具有不同渗透的涨缩管道内微极性流动的同伦分析解

司新毅; 司新辉; 郑连存; 张欣欣

doi:10.3879/j.issn.1000-0887.2011.07.005

具有不同渗透的涨缩管道内微极性流动的同伦分析解

doi: 10.3879/j.issn.1000-0887.2011.07.005

河海大学水利水电工程学院,南京 210098;
北京科技大学数理学院,北京 100083;

基金项目: 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)

详细信息

作者简介:
司新毅(1985- ),男,山东聊城人,博士生(E-mai:lhotsauce0079@163.com);司新辉(1978- ),男,山东聊城人,讲师,博士(联系人.Te:l+86-10-62332589;E-mail:sixinhui_ustb@126.com).

中图分类号: O175.8;O357.3
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- 文章访问数: 1785
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- PDF下载量: 655
- 被引次数: 0
出版历程
- 收稿日期: 2010-12-06
- 修回日期: 2011-04-20
- 刊出日期: 2011-07-15

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

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, P. R. China;
Department of Mathematics and Mechanics, University of Science and Technology Beijing, Beijing 100083, P. R. China;
Department of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, P. R. China

摘要

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．
- 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
Abstract: The flow of amicropolar fluid through a porous channel with expanding or contracting walls of different permeability was investigated. Two cases were considered in which the opposing walls undergoeither uniformor 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 param eters. The first conclusion can be made that expan sion ratio and different perm eability have miportant effects on the dynamic characteristics of the fluid. Following Xu. smodel, the second and more general case is that the wall expansion ratiovaries with time. Under this assumption, the govern ing equations were transformed in to non linear partial differential equations that also are solved analytically using HAM procedure. In the process, both algebraic and exponen tialmodels were considered to describe the evolution of a (t) from the initial a₀ to a final state a₁. As a result, it is found that the tmie-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 maybe justifiably ignored.
- homotopy analysis method /
- micropolar fluid /
- expanding or contracting walls /
- porous channel /
- different permeability

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参考文献(43)

