The mixed unsteady heat conduction problem for a half-infinite hollow cylinder

Authors

  • I. M. Turchyn Ivan Franko National University of L’viv, 79000, L’viv, Universytetska str., 1; Kazimierz Wielki University, 85064, Bydgoszcz, Khotkiewicha str., 30, Poland https://orcid.org/0000-0003-0345-1467
  • G. V. Vasylko Ivan Franko National University of L’viv, 79000, L’viv, Universytetska str., 1
  • O. Ya. Ivaskevych Ivan Franko National University of L’viv, 79000, L’viv, Universytetska str., 1

DOI:

https://doi.org/10.17721/1812-5409.2019/1.52

Abstract

Analysis of temperature fields is important for many engineering applications. The account of actual operating conditions of these structures frequently leads to mixed heating condition. The authors of this paper developed a new effective method of solutions derivation for mixed boundary-value unsteady heat conduction problems. This paper considers the cylinder with at the part of surface of which the temperature distribution is known. Outside this area the heat transfer by Newton's law is performed.

To the heat conductivity problem it is applied the Laguerre integral transformation in time variables and integral Fourier transformation in spatial variable. As a result the triangular sequence of ordinary differential equations is obtained. The general solution of these sequences is obtained in the form of algebraic convolution. Taking into account the mixed boundary conditions leads to dual integral equations. For solution of this problem it is proposed the method of Neumann's series. By this method the problem is reduced to the infinite system of algebraic equations, for which the convergence of reduction procedure is proved. Finally, the unknown temperature is submitted as a series of Laguerre polynomials. The coefficient of these series is Fourier integrals.

Key words: unsteady heat conduction problem; mixed boundary conditions; Laguerre polynomials; dual integral equations.

Pages of the article in the issue: 222-225

Language of the article: Ukrainian

References

KOLYANO, Yu. M. (1992) Metody teploprovodnosti i termouprugosti neodnorodnogo tela. Kiev: Naukova Dumka.

SNEDDON, I. (1966) Mixed Boundary-Value Problems in Potential Theory. Amsterdam: North-Holland Publishers Company.

GALAZYUK, V. A. & TURCHIN, I. M. (1998) Quasistatic thermal stress state of a layer with mixed heating conditions. Int. Appl. Mech.. 34 (9). pp. 886-893.

TURCHIN, I.M. (2012) Nonstationary end heating of a multilayer semiinfinite plate. Journ. of Eng. Physics and Thermoph. 85 (6). pp. 1453-1462.

SNEDDON, I. (1951) Fourie transforms. New York: McCraw-Hill Book Company.

TURCHIN, I.M., KOLODIY, Yu.O & TIMAR, I. (2015) Nonstationary axisymmetric temperature field in a two-layer slab under mixed heating conditions. Journ. of Eng. Physics and Thermoph. 88 (5). pp. 1135-1144.

TURCHYN, I.M. & KOLODIY, Yu.O. (2017) Quasistatic plane problem of thermoelasticity for the half space with coating under mixed conditions of heating. Journal of Math. Sci. 233 (2). рр. 145-158.

KOLODIY, Yu.O., TURCHYN, I.M. & KHOMA, V.V. (2017) Zminena nestatsionarna problema teplovidnosti dlya pivbezmezhnogo tsylindra z pokryttyam. Visnyk KNU im. T. Shevchenka Ser.: Phys. & Math. N 3 рр. 91-94.

No 1 (2019)

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How to Cite

Turchyn, I. M., Vasylko, G. V., & Ivaskevych, O. Y. (2019). The mixed unsteady heat conduction problem for a half-infinite hollow cylinder. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 222–225. https://doi.org/10.17721/1812-5409.2019/1.52

Issue

No. 1 (2019)

Section

Differential equations, mathematical physics and mechanics

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