### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 293-308 |

Number of pages | 16 |

Journal | Journal of Mathematical Sciences (United States) |

Volume | 194 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Statistics and Probability

### Cite this

*Journal of Mathematical Sciences (United States)*,

*194*(3), 293-308. https://doi.org/10.1007/s10958-013-1529-9

**Thermal stress state of a cylinder whose subsurface layer has time-dependent thermophysical properties under heating by volume heat sources.** / Panin, S. V.; Martynyak, R. M.; Shvets', R. M.; Yatskiv, O. I.; Bobyk, B. Ya.

Research output: Contribution to journal › Article

*Journal of Mathematical Sciences (United States)*, vol. 194, no. 3, pp. 293-308. https://doi.org/10.1007/s10958-013-1529-9

}

TY - JOUR

T1 - Thermal stress state of a cylinder whose subsurface layer has time-dependent thermophysical properties under heating by volume heat sources

AU - Panin, S. V.

AU - Martynyak, R. M.

AU - Shvets', R. M.

AU - Yatskiv, O. I.

AU - Bobyk, B. Ya

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84898977798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898977798&partnerID=8YFLogxK

U2 - 10.1007/s10958-013-1529-9

DO - 10.1007/s10958-013-1529-9

M3 - Article

VL - 194

SP - 293

EP - 308

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -