谱方法求解变黏度磁流体的边界层流动问题

Spectral Method for Solving the Flow Process in the Boundary Layer of Magnetic Fluid with Variable Viscosity

以变黏度不可压缩磁流体为研究对象,研究稳恒磁场作用下磁流体外掠低温无渗透平板时,由于平板的水平拉伸引起的周围磁流体边界层内的层流流动和传热变化.首先采用相似原理对原控制方程组进行降维和无量纲化处理,并利用谱方法进行数值求解.设磁流体的黏度随温度线性变化,在不改变流场和温度场边界条件的前提下,研究了流体黏度变化参数、电磁参数和普朗特数对无量纲速度和无量纲温度的影响.把采用谱方法得到的结果与四阶龙格库塔法比较,验证了谱方法具有较高的数值稳定性和指数收敛特性.

Focusing on the viscous incompressible magnetic fluid past a stretching impermeable sheet with lower temperature, the laminar flow and the heat transfer in its boundary layer caused by the tensile deformation of the plate were studied under a steady magnetic field. Dimension reducing and dimensionless processing of the original control equations were first carried out based on similarity principle, and then the equations were solved by a spectral method. Assuming that the fluid viscosity varied linearly with temperature, with the constant boundary conditions of flow and temperature fields, the effects were analyzed of the parameters of variable fluid viscosity, the electromagnetic parameters, and the Prandtl number on the flow and temperature fields. Compared with the classical fourth-order Runge-Kutta method, the spectral method is superior in stability and exponential convergence.