,784 北京科技大学学报 2006年第8期 1.0 分析方法，求得该控制方程及其边界条件的相似 解.分析了量纲为一速度∫()的分布，以及在 0.8 不同的渗透参数和抽吸喷注参数情况下壁摩擦系 0.6 数的变化， 0.4 参考文献 0.2 [1]Sakiadis B C.Boundarylayer behavior on a continuous solid surface:I.Boundary-layer equations for two dimensional and 6 10 axisymmetric flow.AIChE J.1961.7.26 [2]Sakiadis B C.Boundarylayer behavior on a continuous solid 图1关于1的速度函数分布(c=一0.3，k1=0.5) surface:I Boundary-layer equations for two dimensional and Fig.1 Dimensionless velocity profile for c=-0.3,=0.5 axisymmetric flow.AIChE J.1961.7:221 [3] Elbashbeshy E M A.Bazid M AA.Heat transfer in a porous 表1不同渗透参数和抽吸喷注参数情况下壁摩擦系数的变化 medium over a stretching surface with internal heat generation Table 1 Skin friction coefficients at different permeability and in and suction or injection.Appl Math Comput.2004.158:799 jection parameters [4]Liao S J.Beyond Perturbation.New York:CRC Press Com- -f'(0) k1=0 k1=1 k1=2 pany:2004 c=-0.1 0.95 1.45 1.95 [5]LiaoSJ.Pop I.Explicit analytic solution for similarity bound- c=0.6 1.30 1.80 2.30 ary layer equations.Int J Heat Mass Transfer,2004.47:75 [6]Liao S J.On the homotopy analysis method for nonlinear prob- lems.Appl Math Comput.2004.147:499 4 结论 [7]Xu H.An explicit analytic solution for free convection about a vertical flat plate embedded in a porous medium by means of 研究了具有抽吸喷注的多孔介质延伸表面上 homotopy analysis method.Appl Math Comput.2004.158: 二维稳态层流的流动问题，通过相似变换和同伦 433 On the homotopy analysis method for solving the boundary layer flow problem over a stretching surface with suction and injection SONG Yi,ZHENG Lianeun),ZHANG Xinxin2) 1)Applied Science School.University of Science and Technology Beijing.Beijing 100083,China 2)Mechanical Engineering School,University of Science and Technology Beijing.Beijing 100083.China ABSTRACI This paper studied two-dimensional steady laminar flow over a porous medium stretching sur- face with suction or injection.The homotopy analysis method,a kind of analytical method,was applied to solve the problem.The solution presents representative profiles for the dimensionless velocity and the skin friction coefficient at different permeability and injection parameters. KEY WORDS boundary layer;stretching surface;suction;injection;nonlinear;homotopy analysis method图1 关于 η的速度函数分布（ c＝－0∙3‚k1＝0∙5） Fig．1 Dimensionless velocity profile for c＝－0∙3‚k1＝0∙5 表1 不同渗透参数和抽吸喷注参数情况下壁摩擦系数的变化 Table1 Skin friction coefficients at different permeability and in￾jection parameters — f″（0） k1＝0 k1＝1 k1＝2 c＝—0∙1 0∙95 1∙45 1∙95 c＝0∙6 1∙30 1∙80 2∙30 4 结论 研究了具有抽吸喷注的多孔介质延伸表面上 二维稳态层流的流动问题．通过相似变换和同伦 分析方法‚求得该控制方程及其边界条件的相似 解．分析了量纲为一速度 f′（η）的分布‚以及在 不同的渗透参数和抽吸喷注参数情况下壁摩擦系 数的变化． 参 考 文 献 ［1］ Sakiadis B C．Boundary-layer behavior on a continuous solid surface：Ⅰ．Boundary-layer equations for two-dimensional and axisymmetric flow．AIChE J‚1961‚7：26 ［2］ Sakiadis B C．Boundary-layer behavior on a continuous solid surface：Ⅱ．Boundary-layer equations for two-dimensional and axisymmetric flow．AIChE J‚1961‚7：221 ［3］ Elbashbeshy E M A‚Bazid M A A．Heat transfer in a porous medium over a stretching surface with internal heat generation and suction or injection．Appl Math Comput‚2004‚158：799 ［4］ Liao S J．Beyond Perturbation．New York：CRC Press Com￾pany‚2004 ［5］ Liao S J‚Pop I．Explicit analytic solution for similarity bound￾ary layer equations．Int J Heat Mass Transfer‚2004‚47：75 ［6］ Liao S J．On the homotopy analysis method for nonlinear prob￾lems．Appl Math Comput‚2004‚147：499 ［7］ Xu H．An explicit analytic solution for free convection about a vertical flat plate embedded in a porous medium by means of homotopy analysis method．Appl Math Comput‚2004‚158： 433 On the homotopy analysis method for solving the boundary layer flow problem over a stretching surface with suction and injection SONG Y i 1）‚ZHENG L iancun 1）‚ZHA NG Xinxin 2） 1） Applied Science School‚University of Science and Technology Beijing‚Beijing100083‚China 2） Mechanical Engineering School‚University of Science and Technology Beijing‚Beijing100083‚China ABSTRACT This paper studied two-dimensional steady laminar flow over a porous medium stretching sur￾face with suction or injection．The homotopy analysis method‚a kind of analytical method‚was applied to solve the problem．The solution presents representative profiles for the dimensionless velocity and the skin friction coefficient at different permeability and injection parameters． KEY WORDS boundary layer；stretching surface；suction；injection；nonlinear；homotopy analysis method ·784· 北 京 科 技 大 学 学 报 2006年第8期