## 留言板

S·侯斯纳因, A·梅姆德, A·阿里. 二阶流体在旋转坐标系中的三维管道流动[J]. 应用数学和力学, 2012, 33(3): 280-291. doi: 10.3879/j.issn.1000-0887.2012.03.002
 引用本文: S·侯斯纳因, A·梅姆德, A·阿里. 二阶流体在旋转坐标系中的三维管道流动[J]. 应用数学和力学, 2012, 33(3): 280-291.
Saira Hussnain, Ahmer Mehmood, Asif Ali. Three Dimensional Channel Flow of Second Grade Fluid in a Rotating Frame[J]. Applied Mathematics and Mechanics, 2012, 33(3): 280-291. doi: 10.3879/j.issn.1000-0887.2012.03.002
 Citation: Saira Hussnain, Ahmer Mehmood, Asif Ali. Three Dimensional Channel Flow of Second Grade Fluid in a Rotating Frame[J]. Applied Mathematics and Mechanics, 2012, 33(3): 280-291.

## 二阶流体在旋转坐标系中的三维管道流动

##### doi: 10.3879/j.issn.1000-0887.2012.03.002

• 中图分类号: O357.1;O361.3

## Three Dimensional Channel Flow of Second Grade Fluid in a Rotating Frame

• 摘要: 就两个水平板构成的旋转系统，在磁场作用下分析二阶磁流体在其间的流动．下表面是一块可伸展的平面，上面是一块多孔的固体平板．选用合适的变换，将质量和动量的守恒方程，简化为耦合的非线性常微分方程组．应用最强大的分析技术， 即同伦分析法(HAM)， 得到该非线性耦合方程组的级数解． 结果用图形给出， 并详细地讨论了无量纲参数Re, λ, Ha2, αK2对速度场的影响．
•  [1] Crane L J. Flow past a stretching sheet[J]. Zeitschrift für Angewandte Mathematik und Physik, 1970, 21(4): 645-647. [2] Gupta P S, Gupta A S. Heat and mass transfer on a stretching sheet with suction or blowing[J]. The Canadian Journal of Chemical Engineering, 1977, 55(6): 744-746. [3] Chen C K, Char M I. Heat transfer of a continuous stretching surface with suction or blowing[J]. Journal of Mathematical Analysis and Applications, 1988, 135(2): 568-580. [4] Grubka L J, Bobba K M. Heat transfer characteristics of a continuous stretching surface with variable temperature[J]. ASME Journal of Heat Transfer, 1985, 107(1): 248-250. [5] Chiam T C. Magnetohydrodynamic heat transfer over a non-isothermal stretching sheet[J]. Acta Mechanica, 1997, 122(1/4): 169-179. [6] Chakrabarti A, Gupta A S. Hydromagnetic flow and heat transfer over a stretching sheet[J]. Quarterly of Applied Mathematics, 1979, 37(1): 73-78. [7] Ali M E. Heat transfer characteristics of a continuous stretching surface[J]. Warme-und Stoffubertragung, 1994, 29(4): 227-234. [8] Dutta B K. Heat transfer from stretching sheet with uniform suction and blowing[J]. Acta Mechanica, 1989, 78(3/4): 255-262. [9] Hassanien I A, Gorla R S R. Heat transfer to micropolar fluid from a non-isothermal stretching sheet with suction and blowing[J]. Acta Mechanica, 1990, 84(1/4): 191-199. [10] Elbashbeshy E M A. Heat transfer over a stretching surface with variable surface heat flux[J]. Journal of Physics D: Applied Physics, 1998, 31(16): 1951-1954. [11] Xu Q W, Bao W M, Mao R L, Yang G L, Pop I, Na T Y. Unsteady flow past a stretching sheet[J]. Mechanics Research Communications, 1996, 23(4): 413-422. [12] Mehmood A, Ali A. Takhar H S, Shah T. Corrigendum to: “Unsteady three dimensional MHD boundary layer flow due to the impulsive motion of a stretching surface (Acta Mechanica, 146(1), 59-71 (2001))” [J]. Acta Mechanica, 2008, 199(1/4): 241-249. [13] Mehmood A, Ali A, Shah T. Heat transfer analysis of unsteady boundary layer flow by homotopy analysis method[J]. Communcations in Non-Linear Science and Numerical Simulation, 2008, 13(5): 902-912. [14] Devi C D S, Thakhar H S, Nath G. Unsteady three dimensional boundary layer flow due to a stretching surface[J]. International Journal of Heat Mass Transfer, 1986, 29(12): 1996-1999. [15] 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[J]. Applied Mathematics and Computation, 2004, 158(3): 799-807. [16] Troy W C, Overman E A, Ermentrout G B, Keener J P. Uniqueness of flow of a second-order fluid past a stretching sheet[J]. Quarterly of Applied Mathematics, 1987, 44(4): 753-755. [17] Rao B N. Flow of a fluid of second grade over a stretching sheet[J]. International Journal of Non-Linear Mechanics, 1996, 31(4): 547-550. [18] Chang W D, Kazarinoff N D, Lu C. A new family of explicit solutions for the similarity equations modelling flow of a non-Newtonian fluid over a stretching sheet[J]. Archive for Rational Mechanics and Analysis, 1991, 113(2): 191-195. [19] Pontrelli G. Flow of a fluid of second grade over a stretching sheet[J]. International Journal of Non-Linear Mechanics, 1995, 30(3): 287-293. [20] Mehmood A, Ali A. An explicit analytic solution of steady three-dimensional stagnation point flow of second grade fluid toward a heated plate[J]. ASME Journal of Applied