微分约束方法在求解二阶流体精确解上的应用  

Application of Differential Constraints Method on Solving Exact Solutions of a Second-Grade Fluid

作　　者：张道祥[1,2] 冯素晓[1] 卢志明[1] 刘宇陆[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]安徽师范大学数学与计算机科学学院,安徽芜湖241000

出　　处：《应用数学和力学》2009年第4期379-387,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10772110)

摘　　要：利用微分约束方法研究了二阶流体的精确解.通过使用一阶微分约束条件,不仅获得了具有抽吸作用下的Couette和Poiseuille平行流、碰撞射流、平面拉伸流等具有明确物理意义的流动解,而且获得了两类新的精确解.所得精确解表明二阶流体的流动特性不仅依赖于物质粘性参数,而且依赖物质弹性参数.此外讨论了部分边值问题.Differential constraints method is used to investigate analytical solutions for a second-grade fluid flow. By the first-order differential constraint condition, some exact solutions of Poiseuille flows, jet flows and Couette flows subjected to suction or blowing forces, planar elongational flows were derived. In addition, two new classes of exact solutions for a second-grade fluid flow were found. Exact solutions obtained show that the non-Newtonian second-grade flow behavior depends on not only the material viscosity but also the material elasticity. Finally some boundary value problems were discussed.

关 键 词：非Newton流体 微分约束方法 二阶流体 

分 类 号：O357[理学—流体力学] O302[理学—力学]