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Mathematical Problems in Engineering
Volume 2013, Article ID 198695, 12 pages
Research Article

Numerical Simulation and Stability Study of Natural Convection in an Inclined Rectangular Cavity

1Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China
2School of Civil Engineering, The University of Sydney, NSW 2006, Australia

Received 18 December 2012; Accepted 22 January 2013

Academic Editor: Zhijun Zhang

Copyright © 2013 Hua-Shu Dou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper examines the process of instability of natural convection in an inclined cavity based on numerical simulations. The energy gradient method is employed to analyze the physics of the flow instability in natural convection. It is found that the maximum value of the energy gradient function in the flow field correlates well with the location where flow instability occurs. Meanwhile, the effects of the flow time, the plate length, and the inclination angle on the instability have also been discussed. It is observed that the locations of instabilities migrate right as the flow time increased. With the increase of plate length, the onset time of the instability on the top wall of the cavity decreases gradually and the locations of instabilities move to the right side. Furthermore, the locations of instability move left with the increase of the inclination angle in a certain range. However, these positions move right as the accumulation of the heat flux is restrained in the lower left corner of the cavity once the inclination angle exceeds a certain range.