Determination of the thermoelastic state of an eliptical pipe surface for the case of a radiant heat flow from one external side and convective heat exchange from the internal side

Authors

UDC

539.3

EDN

CXLMHD

DOI:

10.31429/vestnik-22-4-24-30

Abstract

The paper is devoted to the issues of thermoelasticity of an elliptical-shaped pipe during uneven heating. It deals with the distribution of the temperature field of an elliptical tube for the case of uneven heating from the outside due to radiation and under a boundary condition of the third kind from the inside. To solve it, the paper considers the solution of the Laplace equation in an elliptic coordinate system. The main method is the Fourier method. The resulting expression of the temperature field of the pipe has an analytical form containing a Fourier series. Based on the obtained dependence, it is established that the temperature field varies according to the sine law. This made it possible to determine the stresses that occur in the cylinder wall. The result obtained can be used in engineering calculations of heat exchangers.

Keywords:

heat transfer, ellipse, thermal stress, Laplace equation, convective heat transfer, radiant heat flux, Fourier method, hypergeometric functions

Author info

  • Alexandr I. Kanareykin

    доцент кафедры высшей математики и физики Российского государственного геологоразведочного университета им. Серго Орджоникидзе (МГРИ)

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Issue

Vol. 22 (2025) No. 4

Pages

24-30

Section

Mechanics

Dates

Submitted

July 29, 2025

Accepted

October 23, 2025

Published

December 2, 2025

How to Cite

[1]
Kanareykin, A.I., Determination of the thermoelastic state of an eliptical pipe surface for the case of a radiant heat flow from one external side and convective heat exchange from the internal side. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2025, т. 22, № 4, pp. 24–30. DOI: 10.31429/vestnik-22-4-24-30

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