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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)293-308
Number of pages16
JournalJournal of Mathematical Sciences (United States)
Volume194
Issue number3
DOIs
Publication statusPublished - 2013

Fingerprint

Thermal Stress
Heat Source
Engine cylinders
Thermal stress
Heating
Thermodynamic properties
Thermoelasticity
Spline Approximation
Integrodifferential equations
Heat Capacity
Stress Distribution
Volterra
Temperature Distribution
Variable Coefficients
Approximation Methods
Integral Operator
Integro-differential Equation
Splines
Specific heat
Cooling

ASJC Scopus subject areas

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

Cite this

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.

In: Journal of Mathematical Sciences (United States), Vol. 194, No. 3, 2013, p. 293-308.

Research output: Contribution to journalArticle

@article{9012c51b02f444569eca3a7a76210c77,
title = "Thermal stress state of a cylinder whose subsurface layer has time-dependent thermophysical properties under heating by volume heat sources",
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.",
author = "Panin, {S. V.} and Martynyak, {R. M.} and Shvets', {R. M.} and Yatskiv, {O. I.} and Bobyk, {B. Ya}",
year = "2013",
doi = "10.1007/s10958-013-1529-9",
language = "English",
volume = "194",
pages = "293--308",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Science and Business Media Deutschland GmbH",
number = "3",

}

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

AN - SCOPUS:84898977798

VL - 194

SP - 293

EP - 308

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -