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Linear instability analysis of convection in a laterally heated cylinder

Published online by Cambridge University Press:  17 April 2014

Bo-Fu Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, Anhui, PR China School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, Hubei, PR China
Zhen-Hua Wan
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, Anhui, PR China
Zhi-Wei Guo*
Affiliation:
School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, Hubei, PR China
Dong-Jun Ma*
Affiliation:
National Space Science Center, Chinese Academy of Sciences, Beijing 100190, PR China
De-Jun Sun*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, Anhui, PR China
*
Email addresses for correspondence: juice@mail.ustc.edu.cn, mdj@ustc.edu.cn, dsun@ustc.edu.cn
Email addresses for correspondence: juice@mail.ustc.edu.cn, mdj@ustc.edu.cn, dsun@ustc.edu.cn
Email addresses for correspondence: juice@mail.ustc.edu.cn, mdj@ustc.edu.cn, dsun@ustc.edu.cn

Abstract

The three-dimensional instabilities of axisymmetric flow are investigated in a laterally heated vertical cylinder by linear stability analysis. Heating is confined to a central zone on the sidewall of the cylinder, while other parts of the sidewall are insulated and both ends of the cylinder are cooled. The length of the heated zone equals the radius of the cylinder. For three different aspect ratios, $A= 1.92 $, 2, 2.1 ($A=\mathrm{height}$/radius), the dependence of the critical Rayleigh number on the Prandtl number (from 0.02 to 6.7) has been studied in detail. For such a kind of laterally heated convection, some interesting stability results are obtained. A monotonous instability curve is obtained for $A= 1.92 $, while the instability curves for $A= 2 $ and $A= 2.1 $ are non-monotonous and multivalued. In particular, an instability island has been found for $A=2$. Moreover, mechanisms corresponding to different instability results are obtained when the Prandtl number changes. At small Prandtl number, the flow is oscillatory unstable, which is dominated by hydrodynamic instability. At intermediate Prandtl number, the interaction between buoyancy and shear in the base flow plays a more important role than pure hydrodynamic instability. At even higher Prandtl number, Rayleigh–Bénard instability becomes the dominant process and the flow loses stability through steady bifurcation.

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Papers
Copyright
© 2014 Cambridge University Press 

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