Determination of the thermoelastic state of the cylindrical tube surface for the case of radiant heat flow from one outside and convective heat exchange from the inside
UDC
539.3EDN
LNCTNJDOI:
10.31429/vestnik-22-2-72-79Abstract
The work is devoted to the issues of thermoelasticity of a cylindrical tube during uneven heating. It deals with the distribution of the temperature field of a cylindrical tube for the case of a radiant heat flow from one outside and under a boundary condition of the third kind from the inside. At the same time, the problem under consideration is stationary. To solve it, the paper considers the solution of the Poisson equation and the Euler equation. 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 law of cosine of the double argument. 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 exchange, temperature field, pipe, thermal stress, Euler equation, convective heat transfer, radiant heat flux, Fourier seriesFunding information
The study did not have sponsorship
References
- Nasikas, A., Karamanos, S.A., Papanicolopulos, S.A., Non-Associative Plasticity for Structural Instability of Cylindrical Shells in the Inelastic Range. University of Edinburgh, 2022. DOI: 10.7488/era/2590
- Fajuyitan, O.K., Sadowski, A., Wadee, A., Length Effects in Elastic Imperfect Cylindrical Shells under Uniform Bending. University of London, 2018.
- Локтева, Н.А., Нестационарное деформирование анизотропной круговой цилиндрической оболочки. Труды МАИ, 2021, № 120, с. 139–145. [Lokteva, N.A., Unsteady deformation of an anisotropic circular cylindrical shell. Trudy MAI = Proc. of MAI, 2021, no. 120, p. 139–145. (in Russian)]
- Kanareykin, A.I., Mathematical modeling of the fuel element of a nuclear reactor taking into account the temperature dependence of the thermal conductivity of the fuel element made of uranium oxide. IOP Conference Series: Earth and Environmental Science, volume 990, IV International scientific and practical conference "Actual problems of the energy complex: physical processes, mining, production, transmission, processing and environmental protection", Moscow, 2022, p. 012012. DOI: 10.1088/1755-1315/990/1/012012
- Kanareykin, A., Analysis of the thermally stressed state of the heat-generating element in the form of an ellipsoid. E3S Web of Conferences, 2024, vol. 549, p. 05006. DOI: 10.1051/E3SCONF/202454905006
- Kanareykin, A., Modeling of the temperature field and thermal stresses of a fuel element with variable volumetric heat release. E3S Web of Conferences, 2024, vol. 592, p. 03009. DOI: 10.1051/E3SCONF/202459203009
- Kanareykin, A., Heat exchange between the heating element and its shell under the boundary condition of the fourth kind. E3S Web of Conferences. International Scientific Siberian Transport Forum - TransSiberia 2023, 2023, p. 07039. DOI: 10.17586/1606-4313-2023-22-3-68-73
- Kanareykin, A., Heat exchange in fuel rods at different cross sections. E3S Web of Conferences. XI International Scientific and Practical Conference Innovative Technologies in Environmental Science and Education (ITSE-2023), EDP Sciences, 2023, p. 02021. DOI: 10.1051/e3sconf/202343102021
- Железнов, Л.П., Серьёзнов, А.Н., Нелинейное деформирование и устойчивость подкрепленной композитной цилиндрической оболочки при осевом сжатии. Полет. Общероссийский научно-технический журнал, 2022, № 2, pp. 40–48. [Zheleznov, L.P., Serebernov, A.N., Nonlinear deformation and stability of a reinforced composite cylindrical shell under axial compression. Polet. Obshcherossiyskiy nauchno-tekhnicheskiy zhurnal = Flight. All-Russian Scientific and Technical Journal, 2022, no. 2, pp. 40–48. (in Russian)]
- Петров, И.И., Фундаментальные решения для ортотропной цилиндрической оболочки. Труды МАИ, 2022, № 124, с. 23–29. [Petrov, I.I., Fundamental solutions for an orthotropic cylindrical shell. Trudy MAI = Proc. of MAI, 2022, no. 124, pp. 23–29. (in Russian)]
