多孔介质中自然对流Brinkman模型的新精确解

J4 ›› 2017, Vol. 34 ›› Issue (6): 691-699.

多孔介质中自然对流Brinkman模型的新精确解

张立华¹,赵琳琳²,刘希强³

1. 德州学院数学系
2. 德州学院
3. 聊城大学数学科学学院

收稿日期:2016-06-24 修回日期:2016-10-19 出版日期:2017-11-28 发布日期:2017-12-11
通讯作者: 张立华

New exact solutions of the Brinkman model describing the natural convection in porous media

Received:2016-06-24 Revised:2016-10-19 Published:2017-11-28 Online:2017-12-11

摘要/Abstract

摘要： 李对称理论是寻求数学物理方程的精确解的系统而有效的方法.利用李对称理论得到了Brinkman模型的对称和约化方程，通过求解约化方程得到了该方程的一些新的精确解，包括变量分离解和行波解,部分变量分离解包含了导热率的各向异性对温度的影响，这些解和行波解是已有文献中所没有报告过的，这种解可以更真实地反映Brinkman模型的自然对流流动现象.

关键词: Brinkman模型，对称，约化，精确解　　

Abstract: The theory of Lie symmetry is a systematic and effective method to find exact solutions of mathematical and physical equations. The symmetries and reduction equations of the Brinkman model are derived by means of Lie symmetry theory. By solving the reduced equations，many new exact solutions of the Brinkman model including solutions of separating variables and traveling wave solutions are obtained. Some variable-separating solutions considers the anisotropic effect of thermal conductivity. These solutions and the traveling wave solutions have not been reported in the existent literature and they can reflect the natural convection more really.

Key words: Brinkman model, symmetry, reduction equations, exact solutions

张立华赵琳琳刘希强. 多孔介质中自然对流Brinkman模型的新精确解[J]. J4, 2017, 34(6): 691-699.

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