MHD flow of a micropolar fluid near a stagnation-point towards a non-linear stretching surface

Abstract The two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an incompressible micropolar fluid over a non-linear stretching surface is studied. The resulting non-linear system of equations is solved analytically using homotopy analysis method (HAM). The convergence of the obtained series solutions is explicitly discussed and given in the form of recurrence formulas. The influence of various pertinent parameters on the velocity, microrotation and skin-friction are shown in the tables and graphs. Comparison is also made with the corresponding numerical results of viscous ( K = 0 )  [R. Cortell, Viscous flow and heat transfer over a nonlinearly stretching sheet, Appl. Math. Comput. 184 (2007) 864–873] and hydrodynamic micropolar fluid ( M = 0 ) [R. Nazar, N. Amin, D. Filip, I. Pop, Stagnation point flow of a micropolar fluid towards a stretching sheet, Internat. J. Non-Linear Mech. 39 (2004) 1227–1235] for linear and non-linear stretching sheet. An excellent agreement is found.

[1]  R. Cortell.  Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet , 2006 .

[2]  S. Abbasbandy.  THE APPLICATION OF HOMOTOPY ANALYSIS METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER , 2006 .

[3]  R. Cortell.  Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing , 2005 .

[4]  Shijun Liao,et al.  On the homotopy analysis method for nonlinear problems , 2004, Appl. Math. Comput..

[5]  J. Peddieson.  An application of the micropolar fluid model to the calculation of a turbulent shear flow , 1972 .

[6]  Tasawar Hayat,et al.  Magnetohydrodynamic flow of an Oldroyd 6-constant fluid , 2004, Appl. Math. Comput..

[7]  K. Cheung,et al.  Homotopy analysis of nonlinear progressive waves in deep water , 2003 .

[8]  Wenchang Tan,et al.  STOKES FIRST PROBLEM FOR AN OLDROYD-B FLUID IN A POROUS HALF SPACE , 2005 .

[9]  Tasawar Hayat,et al.  The influence of Hall current on the rotating oscillating flows of an Oldroyd-B fluid in a porous medium , 2007 .

[10]  Goodarz Ahmadi,et al.  Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate , 1976 .

[11]  T. Hayat,et al.  Series solution for the upper-convected Maxwell fluid over a porous stretching plate , 2006 .

[12]  S. Liao.  An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate , 2006 .

[13]  Fathi M. Allan,et al.  Derivation of the Adomian decomposition method using the homotopy analysis method , 2007, Appl. Math. Comput..

[14]  T. Hayat,et al.  MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel , 2006 .

[15]  T. Hayat,et al.  Homotopy Solutions for a Generalized Second-Grade Fluid Past a Porous Plate , 2005 .

[16]  R. Cortell.  A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet , 2006 .

[17]  T. Hayat,et al.  MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface , 2009 .

[18]  T. Hayat,et al.  Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt , 2007 .

[19]  S. Liao,et al.  Solving solitary waves with discontinuity by means of the homotopy analysis method , 2005 .

[20]  Emad M. Abo-Eldahab,et al.  Flow and heat transfer in a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium with uniform free stream , 2005, Appl. Math. Comput..

[21]  Shijun Liao,et al.  Comparison between the homotopy analysis method and homotopy perturbation method , 2005, Appl. Math. Comput..

[22]  S. Barış,et al.  Three-dimensional stagnation point flow of a second grade fluid towards a moving plate , 2006 .

[23]  S. Liao,et al.  Explicit series solution of travelling waves with a front of Fisher equation , 2007 .

[24]  S. Liao,et al.  Solving the one-loop soliton solution of the Vakhnenko equation by means of the Homotopy analysis method , 2005 .

[25]  M. Mathur,et al.  Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate , 1981 .

[26]  S. Abbasbandy,et al.  Homotopy analysis method for quadratic Riccati differential equation , 2008 .

[27]  T. Hayat,et al.  Analytic solution for flow of Sisko fluid through a porous medium , 2008 .

[28]  T. Hayat,et al.  On the analytic solution of the steady flow of a fourth grade fluid , 2006 .

[29]  Tasawar Hayat,et al.  Couette flow of a third-grade fluid with variable magnetic field , 2006, Math. Comput. Model..

[30]  Song‐Ping Zhu.  An exact and explicit solution for the valuation of American put options , 2006 .

[31]  K. Vajravelu,et al.  Fluid flow over a nonlinearly stretching sheet , 2006, Appl. Math. Comput..

[32]  C. Fetecau,et al.  Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder , 2006 .

[33]  T. Hayat,et al.  The influence of thermal radiation on MHD flow of a second grade fluid , 2007 .

[34]  T. Hayat,et al.  On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder , 2007 .

[35]  T. Hayat,et al.  Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid , 2004 .

[36]  Constantin Fetecau,et al.  UNSTEADY FLOWS OF OLDROYD-B FLUIDS IN A CHANNEL OF RECTANGULAR CROSS SECTION , 2005 .

[37]  T. Hayat,et al.  Couette and Poiseuille flows of an oldroyd 6-constant fluid with magnetic field , 2004 .

[38]  A. C. Smith,et al.  Stagnation flows of micropolar fluids with strong and weak interactions , 1980 .

[39]  Ioan Pop,et al.  Stagnation point flow of a micropolar fluid towards a stretching sheet , 2004 .

[40]  Rafael Cortell,et al.  Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field , 2006 .

[41]  C. Fetecau,et al.  Starting solutions for some unsteady unidirectional flows of a second grade fluid , 2005 .

[42]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[43]  I. Pop,et al.  Unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface , 2003 .

[44]  Rafael Cortell,et al.  Viscous flow and heat transfer over a nonlinearly stretching sheet , 2007, Appl. Math. Comput..

[45]  T. Hayat,et al.  The flow of an elastico-viscous fluid past a stretching sheet with partial slip , 2006 .

[46]  S. Liao.  A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate , 1999, Journal of Fluid Mechanics.