[1]	Berman A S. Laminar flow in channels with porous walls[J]. Journal of Applied Physics, 1953, 24(9): 1232-1235. doi: 10.1063/1.1721476
[2]	Terrill R M, Thomas P W. Laminar flow in a uniformly porous pipe[J]. Applied Science Research, 1969, 21(1): 37-67. doi: 10.1007/BF00411596
[3]	Terrill R M. On some exponentially small terms arising in flow through a porous pipe[J]. The Quarterly Journal of Mechanics and Applied Mathematics, 1973, 26(3): 347-354. doi: 10.1093/qjmam/26.3.347
[4]	Terrill R M. Laminar flow in a uniformly porous channel[J]. The Aeronautical Quarterly, 1964, 15: 299-310.
[5]	Robinson W A. The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls[J]. Journal of Engineering Mathematics, 1976, 10(1): 23-40. doi: 10.1007/BF01535424
[6]	Terrill R M. Laminar flow through parallel and uniformly porous walls of different permeability[J].ZAMP, 1965, 16: 470-482. doi: 10.1007/BF01593923
[7]	Terrill R M, Shrestha G M. Laminar flow through parallel and uniformly porous walls of different permeability[J]. Zeitschrift fur Angewandte Mathematik und Physik, 1965, 16: 470-482. doi: 10.1007/BF01593923
[8]	Uchida S, Aoki H. Unsteady flows in a semi-infinite contracting or expanding pipe[J]. Journal of Fluid Mechanics, 1977,82(2):371-387. doi: 10.1017/S0022112077000718
[9]	Ohki Morimatsu. Unsteady flows in a porous, elastic, circular tube—part 1: the wall contracting or expanding in an axial direction[J]. Bulletin of the JSME, 1980, 23(179): 679-686. doi: 10.1299/jsme1958.23.679
[10]	Goto M, Uchida S. Unsteady flow in a semi-infinite expanding pipe with injection through wall[J]. Journal of the Japan Society for Aeronautical and Space Science, 1990, 33(9): 14-27.
[11]	Bujurke N M, Pai N P, Jayaraman G. Computer extended series solution for unsteady flow in a contracting or expanding pipe[J]. IMA Journal of Applied Mathematics, 1998,60(2): 151-165. doi: 10.1093/imamat/60.2.151
[12]	Majdalani J, Zhou C, Dawson C D. Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability[J]. Journal of Biomechanics, 2002,35(10): 1399-1403. doi: 10.1016/S0021-9290(02)00186-0
[13]	Dauenhauer C E, Majdalani J. Exact self-similarity solution of the Navier-Stokes equations for a porous channel with orthogonally moving walls[J]. Physics of Fluids, 2003, 15(6): 1485-1495. doi: 10.1063/1.1567719
[14]	Majdalani J, Zhou C. Moderate-to-large injection and suction driven channel flows with expanding or contracting walls[J]. Zeitschrift fur Angewandte Mathematik und Mechanik, 2003,83(3): 181-196. doi: 10.1002/zamm.200310018
[15]	Asghar S, Mushtaq M, Hayat T. Flow in a slowly deforming channel with weak permeability:an analytical approach[J]. Nonlinear Analysis:Real World Applications, 2010, 11(1): 555-561. doi: 10.1016/j.nonrwa.2009.01.049
[16]	Si X H, Zheng L C, Zhang X X, Chao Y. Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls[J]. Acta Mechanica Sinica, 2011, 27(2): 208-214. doi: 10.1007/s10409-011-0430-3
[17]	Si X H, Zheng L C, Zhang X X, Chao Y. The flow of a micropolar fluid through a porous channel with expanding or contracting walls[J]. Central European Journal of Physics, 2011, 9(3): 825-834.
[18]	司新辉，郑连存，张欣欣，晁莹. 半渗透涨缩管道内微极性流动解析求解[J].应用数学和力学， 2010, 31(9): 1027-1035.(SI Xin-hui, ZHENG Lian-cun, ZHANG Xin-xin, CHAO Ying. Analytic solution to the micropolar-fluid flow through a semi-porous channel with an expanding or contracting wall[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(9): 1073-1080.)
[19]	Xu H, Lin Z L, Liao S J, Wu J Z, Majdalani J. Homotopy based solutions of the Navier-Stokes equations for a porous channel with orthogonlly moving walls[J]. Physics of Fluids, 2010, 22(5): 053601. doi: 10.1063/1.3392770
[20]	Makukula Z G, Precious Sibanda Motsa S S. A novel numerical technique for two dimensional laminar flow between two moving porous walls[J]. Mathematical Problems in Engineering, 2010. ID 528956. doi: 10.1155/2010/528956.
[21]	Si X H, Zheng L C, Zhang X X, Si X Y, Yang J H. flow of a viscoelastic through a porous channel with expanding or contracting walls[J]. Chinese Physics Letters, 2011, 28(4): 044702. doi: 10.1088/0256-307X/28/4/044702
[22]	Eringen A C. Theory of micropolar fluids[J].Journal of Mathematics & Mechanics, 1966, 16(1): 1-18.
[23]	Eringen A C. Theory of Thermomicropolar fluids[J]. Journal of Mathematical Analysis and Applications, 1972, 38(2): 480-496. doi: 10.1016/0022-247X(72)90106-0
[24]	Ariman T, Turk M A, Sylvester N D. Microcontinuum fluid mechanics—a review[J]. International Journal of Engineering Science, 1973, 11(8): 905-930. doi: 10.1016/0020-7225(73)90038-4
