On series solution for unsteady boundary layer equations in a special third grade fluid

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 8, 2011, Pages 3140-3146

  Abbasbandy, S ^a   Hayat, T ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b QUAID I AZAM UNIVERSITY   (Pakistan)

Author keywords

Homotopy analysis method (HAM); Special third grade fluid; Suction injection; Unsteady boundary layer flow

Indexed keywords

BOUNDARY LAYERS; TIME SERIES ANALYSIS;

ANALYSIS METHOD; BOUNDARY LAYER EQUATIONS; HOMOTOPY ANALYSE METHOD; HOMOTOPY ANALYSIS; SERIES SOLUTIONS; SPECIAL THIRD GRADE FLUID; SUCTION/INJECTION; THIRD GRADE FLUIDS; UNSTEADY BOUNDARY LAYER; UNSTEADY BOUNDARY-LAYER FLOWS;

BOUNDARY LAYER FLOW;

EID: 79952538835     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.11.018     Document Type: Article

References (31)

1. Fosdick R.L., Rajagopal K.R. Anomalous features in the model of " second order fluids" Arch Rat Mech Anal 1979, 70:145-152.
2. Dunn J.E., Rajagopal K.R. Fluids of differential type-critical-review and thermodynamic analysis. Int J Eng Sci 1995, 33:689-729.
3. Rajagopal K.R., Na T.Y., Gupta A.S. Flow of a viscoelastic fluid over a stretching sheet. Rheol Acta 1984, 23:213-215.
4. Rajagopal K.R., Na T.Y., Gupta A.S. A non-similar boundary layer on a stretching sheet in a non-Newtonian fluid with uniform free stream. J Math Phys Sci 1987, 21:189-200.
5. Cortell R. Similarity solutions for flow and heat transfer of viscoelastic fluid over a stretching sheet. Int J Non-lin Mech 1994, 29:155-161.
6. Pakdemirli M. Conventional and multiple deck boundary layer approach to second and third grade fluid. Int J Eng Sci 1994, 32:141-154.
7. Raptis A., Perdikis C. Viscoelastic flow by the presence of radiation. ZAMM 1998, 78:277-279.
8. Lok Y.Y., Phang P., Amin N., Pop I. Unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Int J Eng Sci 2003, 41:173-186.
9. Vajravelu K., Rollins D. Hydromagnetic flow of a second grade fluid over a stretching sheet. Appl Math Comput 2004, 148:783-791.
10. Fetecau C., Fetecau C. Decay of a potential vortex in an Oldroyd-B fluid. Int J Eng Sci 2005, 43:340-351.
11. Fetecau C., Fetecau C. Unsteady flows of Oldroyd-B fluid in a channel of rectangular cross-section. Int J Non-lin Mech 2005, 40:1214-1219.
12. Tan W.C., Masuoka T. Stokes' first problem for a second grade fluid in a porous half space with heated boundary. Int J Non-lin Mech 2005, 40:515-522.
13. Hayat T., Kara A.H. Couette flow of a third grade fluid with variable magnetic fluid. Math Comput Model 2006, 43:132-137.
14. Makinde O.D. Hermite-Padé approximation approach to thermal criticality for a reactive third-grade liquid in a channel with isothermal walls. Int Commun Heat Mass Transfer 2007, 34:870-877.
15. Makinde O.D. Thermal stability of a reactive third grade fluid in a cylindrical pipe: an exploitation of Hermite-Padé approximation technique. Appl Math Comput 2007, 189:690-697.
16. Makinde O.D. On thermal stability of a reactive third-grade fluid in a channel with convective cooling at the walls. Appl Math Comput 2009, 213:270-276.
17. Makinde O.D. Thermal criticality for a reactive gravity driven thin film flow of a third grade fluid with adiabatic free surface down an inclined plane. Appl Math Mech 2009, 30:373-380.
18. Keçebaş A., Yürüsoy M. Similarity solutions of unsteady boundary layer equations of a special third grade fluid. Int J Eng Sci 2006, 44:721-729.
19. Liao S.J. Notes on the homotopy analysis: some definitions and theorems. Commun Nonlin Sci Numer Simul 2009, 14:983-997.
20. Liao S.J. Beyond perturbation: introduction to the homotopy analysis method 2003, Chapman & Hall/CRC Press, Boca Raton.
21. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 2004, 147:499-513.
22. Xu H., Liao S.J., Pop I. Series solutions of unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Acta Mech 2006, 184:87-101.
23. Hayat T., Javed T., Sajid M. Analytic solution for rotating flow and heat transfer analysis of a third-grade fluid. Acta Mech 2007, 191:219-229.
24. Hayat T., Khan M., Sajid M., Asghar S. Rotating flow of a third grade fluid in a porous space with Hall current. Nonlin Dyn 2007, 49:83-91.
25. Abbasbandy S. Homotopy analysis method for generalized Benjamin-Bona-Mahony equation. Z Angew Math Phys (ZAMP) 2008, 59:51-62.
26. Abbasbandy S., Zakaria F.S. Soliton solutions for the fifth-order KdV equation with the homotopy analysis method. Nonlin Dyn 2008, 51:83-87.
27. Abbasbandy S., Yürüsoy M., Pakdemirli M. The analysis approach of boundary layer equations of power-law fluids of second grade. Z Naturforsch A 2008, 63(a):564-570.
28. Khan M., Abbas Z., Hayat T. Analytic solution for flow of Sisko fluid through a porous medium. Transp Porous Med 2008, 71:23-37.
29. Sajid M., Hayat T. Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations. Nonlin Anal: Ser B 2008, 9:2296-2301.
30. Bataineh A.S., Noorani M.S.M., Hashim I. Approximate solutions of singular two-point BVPs by modified homotopy analysis method. Phys Lett A 2008, 372:4062-4066.
31. Parkes E.J., Abbasbandy S. Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method. Numer Meth Partial Differ Eqn 2009, 25:401-408.