非牛顿流体的几类精确解

发布时间：2018-05-03 14:15

本文选题：偶应力流体 + Riabouchinsky流　；参考：《安徽师范大学》2017年硕士论文

【摘要】：非牛顿流体在工业上具有广泛的应用,因此吸引了众多学者的研究.非牛顿流体的控制方程是一个高维的非线性微分方程,其精确解求解非常困难,至今找到的精确解数量非常有限.对于非牛顿流体的精确解,它有助于我们了解和认识非牛顿流体的特性,为工业生产和生活提供指导依据.因此,研究非牛顿流体的精确解具有重要的理论价值和现实意义.本文利用Nemeyi提出的逆方法,求解了偶应力流体和二阶流体的几类精确解.主要结果如下:1.我们得到了偶应力流体的Riabouchinsky型精确解,并且发现速度场和流函数强烈地依赖于偶应力流体的物质参数.2.通过预设涡量场分布的条件下,研究在多孔介质和霍尔电流效应定常和非定常条件下二阶流体的精确解.我们得到了带有垂向上有抽(吸)作用的平行流动以及随时间按指数衰减的流动精确解.
[Abstract]:Non-Newtonian fluid has been widely used in industry, so it has attracted many scholars. The governing equation of non-Newtonian fluid is a high dimensional nonlinear differential equation, and its exact solution is very difficult to solve. The number of exact solutions found so far is very limited. For the exact solution of non-Newtonian fluid, it is helpful for us to understand and understand the characteristics of non-Newtonian fluid and to provide guidance for industrial production and daily life. Therefore, it is of great theoretical and practical significance to study the exact solutions of non-Newtonian fluids. In this paper, the inverse method proposed by Nemeyi is used to solve several kinds of exact solutions of even stress fluid and second order fluid. The main results are as follows: 1. We obtain the Riabouchinsky type exact solution of the fluid with couple stress and find that the velocity field and the flow function are strongly dependent on the material parameters of the fluid with couple stress. The exact solution of the second order fluid in porous media and under the condition of steady and unsteady Hall current effect is studied under the condition of preset vorticity field distribution. We obtain the exact solutions of the parallel flow and the exponential decay of the flow over time.
【学位授予单位】：安徽师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.29

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