ZHU Jing, ZHENG Lian-cun, ZHANG Zhi-gang. Effect of the Slip Condition on the MHD Stagnation-Point Flow Over a Power-Law Stretching Sheet[J]. Applied Mathematics and Mechanics, 2010, 31(4): 411-419. doi: 10.3879/j.issn.1000-0887.2010.04.003
Citation: ZHU Jing, ZHENG Lian-cun, ZHANG Zhi-gang. Effect of the Slip Condition on the MHD Stagnation-Point Flow Over a Power-Law Stretching Sheet[J]. Applied Mathematics and Mechanics, 2010, 31(4): 411-419. doi: 10.3879/j.issn.1000-0887.2010.04.003

Effect of the Slip Condition on the MHD Stagnation-Point Flow Over a Power-Law Stretching Sheet

doi: 10.3879/j.issn.1000-0887.2010.04.003
  • Received Date: 2009-11-25
  • Rev Recd Date: 2010-01-26
  • Publish Date: 2010-04-15
  • The steady two-dimensionalm agnetohyd rodynamic stagnation flow towards a nonlinear stretching surface was studied.The no slip condition on the solid boundary was replaced by the partial slip cond ition.A scaling group of transformations was applied to get the invariants. Using the invariants,a third order ordinary differential equation corresponding to the momentum was obtained.The analytical solution was obtained in the series form with the help of homotopy analysis method.The reliability and efficiency of series solutions were illustrated by good agreement with numerical results in the literature.Besides,the effects of the slip parameter,the magnetic field parameter,velocity ratio parameter,suction velocity parameter and the power law exponent on the flow were investigated.Results show that the velocity and shear stress pro files are greatly in fluenced by these parameters.
  • loading
  • [1]
    Mooney M. Explicit formulas for slip and fluidity[J]. J Rheology,1931,2(2):210-222. doi: 10.1122/1.2116364
    [2]
    Rao I J, Rajagopal K R. The effect of the slip condition on the flow of fluids in a channel[J]. Acta Mech,1999, 135(3): 113-126. doi: 10.1007/BF01305747
    [3]
    Khaled A R A, Vafai K. The effect of slip condition on Stokes and Couette flows due to an oscillating wall: exact solutions[J]. Int J Non-Linear Mech,2004, 39(5): 795-804. doi: 10.1016/S0020-7462(03)00043-X
    [4]
    Wang C Y. Flow due to a stretching boundary with partial slip―an exact solution of the Navier-Stokes equations[J]. Chem Eng Sci, 2002, 57(17): 3745-3747. doi: 10.1016/S0009-2509(02)00267-1
    [5]
    Wang C Y. Stagnation slip flow and heat transfer on a moving plate[J]. Chem Eng Sci, 2006, 61(23): 7668-7672. doi: 10.1016/j.ces.2006.09.003
    [6]
    Hayat T, Masood K, Ayub M. The effect of the slip condition on flows of an Oldroyd 6-constant fluid[J]. J Comput Appl Math, 2007, 202(2): 402-413. doi: 10.1016/j.cam.2005.10.042
    [7]
    乔德哈瑞 R C, 吉哈 A K. 化学反应对竖直平板边界磁流体动力学微极流体滑流的影响[J].应用数学和力学,2008,29(9):1069-1082.
    [8]
    Andersson H I, Rousselet M. Slip flow over a lubricated rotating disk[J]. Int J Heat Fluid Flow, 2006, 27(2): 329-335. doi: 10.1016/j.ijheatfluidflow.2005.09.002
    [9]
    Labropulu F, Li D. Stagnation-point flow of a second-grade fluid with slip[J]. Int J Non-Linear Mech, 2008, 43(9): 941-947. doi: 10.1016/j.ijnonlinmec.2008.07.004
    [10]
    朱婧,郑连存,张欣欣.具有延伸表面的驻点流动和传热问题的级数解[J].应用数学和力学,2009,30(4):432-442.
    [11]
    莫嘉琪.具有边界摄动弱非线性反应扩散方程的奇摄动[J].应用数学和力学,2008,29(8):1003-1089.
    [12]
    林苏榕,莫嘉琪.超抛物型方程的非线性奇摄动问题[J].应用数学和力学,2008,29(10):1249-1253.
    [13]
    苏晓红,郑连存,蒋锋.幂律流体边界层方程的近似解析解和壁摩擦因数的近似值[J].应用数学和力学,2008,29(9):1101-1106.
    [14]
    梁祖峰,唐晓艳.用Adomian分解法求解分数阻尼梁的解析解[J].应用数学和力学,2007,28(2):200-209.
    [15]
    张善元,刘志芳.有限变形弹性杆中三种非线性弥散波[J].应用数学和力学,2008,29(7):908-917.
    [16]
    Liao S J. Beyond Perturbation: Introduction to Homotopy Analysis Method[M]. Boca Raton:Chapman Hall/CRC, 2003.
    [17]
    Liao S J. On the homotopy analysis method for nonlinear problems[J]. Appl Math Comput, 2004, 147(2): 499-513. doi: 10.1016/S0096-3003(02)00790-7
    [18]
    Hayat T, Abbas Z, Sajid M. Series solution for the upper-convected Maxwell fluid over a porous stretching plate[J]. Phys Lett A, 2006, 358(6): 396-403. doi: 10.1016/j.physleta.2006.04.117
    [19]
    Xu H, Liao S J. Series solutions of unsteady magnetohydrodynamic flows of non-Newtonian fluids caused by an impulsively stretching plate[J]. J Non-Newton Fluid, 2005, 129(1): 46-55. doi: 10.1016/j.jnnfm.2005.05.005
    [20]
    Tan Y, Xu H, Liao S J. Explicit series solution of travelling waves with a front of Fisher equation[J]. Chaos Soliton Fract, 2007, 31(2): 462-472. doi: 10.1016/j.chaos.2005.10.001
    [21]
    Liao S J. An optimal homotopy-analysis approach for strongly nonlinear differential equations[J]. Commun Nonlinear Sci Numer Simul, 2009. doi: 10.1016/j. cnsns. 2009. 09.002.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1339) PDF downloads(1227) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return