【作者】 陈良；

【导师】 李明军；

【作者基本信息】 湘潭大学 ， 计算数学， 2010， 硕士

【摘要】 我们研究在外加磁场和有磁化强度存在的情况下一种流体在刚硬多孔介质中的渗透定律，这一流体是稳态、不可压缩、缓慢、粘性、牛顿铁磁流体。根据孔尺寸的扩大比率流，我们得到了磁场下的渗透定律。我们也得到磁场的宏观等效模型。我们使用了多尺度渐进展开方法，得到了严格无任何宏观方程形式上的先决条件的宏观行为。宏观质量流量取决于在宏观磁力，压力梯度和磁压力梯度，正如Markus zahn和Rold E.Rosenweig在他们实验中所描述的。特别是，渗透定律表现出类似普通流体的达西定律，其中添加了与宏观磁压梯度和磁力成正比的项。渗透率张量是对称和正定的。更多还原

【Abstract】 We investigate the filtration law in rigid porous media for steady-state slow?ow of an incompressible and viscous Newtonian magnetic ?uid in the presenceof the external magnetic field and the intensity of magnetization. The seepagelaw under a magnetic field is obtained by upscaling the ?ow at the pore scale.The macroscopic equivalent model for the magnetic field is also obtained. We usethe method of multiple-scale expansions which gives rigorously the macroscopicbehavior without any preconditions on the form of the macroscopic equations.The macroscopic mass ?ow depends on the macroscopic magnetic force and thegradient of pressure and of magnetic pressure, as Markus Zahn and Rold E.Rosensweig had described in their experiments. In particular, the filtration lawis shown to resemble Darcy’s law of common ?uid but with some additional termsproportional to the macroscopic gradient of the magnetic pressure and magneticforce. The permeability tensor is symmetric and positive.更多还原