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
Keywords:
polar-orthotropic annular plate, temperature, stationary equation of heat conductivity, Volterra integral equation of the second kind, reverse conical ring plateAbstract
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.
References
- 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.
- 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.
- 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.
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