温敏MHD旋转圆盘流动与传热问题数值研究  

Numerical study of temperature sensitive MHD rotating disk flow and heat transfer problems

作　　者：李胜男[1] 李明军[2] 

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034 [2]湘潭大学数学与计算科学学院,湘潭411105

出　　处：《应用力学学报》2018年第2期365-371,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11171281);辽宁省自然科学基金(201602673)

摘　　要：研究了温敏三维定常MHD旋转圆盘流动数值解问题。其中热传导系数和粘性系数均是温度的函数。通过物理分析得到Navier-Stokes控制方程组,利用相似变换,将N-S控制方程组转化为常微分方程组,再利用打靶法计算此常微分方程组的数值解。分别对不同磁相互作用参数、流体粘性参数、普朗特数及温敏系数下的横向、纵向、垂向速度分量及温度进行数值计算,并分析其变化趋势。通过与文献结果比较,发现霍尔电流会改变横向速度、垂向速度、温度与磁相互作用参数的单调关系,也会改变垂向速度与流体粘性参数的单调关系。同时也发现当磁场给定时,在考虑霍尔电流情况下,不同流体粘性参数对应的横向速度存在共同的极值点0.40;在不考虑霍尔电流情况下,横向速度的极值点分布在区间[0.43,0.46]内,垂向速度关于流体粘性参数的单调性变化交点分布在[0.8045,0.8225]内。The numerical solution of the temperature sensitive three-dimensional MHD rotating disk flow problem is studied. The thermal conductivity and viscosity are considered as functions of temperature. The governing Navier-Stokes equations are obtained through physical analysis. The governing Navier-Stokes equations are transformed into a set of ordinary differential equations(ODEs) by similarity transformation. The transformed ODEs are solved numerically using shooting method. Numerical calculations of the transverse, longitudinal and vertical velocity components and temperature for various magnetic interaction parameters, fluid viscosity parameters, Prandtl numbers and temperature sensitivity coefficient are carried out, and then their variation trends are analyzed. By comparing with the literature results, it is found that the Hall current will change the monotonic relationship between the transverse velocity, the vertical velocity and the temperature and the magnetic interaction parameter, and also change the monotonic relationship between the vertical velocity and the fluid viscosity parameter. It is also found that when the magnetic field is given, the transverse velocity of the different fluid viscosity parameters in the hall current situation has a common extreme value of 0.40. In the absence of the Hall current situation, the extreme value points of the transverse velocity are distributed in the interval [0.43, 0.46], and the monotonic change intersection of vertical velocity for the variation of the fluid viscosity parameters is distributed in [0.8045, 0.8225].

关 键 词：旋转圆盘 MHD流动 传热 霍尔电流 打靶法 

分 类 号：O242[理学—计算数学]