 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ΟΜΜ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 77, Issue 6 / 2013 | Next article >> |
| V.K. Andreyev and V.B. Bekezhanova, "The free-parameter solution of the convection equations in a vertical cylinder with a volume heat source," J. Appl. Math. Mech. 77 (6), 595-602 (2013) |
| Year |
2013 |
Volume |
77 |
Issue |
6 |
Pages |
595-602 |
| Title |
The free-parameter solution of the convection equations in a vertical cylinder with a volume heat source |
| Author(s) |
V.K. Andreyev (Krasnoyarsk, Russia)
V.B. Bekezhanova (Krasnoyarsk, Russia, bekezhanova@mail.ru) |
| Abstract |
An exact solution of the free-convection equations is constructed in the Oberbeck-Boussinesq approximation, describing the flow of a viscous heat-conducting fluid in a vertical cylinder of large radius when heated by radiation. The initial problem is reduced to an operator equation with an extremely non-linear operator, satisfying Schauder's theorem in C[0,1]. An iteration procedure is proposed for determining the independent parameter, that occurs in the solution, which enables three different values to be obtained and, correspondingly, three classes of solution of the initial problem. The linear stability of all the solutions obtained is investigated and it is shown that, for chosen values of the problem parameters, the most dangerous one is the plane wave mode and two instability mechanisms are present. The flow structure and the type of instability depend considerably on the values of the free parameter. |
| Received |
20 August 2012 |
| Link to Fulltext |
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