A uniformly valid series solution to the unsteady stagnation-point flow towards an impulsively stretching surface

Science China: Physics, Mechanics and Astronomy

Volumn 53, Issue 3, 2010, Pages 521-526

  Cheng, Jun ^a   Dai, Shi Qiang ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

Homotopy analysis method; Stagnation point; Stretching sheet; Unsteady boundary layer flows

Indexed keywords

EXPLICIT FORMULA; HOMOTOPIES; HOMOTOPY ANALYSIS METHODS; INCOMPRESSIBLE VISCOUS FLUIDS; LOCAL FRICTION; NUMERICAL TESTS; PERTURBATION SOLUTIONS; PHYSICAL PARAMETERS; SERIES SOLUTIONS; SPATIAL REGIONS; STAGNATION POINTS; STAGNATION-POINT FLOW; STRETCHING SHEET; STRETCHING SURFACE; STRETCHING VELOCITY;

BOUNDARY LAYER FLOW; BOUNDARY LAYERS; FRICTION; TWO DIMENSIONAL;

PAPER SHEETING;

EID: 77953175838     PISSN: 16747348     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11433-010-0122-1     Document Type: Article

References (21)

1. Nazar R, Amin N, Filip D, et al. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. Int J Eng Sci, 2004, 42:1241-1253
2. Liao S J. The proposed homotopy analysis technique for the solution of nonlinear problems. Dissertation for Doctoral Degree. Shanghai: Shanghai Jiao Tong University, 1992
3. Liao S J. Homotopy analysis method: An analytic technique not depending on small parameters. Shanghai J Mech, 1997, 18:196-200
4. Liao S J. Numerically solving nonlinear problems by the homotopy analysis method. Comput Mech, 1997, 20:530-540
5. Liao S J. Notes on the homotopy analysis method Some de n itions and theorems. Commun Nonlinear Sci Numer Simul, 2009, 14:983-997
6. Yamashita M, Yabushita K, Tsuboi K. An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method. J Phys A, 2007, 40:8403-8416
7. Liao S J. An optimal homotopy-analysis approach for strongly nonlinear di e rential equations. Commun Nonlinear Sci Numer Simul, 2010, doi: 10.1016/j.cnsns.2009.09.002
8. Cheng J, Liao S J, Mohapatra R N, et al. Series solutions of nano boundary layer o ws by means of the homotopy analysis method. J Math Anal Appl, 2008, 343:233-245
9. Cheng J, Liao S J, Mohapatra R N, et al. Series solutions of stagnation slip o w and heat transfer by the homotopy analysis method. Sci China Ser G-Phys Mech Astron, 2009, 52:893-899
10. Xu H, Liao S J. Laminar o w and heat transfer in the boundary-layer of non-Newtonian u ids over a stretching a t sheet. Comput Math Appl, 2009, 57:1425-1431
11. Yao B. Series solution of the temperature distribution in the Falkner-Skan wedge o w by the homotopy analysis method. Euro J Mech-B/Fluids, 2009, 28:689-693
12. Abbasbandy S, Hayat T. Solution of the MHD Falkner-Skan o w by homotopy analysis method. Commun Nonlinear Sci Numer Simul, 2009, 14:3591-3598
13. Liao S J. A general approach to get series solution of non-similarity boundary-layer flows. Commun Nonlinear Sci Numer Simul, 2009, 14:2144-2159
14. Cheng J, Liao S J, Pop I. Analytic series solution for unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium. Transport Porous Media, 2005, 61:365-379
15. Liao S J. An analytic solution of unsteady boundary-lay o ws caused by an impulsively stretching plate. Commun Nonlinear Sci Numer Simul, 2006, 11:326-339
16. Xu H, Liao S J. A series solution of the unsteady Von Karman swirling viscous o ws. Acta Appl Math, 2007, 47:215-231
17. Xu H, Liao S J, Pop I. Series solutions of unsteady three-dimensional mhd o w and heat transfer in the boundary layer over an impulsively stretching plate. Euro Mech-B/Fluids, 2007, 26:15-27
18. Sajid M, Ahmad I, Hayat T, et al. Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet. Commun Nonlinear Sci Numer Simul, 2008, 13:2193-2202
19. Mehmood A, Ali A. Unsteady boundary layer flow due to an impulsively started moving plate. In: Proceedings of the Institution of Mechanical Engineers, Part G. London: Professional Engineering Publishing, 2007, 221:385-390
20. Mehmood A, Ali A, Takhar H S, et al. Unsteady three-dimensional MHD boundary-layer o w due to the impulsive motion of a stretching surface. Acta Mech, 2008, 199:241-249
21. Liao S J. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press, 2003