T. Hayat, M. Nawaz, S. Obaidat. Axisymmetric Magnetohydrodynamic flow of a Micropolar Fluid Between Unsteady Stretching Surfaces[J]. Applied Mathematics and Mechanics, 2011, 32(3): 344-356. doi: 10.3879/j.issn.1000-0887.2011.03.010
Citation: T. Hayat, M. Nawaz, S. Obaidat. Axisymmetric Magnetohydrodynamic flow of a Micropolar Fluid Between Unsteady Stretching Surfaces[J]. Applied Mathematics and Mechanics, 2011, 32(3): 344-356. doi: 10.3879/j.issn.1000-0887.2011.03.010

Axisymmetric Magnetohydrodynamic flow of a Micropolar Fluid Between Unsteady Stretching Surfaces

doi: 10.3879/j.issn.1000-0887.2011.03.010
  • Received Date: 2010-08-17
  • Rev Recd Date: 2010-12-01
  • Publish Date: 2011-03-15
  • This investigation examines the time dependent MHD flow problem of a micropolar fluid between two radially stretching sheets.Both the cases (n=0,0.5) of strong and weak concentrations of microelements are taken into account.Suitable transformations were employed for the conversion of partial differential equations into the ordinary differential equations.The solutions of the resulting problems were developed by a homotopy analysis method (HAM).Angular velocity,skin friction coefficient and wall couple stress coefficient were illustrated for various parameters of interest.
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  • [1]
    Eringen A C. Theory of micropolar fluids[J]. J Math, 1966, 16(1): 1-18.
    [2]
    Gorla R S R, Mansour M A, Mohammedien A A. Combined convection in an axisymmetric stagnation flow of micropolar fluid[J]. Int J Num Meth Heat Fluid Flow, 1996, 6(4): 47-55.
    [3]
    Gorla R S R, Takhar H S. Boundary layer flow of micropolar fluid on rotating axisymmetric surfaces with a concentrated heat source[J]. Acta Mechanica, 1994, 105(1/4): 1-10. doi: 10.1007/BF01183937
    [4]
    Guram G S, Smith A C. Stagnation flows of micropolar fluids with strong and weak interactions[J]. Compu Math Appl, 1980, 6(2): 213-233.
    [5]
    Kumari M, Nath G. Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point[J]. Int J Eng Sci, 1984, 22(16): 755-768. doi: 10.1016/0020-7225(84)90048-X
    [6]
    Abdullah I, Amin N. A micropolar fluid model of blood flow through a tapered artery with a stenosis[J]. Mathematical Methods in the Applied Sciences, 2010, 33(16): 1910-1923.doi: 10.1002/mma.1303.
    [7]
    Seddeek M A. Flow of a magneto-micropolar fluid past a continuously moving plate[J]. Phy Lett A, 2003, 306(4): 255-257. doi: 10.1016/S0375-9601(02)01513-X
    [8]
    Nazar R, Amin N, Filip D, Pop I. Stagnation point flow of a micropolar fluid towards a stretching sheet[J]. Int J Non-Linear Mech, 2004, 39(7): 1227-1235. doi: 10.1016/j.ijnonlinmec.2003.08.007
    [9]
    Takhar H S, Bhargava R, Agrawal R S, Balaji A V S. Finite element solution of a micropolar fluid flow and heat transfer between two porous discs[J]. Int J Eng Sci, 2000, 38(17):1907-1922. doi: 10.1016/S0020-7225(00)00019-7
    [10]
    Abo-Eldahab E M, Ghonaim A F. Radiation effects on heat transfer of a micropolar fluid through a porous medium[J]. Appl Math Comp, 2005, 169(1):500-510. doi: 10.1016/j.amc.2004.09.059
    [11]
    Nazar R, Amin N, Pop I. Free convection boundary layer flow on an isothermal sphere in a micropolar fluid[J]. Int Comm Heat Mass Trans, 2002, 29:377-386. doi: 10.1016/S0735-1933(02)00327-5
    [12]
    Sahoo B. Effects of partial slip on axisymmetric flow of an electrically conducting viscoelastic fluid past a stretching sheet[J]. Cent Eur J Phys, 2010, 8(3):498-508. doi: 10.2478/s11534-009-0105-x
    [13]
    萨胡 B. 二阶流体通过径向伸展平面时滑移、黏性耗散、焦耳热对MHD流动的影响[J]. 应用数学和力学,2010, 31(2): 150-162. (Sahoo B. Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(2):159-173.)
