The free-parameter solution of the convection equations in a vertical cylinder with a volume heat source

被引:1
|
作者
Andreyev, V. K.
Bekezhanova, V. B.
机构
来源
PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS | 2013年 / 77卷 / 06期
基金
俄罗斯基础研究基金会;
关键词
RECTANGULAR CAVITY; ADVECTIVE FLOW; INSTABILITY; BOUNDARIES; STABILITY; CHANNEL;
D O I
10.1016/j.jappmathmech.2014.03.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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. (C) 2014 Elsevier Ltd. All rights reserved.
引用
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页码:595 / 602
页数:8
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