The effect of a weak heterogeneity of a porous medium on natural convection
The effect of a weak heterogeneity of a porous medium on natural convection
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多孔介质弱非均质性对自然对流的影响
DOI：
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发表时间：
1993
影响因子：
3.7
通讯作者：
P. Vadasz
中科院分区：
文献类型：
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作者：
C. Braester;P. Vadasz
提出了多孔介质弱非均质性对自然对流影响的研究结果。介质不均匀性由渗透率和有效导热率的空间变化来表示。作为一般规则，异质多孔介质中水平热梯度的存在为自然对流的发生提供了充分的条件。研究了这种条件对受等温顶部和底部边界条件影响的水平层或矩形域的影响。结果导致对允许静止解决方案的热导率函数类别的限制。应用弱非线性理论，得到了从下方加热的矩形弱异质多孔域的解析解，与基本静止解一致。对流的幅度是从普通的非齐次微分方程获得的，其中强迫项代表相对于有效热导率的介质不均匀性。获得了通过临界瑞利数的平滑过渡，从而消除了在瑞利数的临界值处通常出现在具有完美边界的均匀域中的分叉。在一定范围的略超临界瑞利数内，对称热导函数显示出增强对称流动，而反对称函数有利于反对称流动。除高阶解外，渗透率的弱非均质性起着相对被动的作用，不会影响前阶解。相反，有效热导率的弱异质性确实对最终的流动模式有显着影响。
The results of an investigation on the effect of a weak heterogeneity of a porous medium on natural convection are presented. A medium heterogeneity is represented by spatial variations of the permeability and of the effective thermal conductivity. As a general rule the existence of horizontal thermal gradients in heterogeneous porous media provides a sufficient condition for the occurrence of natural convection. The implications of this condition are investigated for horizontal layers or rectangular domains subject to isothermal top and bottom boundary conditions. Results lead to a restriction on the classes of thermal conductivity functions which allow a motionless solution. Analytical solutions for rectangular weak heterogeneous porous domains heated from below, consistent with a basic motionless solution, are obtained by applying the weak nonlinear theory. The amplitude of the convection is obtained from an ordinary non-homogeneous differential equation, with a forcing term representative of the medium heterogeneity with respect to the effective thermal conductivity. A smooth transition through the critical Rayleigh number is obtained, thus removing a bifurcation which usually appears in homogeneous domains with perfect boundaries, at the critical value of the Rayleigh number. Within a certain range of slightly supercritical Rayleigh numbers, a symmetric thermal conductivity function is shown to reinforce a symmetrical flow while antisymmetric functions favour an antisymmetric flow. Except for the higher-order solutions, the weak heterogeneity with respect to permeability plays a relatively passive role and does not affect the solutions at the leading order. In contrast, the weak heterogeneity with respect to the effective thermal conductivity does have a significant effect on the resulting flow pattern.