    [14]
    Hayat T, Nawaz M. Effect of heat transfer on magnetohydrodynamic axisymmetric flow between two stretching sheets[J]. Z Naturforsch, 2010, 65(11):1-8.
    [15]
    Liao S J. Beyond Perturbation: Introduction to Homotopy Analysis Method[M]. Boca Raton: Chapman and Hall CRC Press, 2003.
    [16]
    Liao S J. Notes on the homotopy analysis method: some definitions and theorems[J]. Comm Nonlinear Sci Num Simu, 2009, 14(4): 983-997. doi: 10.1016/j.cnsns.2008.04.013
    [17]
    Liao S J. A new branch of solutions of unsteady boundary layer flows over an impermeable stretched plate[J]. Int J Heat Mass Transfer, 2005, 48(12): 2529-2539. doi: 10.1016/j.ijheatmasstransfer.2005.01.005
    [18]
    Cheng J, Liao S J. Series solutions of nano-boundary layer flows by means of the homotopy analysis method[J]. J Math Anal Appl, 2008, 343(1): 233-245. doi: 10.1016/j.jmaa.2008.01.050
    [19]
    Abbasbandy S. Homotopy analysis method for the Kawahara equation[J]. Nonlinear Analysis: Real World Applications, 2010, 11(1): 307-310.
    [20]
    Abbasbandy S, Hayat T. Solution of the MHD Falkner-Skan flow by homotopy analysis method[J]. Comm Nonlinear Sci Num Simu, 2009, 14(9/10): 3591-3598. doi: 10.1016/j.cnsns.2009.01.030
    [21]
    Abbasbandy S, Shirzadi A. A new application of the homotopy analysis method: Solving the Sturm—Liouville problems[J]. Comm Nonlinear Sci Num Simu, 2011, 16(1): 112-126. doi: 10.1016/j.cnsns.2010.04.004
    [22]
    Hashim I, Abdulaziz O, Momani S. Homotopy analysis method for fractional IVPs[J]. Comm Nonlinear Sci Numer Simu, 2009, 14(3): 674-684.
    [23]
    Bataineh A S, Noorani M S M, Hashim I. On a new reliable modification of homotopy analysis method[J]. Comm Nonlinear Sci Numer Simu, 2009, 14(2): 409-423. doi: 10.1016/j.cnsns.2007.10.007
    [24]
    Bataineh A S, Noorani M S M, Hashim I. Modified homotopy analysis method for solving systems of second-order BVPs[J]. Comm Nonlinear Sci Num Simu, 2009, 14(2): 430-442. doi: 10.1016/j.cnsns.2007.09.012
    [25]
    Allan F M. Derivation of the Adomian decomposition method using the homotopy analysis method[J]. Appl Math Comp, 2007, 190(1): 6-14. doi: 10.1016/j.amc.2006.12.074
    [26]
    Hayat T, Nawaz M. Soret and Dufour effects on the mixed convection flow of a second grade fluid subject to Hall and ion-slip currents[J]. Int J Num Methods Fluids. doi: 10.1002/fld.2405.
    [27]
    Hayat T, Qasim M, Abbas Z. Radiation and mass transfer effects on the magnetohydrodynamic unsteady flow induced by a stretching sheet[J]. Z Naturforch A, 2010, 65(3): 231-239.
    [28]
    Hayat T, Mustafa M, Pop I. Heat and mass transfer for Soret and Dufour’s effect on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with a viscoelastic fluid[J]. Comm Nonlinear Sci Num Simu, 2010, 15(5):1183-1196. doi: 10.1016/j.cnsns.2009.05.062
    [29]
    Hayat T, Nawaz M. Magnetohydrodynamic three-dimensional flow of a second-grade fluid with heat transfer[J]. Z Naturforsch A, 2010, 65(8): 683-691.
    [30]
    Hayat T, Nawaz M. Hall and ion-slip effects on three-dimensional flow of a second grade fluid[J]. Int J Num Methods Fluids. doi: 10.1002/fld.2251.
    [31]
    Hayat T, Awais M. Three-dimensional flow of an upper-convected Maxwell (UCM) fluid[J]. Int J Num Methods Fluids. doi: 10.1002/fld.2289.
    [32]
    Hayat T, Mustafa M, Mesloub S. Mixed convection boundary layer flow over a stretching surface filled with a Maxwell fluid in the presence of Soret and Dufour’s effects[J]. Z Naturforsch A , 2010, 65(5):401-410.
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