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IssuesArchive of Issues2013-6pp.595-602

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

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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 http://www.sciencedirect.com/science/article/pii/S002189281400015X
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