Mechanics, 2008, 75(6): 061003. [21] Ariel P D. A numerical algorithm for computing the stagnation point flow of a second grade fluid with/without suction[J]. Journal of Computational and Applied Mathematics, 1995, 59(1): 9-24. [22] Vajravelu K, Roper T. Flow and heat transfer in a second grade fluid over a stretching sheet[J]. International Journal of Non-Linear Mechanics, 1999, 34(6): 1031-1036. [23] Baris S, Dokuz M S. Three dimensional stagnation point flow of a second grade fluid towards a moving plate[J]. International Journal of Engineering Science, 2006, 44(1/2): 49-58. [24] Ferrario C, Passerini A, Thater G. Generalization of the Lorenz model to the two dimensional convection of second grade fluid[J]. International Journal of Non-Linear Mechanics, 2004, 39(4): 581-591. [25] Xu H, Liao S J. Series solutions of unsteady Magnetohydrodynamics flows of non-Newtonian fluids caused by an impulsively stretching plate[J]. Journal of Non-Newtonian Fluid Mechanics, 2005, 129(1): 46-55. [26] Huilgol R R, Keller H B. Flow of viscoelastic fluids between rotating disks: part I[J]. Journal of Non-Newtonian Fluid Mechanics, 1985, 18(1): 101-110. [27] Huilgol R R, Rajagopal K R. Non-axisymmetric flow of a viscoelastic fluid between rotating disks[J]. Journal of Non-Newtonian Fluid Mechanics, 1987, 23: 423-434. [28] Vajravelu K. Analytical and numerical solutions of a coupled non-linear system arising in a three-dimensional rotating flow[J]. International Journal of Non-Linear Mechanics, 2004, 39(1): 13-24. [29] Liao S J. Beyond Perturbation: Introduction to the Homotopy Analysis Methods[M]. Boca Raton: Chapman & Hall/CRC Press, 2003. [30] Hilton P H. An Introduction to Homotopy Theory[M]. Cambridge: Cambridge University Press, 1953. [31] Sen S. Topology and Geometry for Physicists[M]. Florida: Academic Press, 1983. [32] Yang C, Liao S J. On the explicit, purely analytic solution of von Karman swirling viscous flow[J]. Communcations in Non-Linear Science and Numerical Simulation, 2006, 11(1): 83-93. [33] Abbasbandy S. Homotopy analysis method for heat radiation equations[J]. International Communications in Heat and Mass Transfer, 2007, 34(3): 380-387. [34] Ziabaksh Z, Domairy G. Solution of the laminar viscous flow in a semi-porous channel in the presence of uniform magnetic field by using the homotopy analysis method[J]. Communcations in Non-Linear Science and Numerical Simulation, 2009, 14(4): 1284-1294. [35] Liao S J. A uniformly valid analytic solution of 2D viscous flow past a semi infinite flat plate[J]. Journal of Fluid Mechanics, 1999, 385: 101-128. [36] Liao S J, Cheung K F. Homotopy analysis of nonlinear progressive waves in deep water[J]. Journal of Engineering Mathematics, 2003, 45(2): 105-116. [37] Xu H, Liao S J. An explicit analytic solution for convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream[J]. International Journal of Engineering Science, 2005, 43(10): 859-874. [38] Liao S J. On the analytic solution of magnetohydrodynamic flow of non-Newtonian fluids over a stretching sheet[J]. Journal of Fluid Mechanics, 2003, 488: 189-212. [39] Mehmood A, Ali A. Analytic solution of generalized three-dimensional flow and heat transfer over a stretching plane wall[J]. International Communications Heat and Mass Transfer, 2006, 33(10): 1243-1252. [40] Mehmood A, Ali, A. Analytic solution of three-dimensional viscous flow and heat transfer over a stretching flat surface by homotopy analysis method[J]. ASME-Journal of Heat Transfer, 2008, 130(12): 121701. [41] Liao S J. On the homotopy analysis method for nonlinear problems[J]. Applied Mathematics and Computation, 2004, 147(2): 499-513. [42] Liao S J. An approximate solution technique which does not depend upon small parameters—part 2: an application in fluid mechanics[J]. International Journal of Non-Linear Mechanics, 1997, 32(5): 815-822. [43] Shercliff J A. A Textbook of Magnetohydrodynamics[M]. Oxford: Pergamon Press, 1965. [44] Rivlin R S, Ericksen J L. Stress deformation relations for isotropic matherials[J]. Journal of Rational Mechanics and Analysis, 1955, 4(5

##### 计量
• 文章访问数:  1148
• HTML全文浏览量:  21
• PDF下载量:  912
• 被引次数: 0
##### 出版历程
• 收稿日期:  2010-10-18
• 修回日期:  2011-12-05
• 刊出日期:  2012-03-15

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