An efficient analytical approach for MHD viscous flow over a stretching sheet via homotopy perturbation sumudu transform method

Abstract In this paper, we present an efficient analytical approach based on new homotopy perturbation sumudu transform method (HPSTM) to investigate the magnetohydrodynamics (MHD) viscous flow due to a stretching sheet. The viscous fluid is electrically conducting in the presence of magnetic field and the induced magnetic field is neglected for small magnetic Reynolds number. Finally, some numerical comparisons among the new HPSTM, the homotopy perturbation method and the exact solution have been made. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.

[1]  Davood Domiri Ganji,et al.  Explicit Solutions of Helmholtz Equation and Fifth-order KdV Equation using Homotopy Perturbation Method , 2006 .

[2]  R. Usha,et al.  The Axisymmetric Motion of a Liquid Film on an Unsteady Stretching Surface , 1995 .

[3]  Ji-Huan He Homotopy perturbation technique , 1999 .

[4]  Ahmet Yildirim,et al.  An Algorithm for Solving the Fractional Nonlinear Schrödinger Equation by Means of the Homotopy Perturbation Method , 2009 .

[5]  T. Hayat,et al.  Homotopy Perturbation Method and Axisymmetric Flow over a Stretching Sheet , 2006 .

[6]  Taylan Altan,et al.  Metal Forming : Fundamentals and Applications , 1983 .

[7]  Shyam L. Kalla,et al.  ANALYTICAL INVESTIGATIONS OF THE SUMUDU TRANSFORM AND APPLICATIONS TO INTEGRAL PRODUCTION EQUATIONS , 2003 .

[8]  T C Chaim,et al.  HYDROMAGNETIC FLOW OVER A SURFACE STRETCHING WITH A POWER-LAW VELOCITY , 1995 .

[9]  P. D. Ariel,et al.  MHD flow of a viscoelastic fluid past a stretching sheet with suction , 1994 .

[10]  G. K. Watugala,et al.  Sumudu Transform - a New Integral Transform to Solve Differential Equations and Control Engineering Problems , 1992 .

[11]  B. C. Sakiadis Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface , 1961 .

[12]  Ji-Huan He,et al.  Addendum:. New Interpretation of Homotopy Perturbation Method , 2006 .

[13]  M. Noor,et al.  Traveling Wave Solutions of Seventh-order Generalized KdV Equations Using He's Polynomials , 2009 .

[14]  I. M. Hall,et al.  On the series solution to the laminar boundary layer with stationary origin on a continuous, moving porous surface , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[16]  Yasir Khan,et al.  An effective modification of the homotopy perturbation method for MHD viscous flow over a stretching sheet , 2013 .

[17]  Chao-Yang Wang,et al.  The three‐dimensional flow due to a stretching flat surface , 1984 .

[18]  Ji-Huan He HOMOTOPY PERTURBATION METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS , 2006 .

[19]  Ji-Huan He,et al.  Α Review on Some New Recently Developed Nonlinear Analytical Techniques , 2000 .

[20]  Ji-Huan He,et al.  Asymptotology by homotopy perturbation method , 2004, Appl. Math. Comput..

[21]  Hossein Jafari,et al.  Application of Homotopy-Perturbation Method for Solving Gas Dynamics Equation , 2008 .

[22]  B. C. Sakiadis Boundary‐layer behavior on continuous solid surfaces: I. Boundary‐layer equations for two‐dimensional and axisymmetric flow , 1961 .

[23]  Devendra Kumar,et al.  Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations , 2011 .

[24]  Fethi Bin Muhammed Belgacem,et al.  Introducing and Analysing Deeper Sumudu Properties , 2006 .

[25]  Ahmet Yildirim,et al.  A Comparative Study of He's Homotopy Perturbation Method for Determining Frequency-amplitude Relation of a Nonlinear Oscillator with Discontinuities , 2007 .

[26]  H. Andersson MHD flow of a viscoelastic fluid past a stretching surface , 1992 .

[27]  Ji-Huan He New interpretation of homotopy perturbation method , 2006 .

[28]  P. Donald Ariel,et al.  Extended homotopy perturbation method and computation of flow past a stretching sheet , 2009, Comput. Math. Appl..

[29]  Chaoyang Wang Liquid film on an unsteady stretching surface , 1990 .

[30]  Asghar Ghorbani,et al.  He's Homotopy Perturbation Method for Calculating Adomian Polynomials , 2007 .

[31]  Kirill Ilinski,et al.  New application of functional integrals to classical mechanics , 2005 .

[32]  Ji-Huan He,et al.  The homotopy perturbation method for nonlinear oscillators with discontinuities , 2004, Appl. Math. Comput..

[33]  A. A. Karaballi,et al.  Sumudu transform fundamental properties investigations and applications. , 2006 .

[34]  Asghar Ghorbani,et al.  Beyond Adomian polynomials: He polynomials , 2009 .

[35]  P. S. Gupta,et al.  Heat and mass transfer on a stretching sheet with suction or blowing , 1977 .

[36]  A. Acrivos,et al.  Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier—Stokes equations with reverse flow , 1981, Journal of Fluid Mechanics.

[37]  P. Donald Ariel,et al.  Computation of MHD flow due to moving boundaries , 2009, Int. J. Comput. Math..

[38]  Ji-Huan He,et al.  Recent development of the homotopy perturbation method , 2008 .

[39]  T. C. Chiam Hydromagnetic flow over a surface stretching with a power-law velocity , 1995 .

[40]  Ji-Huan He A coupling method of a homotopy technique and a perturbation technique for non-linear problems , 2000 .

[41]  E. G. Fisher,et al.  Extrusion of plastics , 1976 .

[42]  D. Ganji The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer , 2006 .

[43]  L. Crane Flow past a stretching plate , 1970 .

[44]  C. Wang,et al.  Slip flow due to a stretching cylinder , 1988 .