同伦分析法求解非线性多孔收缩表面上黏性磁流体的流动

S·纳丁; A·候赛因

doi:10.3879/j.issn.1000-0887.2009.12.008

同伦分析法求解非线性多孔收缩表面上黏性磁流体的流动

doi: 10.3879/j.issn.1000-0887.2009.12.008

奎德伊阿扎穆大学数学系,伊斯兰堡 45320,巴基斯坦

详细信息

中图分类号: O361.3
计量
- 文章访问数: 1335
- HTML全文浏览量: 100
- PDF下载量: 632
- 被引次数: 0
出版历程
- 收稿日期: 2009-02-12
- 修回日期: 2009-08-25
- 刊出日期: 2009-12-15

MHD Flow of a Viscous Fluid on a Non-Linear Porous Shrinking Sheet by Homotopy Analysis Method

Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, Pakistan

摘要

摘要: 研究在非线性多孔收缩表面上黏性磁流体(MHD)的流动．先用相似变换简化其控制方程，然后用同伦分析法(HAM)求解该简化问题．用图表的形式对问题的相关参数进行讨论，发现在有磁流体时，收缩解存在．同时得到，在不同参数下f″(0)的解是收敛的．
- MHD流动 /
- 驻点流动 /
- 收缩表面 /
- HAM解
Abstract: The MHD flow of a viscous fluid towards a non-linear porous shrinking sheet was investigated.The governing equations were simplified by similarity transformations and then the reduced problem was solved by homotopy analysis method(HAM).The pertinent parameters appeared in the problem were discussed graphically and through the tables.It is found that the shrinking solutions in the presence of MHD exit.It is also observed from the tables that solutions for f"(0) with different values of parameters are convergent.
- MHD flow /
- stagnation flow /
- shrinking sheet /
- HAM solutions

HTML全文

参考文献(28)

