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
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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 journal › Article
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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 -