The effect of imperfectly insulated sidewalls on natural convection in porous media
The effect of imperfectly insulated sidewalls on natural convection in porous media
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不完美隔热侧壁对多孔介质自然对流的影响
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
C. Braester
中科院分区：
文献类型：
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作者：
P. Vadasz;C. Braester
本文给出了微超临界瑞利数下非理想隔热侧壁对多孔介质中自然对流影响的研究结果。利用弱非线性理论，得到了非理想隔热侧壁下加热的矩形区域的解析解。该解能够确定对流的幅度和流动的方向。振幅由一个普通的非齐次微分方程式产生，其中一个强迫项表示通过侧壁的热泄漏。稳态振幅解表明，通过临界Rayleigh数的过渡是光滑的，不同于完全绝缘侧壁的情况，在临界Rayleigh数处通常出现分叉。结果表明，在一定的微超临界瑞利数范围内，对流的大小和方向由侧壁的热泄漏唯一决定，且与初始条件无关。亚临界对流是由于侧壁绝缘不完善而产生的，使得能够平稳过渡通过临界瑞利值。当瑞利数较高时，出现三分支分叉。对对应于这两个分支的解的稳定性分析表明，对应于两个最高值的幅度是稳定的，而对应于第三个最高值的幅度是不稳定的。
SummaryThe paper presents the results of an investigation of the effect of imperfectly insulated sidewalls on natural convection in porous media at slightly supercritical Rayleigh numbers. An analytical solution for a rectangular domain with imperfectly insulated sidewalls and heated from below, was obtained through the weak nonlinear theory. The solution enables the determination of the amplitude of the convection and the direction of the flow. The amplitude results from an ordinary nonhomogeneous differential equation, with a forcing term representing the heat leakage through the lateral walls. The steady state amplitude solution shows that the transition through the critical Rayleigh number is smooth, differing from the case of perfectly insulated sidewalls where a bifurcation usually appears at the critical Rayleigh number. As a result, within a certain range of slightly supercritical Rayleigh number values, the amplitude and the direction of the convection currents are uniquely determined by the heat leakage through the lateral walls and they are independent of the initial conditions. A subcritical convection occurs as a result of the imperfectly insulated sidewalls, enabling the smooth transition through the critical Rayleigh value. A three-branch bifurcation develops at a higher Rayleigh number. A stability analysis of the solutions, corresponding to these branches, shows that the amplitudes which correspond to the two highest values are stable, while the third is unstable.