广义二阶流体的脉冲泊肃叶流动分析

讨论了广义二阶流体的脉冲泊肃叶流动,引入黎曼-刘维尔分数阶微分建立本构方程,结合不可压缩流体时间分数阶动量方程,得到控制方程.利用傅里叶正弦变换和分数阶拉普拉斯变换,获得流体速度解析解.利用Stehfest算法对结果进行数值模拟,通过图像讨论了分数阶参数以及延迟时间对流动的影响.结果表明速度过冲现象主要取决于动量方程的时间分数阶参数. 

Analysis of the impulse Poiseuille flow of generalized second grade fluid

The impulse Poiseuille flow of generalized second grade fluid was discussed in this paper. Combining the Riemann-Liouville fractional constitutive equation of second grade fluid with the fractional momentum equation of incompressible fluid,a new governing equation was established. The velocity analytical solution was obtained based on the Fourier sine transform and the fractional Laplace transform. The numerical simulation was performed by Stehfest algorithm method. The influences of various relevant parameters such as fractional derivative parameters and retardation time were elucidated through graphs. The results show that the velocity overshoot phenomenon mainly depends on the time fractional parameter of the momentum equation.