The influence of the length of heat sources on the external border on the temperature distribution in profiled polar-orthotropic ring plates taking into account there heat exchange with the external environment

  • Uladzimir V. Karalevich International Center of Modern Education, 61 Štěpánská Street, Prague 1, PSČ 110 00, Czech
  • Dmitrij G. Medvedev Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
DOI: https://doi.org/10.33581/2520-6508-2020-3-86-91

Abstract

We study the influence of N extended heat sources at external boundaries on the nonaxisymmetric temperature distribution on profiled polar-orthotropic ring plates and take into account heat exchange with the external environment. The solution of the stationary heat conduction problem for anisotropic annular plates of a random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conductivity problem for a reverse conical polar-orthotropic ring plate is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.

Author Biographies

Uladzimir V. Karalevich, International Center of Modern Education, 61 Štěpánská Street, Prague 1, PSČ 110 00, Czech

lecturer

Dmitrij G. Medvedev, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

doctor of science (pedagogics), PhD (physics and mathematics), docent; first vice-rector

References

  1. Karalevich UV. Solution of nonaxisymmetric stationary problem of heat conductivity for polar-orthotropic ring plate of variable thickness with account of heat transfer with external environment. Journal of the Belarusian State University. Mathematics and Informatics. 2020;1:47–58. Russian. DOI: 10.33581/2520-6508-2020-1-47-58.
  2. Uzdalev AI, Bryukhanova EN. [Equations of thermal conductivity for plates of variable thickness with inhomogeneous thermophysical properties]. In: Uzdalev AI, editor. Zadachi prikladnoi teorii uprugosti [Problems of applied theory of elasticity]. Saratov: Saratovskii politekhnicheskii institut; 1985. p. 3–7. Russian.
  3. Karalevich UV. Stationary temperature fields in the anisotropic ring plates of variable thickness considering the heat exchange with external environment. Journal of the Belarusian State University. Mathematics and Informatics. 2018;2:58–66. Russian.
Published
2020-12-08
Keywords: polar-orthotropic annular plate, temperature, stationary equation of heat conductivity, Volterra integral equation of the second kind, reverse conical ring plate
How to Cite
Karalevich, U. V., & Medvedev, D. G. (2020). The influence of the length of heat sources on the external border on the temperature distribution in profiled polar-orthotropic ring plates taking into account there heat exchange with the external environment. Journal of the Belarusian State University. Mathematics and Informatics, 3, 86-91. https://doi.org/10.33581/2520-6508-2020-3-86-91
Issue
No 3 (2020): Journal of the Belarusian State University. Mathematics and Informatics
Section
Short Communications

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