温敏MHD平板驻点流动及旋转圆盘流动问题的数值研究

发布时间：2018-03-22 06:13

本文选题：MHD流动与传热　切入点：变粘性系数　出处：《沈阳师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：平板驻点流动问题是流体力学基础中的经典问题,而关于其数值解的研究也一直在持续。在Hiemenz首先研究了二维平板驻点流动并计算出了N-S方程的精确解之后,许多其他研究者也在不同方面进行了研究并取得了优秀的成果。随着研究的不断深入,二维问题也逐步扩展到三维空间,其中最具代表性的问题便是旋转圆盘流动问题。但之前的大部分研究只考虑了平板运动、平板传热及外加热源等单一因素或单一变物性参数变化对整个流场的影响。本文同时考虑多个因素对流场的影响,主要研究温敏二维MHD平板驻点流动及三维旋转圆盘流动问题,其中粘性系数和热传导系数均为温度的函数,同时考虑磁场对流场的影响。论文分为五部分:第一章,介绍了平板驻点流动及旋转圆盘流动问题的研究背景及本文的研究意义;第二章,介绍了基本的平板驻点流动及旋转圆盘流动问题,包括相似解的设定,边界条件的转化,以及求解基本问题的方法;第三章,研究了温敏MHD平板驻点流动问题。首先对问题进行物理分析得到N-S方程组,然后运用相似变换将N-S方程组转化为常微分方程组并用打靶法数值求解,最后详细分析了流场量随各参数的变化趋势;第四章,研究了温敏MHD旋转圆盘流动问题。首先对问题进行物理分析得到N-S方程组,然后运用相似变换将N-S方程组转化为常微分方程组并用打靶法数值求解,最后详细分析了流场量随各参数的变化趋势,并与文献[20]的结果进行了比较;第五章,对第三章及第四章的结论进行比较和总结。
[Abstract]:The stationary point flow problem is a classical problem on the basis of hydrodynamics, and the study of its numerical solution has been continuing. After Hiemenz first studied the two-dimensional stationary point flow and calculated the exact solution of N-S equation. Many other researchers have also carried out research in different fields and achieved excellent results. As the research continues to deepen, the two-dimensional problem has gradually expanded to three-dimensional space. The most representative of these problems is the flow of rotating disks. But most previous studies have only considered plate motion. The influence of single or single variable physical parameters such as plate heat transfer and external heat source on the whole flow field is studied in this paper. Considering the influence of multiple factors on the flow field, this paper mainly studies the flow at the stationary point of the two-dimensional MHD plate and the three-dimensional rotating disk flow. The viscosity coefficient and heat conduction coefficient are both functions of temperature, and the influence of magnetic field flow field is considered. The thesis is divided into five parts: the first chapter introduces the research background and significance of the flow problem of flat plate stationary point flow and rotating disk flow. In the second chapter, the basic problems of stationary point flow and rotating disk flow are introduced, including the setting of similar solutions, the transformation of boundary conditions, and the methods to solve the basic problems. In this paper, the stationary point flow problem of a thermo-sensitive MHD plate is studied. Firstly, the N-S equations are obtained by physical analysis, then the N-S equations are transformed into ordinary differential equations by similar transformation and solved numerically by the shooting method. Finally, the variation trend of flow field with various parameters is analyzed in detail. In chapter 4, the temperature sensitive MHD rotating disk flow problem is studied. Firstly, the N-S equations are obtained by physical analysis of the problem. Then the N-S equations are transformed into ordinary differential equations by similar transformation and numerically solved by shooting method. Finally, the variation trend of flow field with various parameters is analyzed in detail, and compared with the results of reference [20]. The conclusion of the third and fourth chapters are compared and summarized.
【学位授予单位】：沈阳师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O35

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