李对称理论是寻求数学物理方程精确解的有效方法。基于李对称理论得到了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没有报道过的,可以更真实地反映Brinkman模型的自然对流流动现象。

Lie symmetry theory is an effective method to find exact solution of mathematical and physical equations. The symmetry and reduced equations of Brinkman model are derived based on Lie symmetry theory. Some new exact solutions of the equation are obtained by solving the reduced equations, including variable separation and traveling wave solutions. Some variable separation solutions contain the effect of anisotropy of thermal conductivity on temperature. These solutions and traveling wave solutions are not reported in the existent literature, and they can more realistically reflect the natural convection flow in Brinkman model.