Cylindrical Tank Filled With a Liquid in a Three-Dimensional Temperature Field

In the cylindrical coordinate system, we construct an exact solution of the threedimensional thermoelasticity problem for a tank filled with a liquid. After determining the temperature field from the heat conduction equation, we solve the equations of the asymmetrical problem of the theory of elasti...

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Bibliographic Details
Published in:Russian mathematics 2018-02, Vol.62 (2), p.19-27
Main Authors: Gur’yanov, N. G., Tyuleneva, O. N.
Format: Article
Language:English
Subjects:
Boundary value problems
Conduction heating
Conductive heat transfer
Cylindrical coordinates
Cylindrical tanks
Elasticity
Heat transfer
Mathematical analysis
Mathematics
Mathematics and Statistics
Temperature distribution
Thermoelasticity
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Summary:In the cylindrical coordinate system, we construct an exact solution of the threedimensional thermoelasticity problem for a tank filled with a liquid. After determining the temperature field from the heat conduction equation, we solve the equations of the asymmetrical problem of the theory of elasticity. In doing so, the system of resolving equations is reduced to four separate equations with respect to the displacements of the construction. Several exact solutions of boundary-value problems are found. The results are presented in the form of rather simple formulas.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X18020032