 2/10 Dm. Pozharsky St., Kharkiv, 61046, Ukraine, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.12369

Keywords:

S-functions, mathematical modeling, thermal processes, structural difference model

Abstract

The article presents the approximate continuously differentiable, analytical and regional analytical solutions of the thermal conduction problems for doubly connected domains with piecewise smooth boundary. The use of S-functions eliminated the singular features in the corner points of the boundary.

Based on solutions, using nine- and three-layer difference schemes with respect to time and coordinates, we have built the conservative structural difference mathematical models of the high-speed thermal processes for doubly-connected domains of complex shape. This permits for the first time in the world scientific practice to analyze qualitatively the fine structure of the dynamic processes, including the non-stationary thermal conduction without changing the algorithms for calculating the temperature fields of structural elements when changing the functional dependence in time of the heat exchange coefficient and the ambient temperature. The use of S-functions, in order to take into account the geometrical information in the solution structures of the unsteady thermal conduction problems permits to build the appropriate structures of solution and included to them basic functions by physically adequate fast thermal processes on the surface of the structural elements. The use of the interpolation formula in time for coefficients with the basic functions in the interpolation nodes permits to obtain the approximate analytical solutions of the high-speed thermal processes in analytical form with respect to coordinates and time under intense heat exchange on the surfaces of structural elements

Author Biographies

Анатолій Павлович Слесаренко, The A.N. Podgorny Institute for Mechanical Engineering Problems of the NAS of Ukraine. 2/10 Dm. Pozharsky St., Kharkiv, 61046, Ukraine

Doctor of physical-mathematical sciences, professor, leading researcher, laureate of State Prize of Ukraine.

Юлія Олегівна Кобринович, The A.N. Podgorny Institute for Mechanical Engineering Problems of the NAS of Ukraine. 2/10 Dm. Pozharsky St., Kharkiv, 61046, Ukraine

Post-graduate student

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Published

2013-04-25

How to Cite

Слесаренко, А. П., & Кобринович, Ю. О. (2013). S-functions in mathematical modeling of high-speed thermal processes for doubly connected domains. Eastern-European Journal of Enterprise Technologies, 2(4(62), 39–44. https://doi.org/10.15587/1729-4061.2013.12369

Issue

Vol. 2 No. 4(62) (2013): Mathematics and cybernetics - fundamental and applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2014 Анатолій Павлович Слесаренко, Юлія Олегівна Кобринович

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