Summary
In this communication, we make corrections to the numerical results presented in the paper published by Takhar et al. (Acta Mech 146: 59–71, 2001) by giving a purely analytic solution to the problem. The present analytic solution obtained by homotopy analysis method is highly accurate and uniformly valid for all values of the dimensionless time 0 ≤ ξ ≤ 1. A comparison is made with the results already present in the literature.
Similar content being viewed by others
References
Takhar H.S., Chamkha J.A. and Nath G. (2001). Unsteady three-dimensional MHD boundary-layer flow due to the impulsive motion of a stretching surface. Acta Mech. 146: 59–71
Liao S.J. (2006). An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Commun. Nonlinear Sci. Numer. Simul. 11: 326–339
Xu H. and Liao S.J. (2005). Series solutions of unsteady magnetohydrodynamic flows of non–Newtonian fluids caused by an impulsively stretching plate. J. Non-Newtonian Fluid Mech. 129: 46–55
Ali A. and Mehmood A. (2008). Homotopy analysis of unsteady boundary layer flow adjacent to permeable stretching surface in a porous medium. Commun. Nonlinear Sci. Numer. Simul. 13: 340–349
Mehmood A., Ali A. and Shah T. (2008). Heat transfer analysis of unsteady boundary layer flow by homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. 13: 902–912
Wang C.Y. (1984). The three-dimensional flow due to a stretching flat surface. Phys. Fluids 27(8): 1915–1917
Liao S.J. (2003). Beyond Perturbation: Introduction to Homotopy Analysis Method. Chapman & Hall/CRC Press, London/Boca Raton
Hilton P.J. (1953). An Introduction to Homotopy Theory. Cambridge University Press, London
Sen S. (1983). Topology and Geometry for Physicists. Academic, FL
Xu H., Liao S.J. and Pop I. (2006). Series solutions of unsteady boundary-layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Acta Mech. 184: 87–101
Liao S.J. (1999). A uniformly valid analytical solution of 2D viscous flow past a semi infinite flat plate. J. Fluid Mech. 385: 101–128
Liao S.J. (1999). An explicit, totally analytic approximate solution for Blasius viscous flow problems. Int. J. Nonlinear Mech. 34: 759–778
Liao S.J. (2002). An analytic approximation of the drag coefficient for the viscous flow past a sphere. Int. J. Nonlinear Mech. 37: 1–18
Liao S.J. and Campo A. (2002). Analytic solutions of the temperature distribution in Blasius viscous flow problems. J. Fluid Mech. 453: 411–425
Liao S.J. and Cheung K.F. (2003). Homotopy analysis of nonlinear progressive waves in deep water. J. Engng Math. 45(2): 105–116
Wang C. (2003). On the explicit analytic solutions of Cheng–Chang equations. Int. J. Heat Mass Transf. 46(101): 1855–1860
Xu H. (2004). An explicit analytic solution for free convection about a vertical flat plate embedded in a porous media by means of homotopy analysis method. Appl. Math. Comput. 158: 433–443
Liao S.J. (2004). On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147: 499–513
Yang C. and Liao S.J. (2006). On the explicit, purely analytic solution of Von Karman swirling viscous flow. Commun. Nonlinear Sci. Numer. Simul. 11(1): 83–93
Liao S.J. (2005). A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Int. J. Heat Mass Transf. 48: 2529–2539
Allan F.M. and Syam M.I. (2005). On analytic solution of the non-homogeneous Blasius problem. J. Comput. Appl. Math. 182: 355–365
Mehmood A. and Ali A. (2006). Analytic solution of generalized three-dimensional flow and heat transfer over a stretching plane wall. Int. Commun. Heat Mass Transf. 33: 1243–1552
Mehmood, A., Ali, A.: An explicit analytic solution of steady three-dimensional stagnation point flow of second grade fluid towards a heated plate. ASME J. Appl. Mech. (2007) (in press)
Liao S.J. (2005). A challenging nonlinear problem for numerical techniques. J. Comput. Appl. Math. 181: 467–472
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mehmood, A., Ali, A., Takhar, H.S. et al. Unsteady three-dimensional MHD boundary-layer flow due to the impulsive motion of a stretching surface (Acta Mech. 146, 59–71, 2001). Acta Mech 199, 241–249 (2008). https://doi.org/10.1007/s00707-007-0555-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-007-0555-4