Journal of Mathematical Sciences

, Volume 194, Issue 3, pp 293–308 | Cite as

Thermal stress state of a cylinder whose subsurface layer has time-dependent thermophysical properties under heating by volume heat sources

  • S. V. Panin
  • R. M. Martynyak
  • R. M. Shvets’
  • O. I. Yatskiv
  • B. Ya. Bobyk

We propose the structure of the solution of the problem of thermoelasticity for a long cylinder containing a thin subsurface layer with reduced parameters of heat transfer and heat capacity varying as functions of time under the conditions of heating by heat sources whose intensity is also a function of time varying and in the process of cooling by the environment. For the temperature of the cylindrical surface appearing in the structure of the solution, we deduce an integrodifferential equation with variable coefficients and the Volterra-type integral operator. The scheme of the spline approximation method is adapted for its solution. We analyze the temperature and stress distributions in time both on the surface of the cylinder and at different depths depending on the given regularities of changes in the intensity of heat sources and reduced thermophysical parameters of the subsurface layer. We consider the possibility of choosing variable thermophysical parameters partially compensating the action of time-dependent heat sources.


Heat Source Subsurface Layer Circumferential Stress Integrodifferential Equation Thermophysical Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • S. V. Panin
    • 1
  • R. M. Martynyak
    • 2
  • R. M. Shvets’
    • 2
  • O. I. Yatskiv
    • 2
  • B. Ya. Bobyk
    • 2
  1. 1.Institute of Physics of Strength and Materials ScienceSiberian Branch of the Russian Academy of SciencesTomskRussia
  2. 2.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine

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