[1]	Fang T,Liang W,Lee C F.A new solution branch for the Blasius equation[KG1mm]. —A shrinking sheet problem[J].Computers and Mathematics With Applications, 2008,56(12):3088-3095.
[2]	Sajid M,Hayat T.The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet[J].Chaos,Solitons & Fractals,2009,39(3):1317-1323.
[3]	Hayat T,Abbas Z,Javed T,et al.Three-dimensional rotating flow induced by a shrinking sheet for suction[J].Chaos,Solitons & Fractals,2009,39(4):1615-1626.
[4]	Fang T,Zhang J.Closed-form exact solutions of MHD viscous flow over a shrinking sheet[J].Comm in Non-linear Sci and Numer Sim,2009,14(7):2853-2857. doi: 10.1016/j.cnsns.2008.10.005
[5]	Fang T.Boundary layer flow over a shrinking sheet with power-law velocity[J].Int J of Heat and Mass Transfer,2008,51(25/26):5838-5843. doi: 10.1016/j.ijheatmasstransfer.2008.04.067
[6]	Nadeem S,Awais M.Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity[J].Phy Lett A,2008,372(30):4965-4972. doi: 10.1016/j.physleta.2008.05.048
[7]	Hayat T,Javed T,Sajid M.Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface[J].Phy Lett A,2008,372(18):3264-3273. doi: 10.1016/j.physleta.2008.01.069
[8]	Wang C Y.Stagnation flow towards a shrinking sheet[J].Int J of Non-Linear Mech,2008,43(5):377-382. doi: 10.1016/j.ijnonlinmec.2007.12.021
[9]	Hayat T,Abbas Z,Ali N.MHD flow and mass transfer of an upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species[J].Phy Lett A,2008,372(26):4698-4704. doi: 10.1016/j.physleta.2008.05.006
[10]	Chaim T C.Hydromagnetic flow over a surface stretching with a power law velocity[J].Int J of Eng Sci,1995,33(3):429-435. doi: 10.1016/0020-7225(94)00066-S
[11]	Abbas Z,Wanga Y,Hayat T,et al.Hydromagnetic flow in a viscoelastic fluid due to the oscillatory stretching surface[J].Int J of Non-Linear Mech,2008,43(8):783-793. doi: 10.1016/j.ijnonlinmec.2008.04.009
[12]	Mohamed R A,Abbas I A,Abo-Dahab S M.Finite element analysis of hydromagnetic flow and heat transfer of a heat generation fluid over a surface embedded in a non-Darcian porous medium in the presence of chemical reaction[J].Comm Non-Linear Sci Numer Sim,2009,14(4):1385-1395. doi: 10.1016/j.cnsns.2008.04.006
[13]	Hayat T,Ali N.A mathematical description of peristaltic hydromagnetic flow in a tube[J].Applied Mathematics and Computation,2007,18(2):1491-1502.
[14]	Attia H A.Unsteady hydromagnetic Couette flow of dusty fluid with temperature dependent viscosity and thermal conductivity[J].Int J of Non-Linear Mech,2008,43(8):707-715. doi: 10.1016/j.ijnonlinmec.2008.03.007
[15]	Tsai R,Huang K H,Huang J S.The effects of variable viscosity and thermal conductivity on heat transfer for hydromagnetic flow over a continuous moving porous plate with Ohmic heating[J].Appl Therm Eng,2009,29(10):1921-1926. doi: 10.1016/j.applthermaleng.2008.09.005
[16]	Ghosh A K,Sana P.On hydromagnetic flow of an Oldroyd-B fluid near a pulsating plate[J].Acta Astronautica,2009,64(2/3):272-280. doi: 10.1016/j.actaastro.2008.07.016
[17]	Chiam T C.Hydromagnetic flow over a surface stretching with a power-law velocity[J].Int J of Eng Sci,1995,33(3):429-435. doi: 10.1016/0020-7225(94)00066-S
[18]	Liao S J.Comparison between homotopy analysis method and homotopy perturbation method[J].App Math Comput,2005,169(2):1186-1194. doi: 10.1016/j.amc.2004.10.058
[19]	Abbasbandy S.The application of homotopy analysis method to non-linear equations arising in heat transfer[J].Phy Lett A,2006,360(1):109-113. doi: 10.1016/j.physleta.2006.07.065
[20]	Liao S J,Cheung K F.Homotopy analysis of non-linear progressive waves in deep water[J].J of Eng Math,2003,45(2):105-116. doi: 10.1023/A:1022189509293
[21]	Liao S J.Beyond Perturbation[M].Boca Raton: Chapman & Hall/CRC Press,2003.
[22]	Rashidi M M,Domairry G,Dinarvand S.Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method[J].Comm in Nonlinear Sci and Nume Sim,2009,14(3):708-717. doi: 10.1016/j.cnsns.2007.09.015
[23]	Chowdhury M S H,Hashim I,Abdulaziz O.Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems[J].Comm in Nonlinear Sci and Numer Sim,2009,14(2):371-378. doi: 10.1016/j.cnsns.2007.09.005
[24]	Bataineh A S,Noorani M S M,Hashim I.On a new reliable modification of homotopy analysis method[J].Comm in Nonlinear Sci and Numer Sim,2009,14(2):409-423. doi: 10.1016/j.cnsns.2007.10.007
[25]	Bataineh A S,Noorani M S M,Hashim I.Modified homotopy analysis method for solving systems of second-order BVPs[J].Comm in Nonlinear Sci and Numer Sim,2009,14(2):430-442. doi: 10.1016/j.cnsns.2007.09.012
[26]	Bataineh A S,Noorani M S M,Hashim I.Solving systems of ODEs by homotopy analysis method[J].Comm in Nonlinear Sci and Numer Sim,2008,13(10):2060-2070. doi: 10.1016/j.cnsns.2007.05.026
[27]	Sajid M,Ahmad I,Hayat T,et al.Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet[J].Comm in Nonlinear Sci and Numer Sim,2008,13(10):2193-2202. doi: 10.1016/j.cnsns.2007.06.001
[28]	Sajid M,Hayat T.Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations[J].Nonlinear Analysis Real World Applications,2008,9(5):2296-2301. doi: 10.1016/j.nonrwa.2007.08.007