具有不同渗透的涨缩管道内微极性流动的同伦分析解  

Homotopy Analysis Solution for Micropolar Fluid Flow Through Porous Channel With Expanding or Contracting Walls of Different Permeabilities

作　　者：司新毅[1] 司新辉[2] 郑连存[2] 张欣欣[3] 

机构地区：[1]河海大学水利水电工程学院,南京210098 [2]北京科技大学数理学院,北京100083 [3]北京科技大学机械学院,北京100083

出　　处：《应用数学和力学》2011年第7期807-820,共14页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(50936003;50905013);先进金属和材料国家重点实验室项目(2009Z-02)

摘　　要：分析了壁面具有不同渗透的涨缩管道内微极性流体的流动.对于壁面的胀缩,考虑常系数和时间函数的膨胀率两种情况.对于第1种情况,应用同伦分析方法得到该问题的速度和微旋转角度的表达式.并且画图分析了各个不同参数,特别是膨胀系数和不同的渗透率对流体的动力特征的影响.可以得到第1个重要的结论:壁面的膨胀率和不同的渗透对流体的动力特征有重要的影响.根据Xu的模型,考虑了第2种也是更具有一般性的情况,假设壁面的膨胀率随时间的变化而变化.在这样的假设下,控制方程被转化成非线性偏微分方程,并且同样也可以应用HAM方法进行求解.应用代数和指数的模型来描述膨胀率从初始状态到最终状态的演变过程.然而,结果表明包含有时间的解很快地趋向于稳态的解.这样可以得到第2个重要的结论,时间在壁面的膨胀收缩中扮演着次要的角色,可以忽略不计.The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeability was investigated.Two cases were considered in which the opposing walls undergo either uniform or nonuniform motion.In the first case,homotopy analysis method（HAM） was employed to obtain the expressions for velocity and micro-rotation fields.Graphs were sketched for some values of the parameters.The first conclusion can be made that expansion ratio and different permeability have important effects on the dynamic characteristics of the fluid.Following Xu＇s model,the second and more general case is that the wall expansion ratio varies with time.Under this assumption,the governing equations were transformed into nonlinear partial differential equations that also are solved analytically using HAM procedure.In the process,both algebraic and exponential models were considered to describe the evolution of α（t） from the initial α0 to a final state α1.As a result,it is found that the time-dependent solutions approach very rapidly to the steady state behavior.The second important conclusion can be made that the time-dependent variation of the wall expansion ratio plays a secondary role which may be justifiably ignored.

关 键 词：同伦分析方法 微极性流体 涨缩壁面 多孔管道 不同渗透速度 

分 类 号：O175.8[理学—数学] O357.3[理学—基础数学]