[25]	Ariman T, Turk M A, Sylvester N D. Application of Microcontinuum fluid mechanics—a review[J]. International Journal of Engineering, 1974, 12(4): 273-293. doi: 10.1016/0020-7225(74)90059-7
[26]	Eringen A C. Microcontinuum Field Theories Ⅱ:Fluent Media[M]. New York: Springer, 2001.
[27]	Subhadra Ramachandran P, Mathur M N, Ojha S K. Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection[J]. International Journal of Engineering Science, 1979, 17(5): 625-639. doi: 10.1016/0020-7225(79)90131-9
[28]	Takhar H S, Bhargava R, Agrawal R S, Balaji A V S. Finite element solution of micropolar fluid flow and heat transfer between two porous discs[J].International Journal of Engineering Science, 2000, 38(17): 1907-1922. doi: 10.1016/S0020-7225(00)00019-7
[29]	Kelson N A, Farrell T W. Micropolar fluid flow over a porous stretching sheet with strong suction or injection[J].International Communications in Heat and Mass Transfer, 2001, 28(4): 479-488. doi: 10.1016/S0735-1933(01)00252-4
[30]	Muhammad Ashraf, Anwar Kamal M, Syed K S. Numerical study of asymmetric laminar flow of a micropolar fluid in a porous channel[J].Computers & Fluids, 2009, 38(10): 1895-1902.
[31]	Muhammad Ashraf, Anwar Kamal M, Syed K S. Numerical simulation of flow of a micropolar fluid between a porous disk and a non-porous disk[J]. Applied Mathematical Modelling, 2009, 33(4): 1933-1943. doi: 10.1016/j.apm.2008.05.002
[32]	Liao S J. Beyond Perturbation: Introduction to Homotopy Analysis Method[M]. Boca, Raton: Chapman Hall/CRC Press, 2003.
[33]	Liao S J. On the homotopy analysis method for nonlinear problems[J]. Applied Mathematics and Computation, 2004, 147(2): 499-513. doi: 10.1016/S0096-3003(02)00790-7
[34]	Hayat T, Khan M. Homotopy solution for a generalized second grade fluid past a porous plate[J].Nonlinear Dynamics, 2005, 42(4): 395-405. doi: 10.1007/s11071-005-7346-z
[35]	Hayat T, Khan M, Asghar S. Magnetohydrodynamic flow of an oldroyd 6-constant fluid[J].Applied Mathematics and Computation, 2004, 155(2): 417-225. doi: 10.1016/S0096-3003(03)00787-2
[36]	Hayat T, Khan M, Siddiqui A M, Asghar S. Transient flows of a second grade fluid[J].International Journal of Non-Linear Mechanics, 2004, 39(10): 1621-1633. doi: 10.1016/j.ijnonlinmec.2002.12.001
[37]	Abbas Z, Sajid M, Hayat T. MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel[J].Theoretical and Computational Fluid Dynamics, 2006, 20(4): 229-238.
[38]	Sajid M, Hayat T, Asghar S. On the analytic solution of the steady flow of a fourth grade fluid[J]. Physics Letters A, 2006, 355(1): 18-26. doi: 10.1016/j.physleta.2006.01.092
[39]	Sajid M, Abbas Z, Hayat T. Homotopy analysis for boundary layer flow of a micropolar fluid through a porous channel[J].Applied Mathematical Modelling, 2009, 33(11): 4120-4125. doi: 10.1016/j.apm.2009.02.006
[40]	Srinivasacharya D, Ramana Murthy J V, Venugopalam D. Unsteady stokes flow of micropolar fluid between two parallel porous plates[J]. International Journal of Engineering Science, 2001, 39(14): 1557-1563. doi: 10.1016/S0020-7225(01)00027-1
[41]	Rees D A S, Pop I. Free convection boundary layer flow of a micropolar fluid from a vertical flat plate[J].IMA Journal of Applied Mathematics, 1998, 61(2): 179-197. doi: 10.1093/imamat/61.2.179
[42]	Guram G S, Smith A C. Stagnation flows of micropolar fluids with strong and weak interactions[J].Computers & Mathematics With Applications, 1980, 6(2): 213-233.
[43]	Liao S J. An optimal homotopy-analysis approach for strongly nonlinear differential equations[J].Communications in Nonlinear Science and Numerical Simulation, 2010, 15(8): 2003-2016. doi: 10.1016/j.cnsns.2009.09.002

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具有不同渗透的涨缩管道内微极性流动的同伦分析解

doi: 10.3879/j.issn.1000-0887.2011.07.005

作者简介:
司新毅(1985- ),男,山东聊城人,博士生(E-mai:lhotsauce0079@163.com);司新辉(1978- ),男,山东聊城人,讲师,博士(联系人.Te:l+86-10-62332589;E-mail:sixinhui_ustb@126.com).

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

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目录

留言板

具有不同渗透的涨缩管道内微极性流动的同伦分析解

doi: 10.3879/j.issn.1000-0887.2011.07.005

作者简介: 司新毅(1985- ),男,山东聊城人,博士生(E-mai:lhotsauce0079@163.com);司新辉(1978- ),男,山东聊城人,讲师,博士(联系人.Te:l+86-10-62332589;E-mail:sixinhui_ustb@126.com).

计量

出版历程

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

计量

出版历程

目录

作者简介:
司新毅(1985- ),男,山东聊城人,博士生(E-mai:lhotsauce0079@163.com);司新辉(1978- ),男,山东聊城人,讲师,博士(联系人.Te:l+86-10-62332589;E-mail:sixinhui_ustb@126.com).