广义二阶流体管内轴向流动

在流体的本构关系中引入分数阶导数运算，对于介于粘性与弹性之间的流体的描述更具有合理性。本文将这种关系引入二阶流体，研究其管内轴向流动。我们先求出了１／２阶导数的解析解，用以验证Ｌａｐｌａｃｅ数值反演的ＣＲＵＭＰ方法的有效性。然后用ＣＲＵＭＰ法分析二阶流体管内轴向流动的特征。分析表明粘弹性特征越明显的流体，其速度与应力对分数导数的阶数越具有敏感性。

eneral Second Order Fluid Flow in a Pipe

It is more satisfactory for fluid materials between viscous and elastic to introduce the fractional calculus approach into the constitutive relationship. This paper employs the fractional calculus approach to study second fluid flow in a pipe. At first,we derive the analytical solution whose derivate order is half with the analytical solution verifing the reliability of Laplace numeri-cal inversion based on Crump algorithm for the problem,and then we analyze the characteristics of second order fluid flow in a pipe by using Crump method. The results indicate that the more obvious the viscoelastic properties of fluid is, the more sensitive the dependence of velocity and stress on fractional deriva-tive order is.