- Канарейкин, А.И., Уравнение Лапласа в теплофизике. Наукосфера, 2023, № 12-2, с. 241–245. [Kanarekin, A.I., Laplace equation in thermophysics. Naukosfera = Sphere of Science, 2023, no. 12-2, p. 241–245. (in Russian)]
- Захаров, В.А., Верификация методики численного исследования процесса теплообмена в кольцевых каналах теплообменного аппарата. Машиностроение и машиноведение, 2020, № 1(70), с. 14–16. [Zakharov, V.A., Verification of the methodology for numerical investigation of the heat exchange process in the annular channels of a heat exchanger. Mashinostroenie i mashinovedenie = Mechanical Engineering and Machine Science, 2020, no. 1, p. 14–16. (in Russian)]
- Канарейкин, А.И., О частном решении дифференциального уравнения в частных производных без перехода к эллиптической системе координат. Научные труды Калужского государственного университета им. К.Э. Циолковского. Региональная университетская научно-практическая конференция. Сер. "Естественные науки", 2015, с. 140–141. [Kanarekin, A.I., On the partial solution of a partial differential equation without transition to an elliptic coordinate system. Nauchnye trudy Kaluzhskogo gosudarstvennogo universiteta imeni K.E. Tsiolkovskogo. Regional'naya universitetskaya nauchno-prakticheskaya konferentsiya. Seria "Estestvennye nauki" = Scientific papers of Kaluga State University named after K.E. Tsiolkovsky. Regional University Scientific and Practical Conference. Ser. "Natural Sciences", 2015, pp. 140–141. (in Russian)]
- Канарейкин, А.И., Решение краевой задачи Неймана для уравнения Пуассона в цилиндрическом стержне. Международный журнал информационных технологий и энергоэффективности, 2023, т. 8. № 9 (35), с. 73–78. [Kanarekin, A.I., Solution of the Neumann boundary value problem for the Poisson equation in a cylindrical rod. Mezhdunarodnyy zhurnal informatsionnykh tekhnologiy i energoeffektivnosti = International Journal of Information Technology and Energy Efficiency, 2023, vol. 8, no. 9, pp. 73-78. (in Russian)]
- Несис, Е.И., Методы математической физики. Москва, Просвещение, 1977. [Nesis, E.I., Metody matematicheskoy fiziki = Methods of mathematical Physics. Moscow, Prosveshchenie, 1977. (in Russian)]
- Канарейкин, А.И., Теплообмен трубы цилиндрической формы для случая лучистого теплового потока с одной внешней стороны и при граничном условии третьего рода с внутренней стороны. Вестник Международной академии холода, 2024, № 3, c. 78–83. [Kanarekin, A.I., Heat exchange of a cylindrical tube for the case of a radiant heat flow from one outside and under a boundary condition of the third kind from the inside. Vestnik Mezhdunarodnoy akademii kholoda = Bull. of the International Academy of Refrigeration, 2024, no. 3, pp. 78–83. (in Russian)] DOI: 10.17586/1606-4313-2024-23-3-78-83
- Канарейкин, А.И., Теплообмен трубы эллиптической формы для случая лучистого теплового потока с внешней стороны и при конвективном теплообмене с внутренней. Инженерная физика, 2025, № 1, с. 58–64. [Kanarekin, A.I., Elliptical tube heat exchange for the case of radiant heat flow from the outside and during convective heat exchange from the inside. Inzhenernaya fizika = Engineering Physics, 2025, no. 1, pp. 58–64. (in Russian)] DOI: 10.25791/infizik.1.2025.1456
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Dates
Submitted
April 9, 2025
Accepted
June 24, 2025
Published
June 30, 2025
How to Cite
[1]
Kanareykin, A.I., Determination of the thermoelastic state of the cylindrical tube surface for the case of radiant heat flow from one outside and convective heat exchange from the inside. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2025, т. 22, № 2, pp. 72–79. DOI: 10.31429/vestnik-22-2-72-79
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