To calculation of own values in the problem of nonstationary thermal conductivity of a massive full cylinder

Non–stationary heat conductivity the heat transfer occurs in many machines and apparatus. Therefore, the problematic issues of engineering calculation of these processes has great relevance to modern technology. Particular importance has the problems of calculating unsteady temperature fields in massive products, since In this case, as a rule, considerable thermal stresses occur simultaneously inside the material.Consequently, to find the thermal stresses it is necessary to know the unsteady temperature distribution.

The main aim of the study is to develop an effective analytical method that allows to significantly increase the accuracy of engineering calculation of eigenvalues in the problems of thermal conductivity of massive hollow cylindrical bodies.

The method used in the study: the eigenvalues for massive pipes are found in an iterative way. The roots of the characteristic equations obtained by the analytical calculation of the assumptions that the cylindrical wall is not too massive are taken as initial numbers.

The results: а rapidly convergent algorithm for calculating eigenvalues is proposed on the basis of a simple mathematical algorithm.

Keywords

eigenvalues, characteristic equations, boundary conditions, massive cylindrical wall, nonstationary temperature field

Publication date

10.01.2019

Cite Download pdf To download PDF you should sign in

GOST	Vidin Y., Kazakov R., Zlobin V. To calculation of own values in the problem of nonstationary thermal conductivity of a massive full cylinder // Izvestiia Rossiiskoi akademii nauk. Energetika – 2018. – Issue 5 C. 124-130 [Electronic resource]. URL: http://ras.jes.su/energetika/s000233100003222-8-1-en (circulation date: 20.04.2024). DOI: 10.31857/S000233100003222-8
MLA	Vidin, Yu, Kazakov, R., Zlobin, V. "To calculation of own values in the problem of nonstationary thermal conductivity of a massive full cylinder." Izvestiia Rossiiskoi akademii nauk. Energetika 5 (2018):124-130. DOI: 10.31857/S000233100003222-8
APA	Vidin Y., Kazakov R., Zlobin V. (2018). To calculation of own values in the problem of nonstationary thermal conductivity of a massive full cylinder. Izvestiia Rossiiskoi akademii nauk. Energetika (5), pp.124-130 DOI: 10.31857/S000233100003222-8

Размещенный ниже текст является ознакомительной версией и может не соответствовать печатной

Readers community rating: votes 0

1. Vidin Yu.V., Ivanov D.I. Raschet sobstvennykh chisle v zadache nestatsionarnoj te‑ ploperedachi cherez tsilindricheskuyu stenku pri granichnykh usloviyakh na vnutrennej i vneshnej poverkhnostyakh pervogo roda //Vestnik Kuzbasskogo gos. tekhn. univers. 2012. № 5 (93). S. 85–86.

2. Vidin Yu.V., Ivanov D.I. Raschet sobstvennykh chisel v zadachakh nestatsionarnoj te‑ ploperedachi cherez tsilindricheskuyu stenku pri granichnykh usloviyakh vtorogo rola. Vestnik Saratovskogo gos.tekhn.univers. 2012. № 1 (68). S. 15–17.

3. Vidin Yu.V., Zlobin V.S., Ivanov D.I. Nestatsionarnyj teploperenos v neodnorodnykh konstruktsiyakh krivolinejnoj konfiguratsii. Krasnoyarsk: SFU, 2016. 167 s.

4. Segal B.I., Semendyaev K.A. Pyatiznachnye matematicheskie tablitsy. M.: Fizmatlit, 1962. 450 s.

5. Vidin Yu.V., Ivanov D.I. Raschet sobstvennykh chisle v zadache nestatsionarnoj teplo‑ peredachi cherez tsilindricheskuyu stenku pri smeshannykh granichnykh usloviyakh // Vest‑ nik Sibirskogo gos. aehrokosmicheskogo univers. im. akad. M.F. Reshetneva. 2013. № 1 (47). S. 15–18.

6. Abramovits M., Stigan I. Spravochnik po spetsial'nym funktsiyam. M.: Nauka, 1979. 830 s.

7. Lykov A.V. Teoriya teploprovodnosti. M.: Vysshaya shkola, 1967. 600 s.

8. Karslou G., Eger D. Teploprovodnost' tverdykh tel. M.: Nauka, 1964. 487 s.

9. Plyat Sh.N. Raschet temperaturnykh polej betonnykh gidrosooruzhenij. M.: Ehnergiya, 1974. 407 s.

10. Kartashev Eh.M. Analiticheskie metody v teorii teploprovodnosti tverdykh tel. M.: Vysshaya shkola, 2001. 550 s.

11. Belyaev M.N. Ryadno A.A. Metody teorii teploprovodnosti. Ch1,2. M.: Vysshaya shkola, 1982.

12. Farlou S. Uravneniya s chastnymi proizvodnymi dlya nauchnykh rabotnikov i inzhene‑ rov. M.: Mir, 1985. 384 s.

13. Samarskij A.A., Gulin A.V. Chislennye metody: Ucheb. posobie dlya vuzov. M.: Nauka. Gl. red. fiz–mat. lit., 1989. 432 s.

14. Samarskij A.A., Vabishevich P.N. Vychislitel'naya teploperedacha. M.: Editorial URSS, 2003. 784 s.

15. Rychkov S.P. Modelirovanie konstruktsij v srede FemapwithNXNastran. M.: DMK Press, 2013. 784.

16. Bartenev O.V. Sovremennyj fortran.– 3–e izd., dop. i prerab. M.: DIALOG– MIFI, 2000. 449 s.

17. Ketkov Yu.L., Ketkov A.Yu. Shul'ts M.M. MATHLAB7: programmirovanie, chislennye metody. SPB.: BKhV–Peterburg, 2005. 752 s.

18. Roger W. Pryor. Multiphysics modeling using COMSOL. 2011 by Jones and Bartlett Publishers, LLC.