Mathematical modeling of high-temperature nonlinear processes of heat transfer

Authors

  • Анатолий Павлович Слесаренко Institute of Mechanical Engineering Problems named by Podgorniy, NASU Komandarm Uborevich 14-24, Kharkov, 61114, Ukraine
  • Игорь Романович Венгеров Institute of Physics of Mining Processes R. Luxemburg 72, Donetsk, 83114, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.9136

Keywords:

mathematical modeling, high-temperature processes, massifs, analytical and numerical methods.

Abstract

Mathematical modeling of thermal conditions of massifs during underground fires is the theoretical basis for engineering calculations, planning and firefighting.
The article suggests approximate analytical and numerical methods of mathematical modeling of high-temperature heating of a semi-infinite massif taking into account the dependence of its thermalphysic parameters on temperature.
We have examined four mathematical models based on the first and third boundary problems of nonlinear heat transfer with constant and variable temperatures of the heating medium (gas fire).
We have used the method of approximation of unsteady temperature fields, the method of stratification of the decision area, and the method of chronostratification (partitioning of process on the final time intervals).
We have obtained the solutions in forms, which can reduce them “to the number” with a PC; we have estimated the error of the approximate methods, which is less than 5%. The results can be used to improve the reliability, efficiency and quality of engineering calculations in mining industry.

Author Biographies

Анатолий Павлович Слесаренко, Institute of Mechanical Engineering Problems named by Podgorniy, NASU Komandarm Uborevich 14-24, Kharkov, 61114

Professor

Laureate of the State Prize of Ukraine

Leading scientific researcher

Игорь Романович Венгеров, Institute of Physics of Mining Processes R. Luxemburg 72, Donetsk, 83114

Senior scientific researcher

References

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  2. Венгеров, И.Р. Теплофизика шахт и рудников. Математические модели. – Монография в 2-х томах, том 1 [Текст] / И.Р. Венгеров. - Донецк: Норд-Пресс.- 2008. – 632 с.
  3. Венгеров, И.Р. Теплофизика шахт и рудников. Математические модели. – Монография в 2-х томах, том 2 [Текст] / И.Р. Венгеров. - Донецк: Донбасс. – 2012. – 685 с.
  4. Колесников, П.М. Методы теории переноса в нелинейных средах [Текст] / П.М. Колесников. – Минск: Наука и техника. – 1981. – 336 с.
  5. Коздоба, Л.А. Вычислительная теплофизика [Текст] / Л.А. Коздоба. – Киев: Наукова думка. – 1992. – 352 с.
  6. Зельдович, Я.Б. Физика ударных волн и высокотемпературных гидродинамических явлений, изд. 2-е, доп. [Текст] / Я.Б. Зельдович, Ю.П. Райзер. – Москва: Наука. – 1966. – 688 с.

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Published

2013-02-05

How to Cite

Слесаренко, А. П., & Венгеров, И. Р. (2013). Mathematical modeling of high-temperature nonlinear processes of heat transfer. Eastern-European Journal of Enterprise Technologies, 1(4(61), 4–10. https://doi.org/10.15587/1729-4061.2013.9136

Issue

Vol. 1 No. 4(61) (2013): Mathematics and cybernetics - fundamental and applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2014 Анатолий Павлович Слесаренко, Игорь Романович Венгеров

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