The application of homotopy perturbation method for MHD flows of UCM fluids above porous stretching sheets

Computers and Mathematics with Applications

Volumn 59, Issue 10, 2010, Pages 3328-3337

  Raftari, Behrouz ^a,b   Yildirim, Ahmet ^a,b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b EGE UNIVERSITY   (Turkey)

Author keywords

Homotopy perturbation method; MHD flow; Porous stretching sheet; UCM fluid

Indexed keywords

ANALYTIC SOLUTION; ANALYTICAL EXPRESSIONS; ANALYTICAL SOLUTIONS; APPROXIMATE ANALYTICAL SOLUTIONS; HOMOTOPY ANALYSIS METHODS; HOMOTOPY PERTURBATION METHOD; MHD FLOW; NONLINEAR DIFFERENTIAL EQUATION; NONLINEAR PROBLEMS; POWER SERIES; STRETCHING SHEET; UCM FLUID; UPPER-CONVECTED MAXWELL FLUIDS;

DIFFERENTIAL EQUATIONS; FLUIDS; LINEARIZATION; NONLINEAR EQUATIONS;

PERTURBATION TECHNIQUES;

EID: 77953131633     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.03.018     Document Type: Article

References (46)

1. Agassant J.F., Avens P., Sergent J., and Carreau P.J. Polymer, Processing: Principles and Modeling (1991), Hanser Publishers, Munich
2. Lazurkin J.S. Cold-drawing of glass-like and crystalline polymers. J. Polym. Sci. 30 121 (1958) 595-604
3. Ginzburg B.M. On the cold drawing of semicrystalline polymers. J. Macromol. Sci. Part B 44 2 (2005) 217-223
4. Casas F., Alba-Simionesco C., Lequeux F., and Montes H. Cold drawing of polymers: plasticity and aging. J. Non-Cryst. Solids 352 42-49 (2006) 5076-5080
5. Bird R.B., Armstrong R.C., and Hassager O. Dynamics of Polymeric Liquids, vols. I and II (1987), Wiley, New York
6. Dandapat B.S., and Gupta A.S. Flow and heat transfer in a viscoelastic fluid over a stretching sheet. Internat. J. Non-Linear Mech. 24 3 (1989) 215-219
7. Subhas A., and Veena P. Viscoelastic fluid flow and heat transfer in a porous medium over a stretching sheet. Internat. J. Non-Linear Mech. 33 3 (1998) 531-540
8. Cortell R. A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet. Appl. Math. Comput. 168 (2005) 557-566
9. Cortell R. Effects of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet. Phys. Lett. A 357 (2006) 298-305
10. Cortell R. 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. Int. J. Heat Mass Transfer 49 (2006) 1851-1856
11. Hayat T., Khan M., and Asghar S. Magnetohydrodynamic flow of an Oldroyd 6-constant fluid. Appl. Math. Comput. 155 (2004) 417-425
12. Chakrabarti A., and Gupta A.S. Hydromagnetic flow heat and mass transfer over a stretching sheet. Quart. Appl. Math. 37 (1973) 73-78
13. Kandasamy R., Periasamy K., and Sivagnana Prabhu K.K. Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects. Int. J. Heat Mass Transfer 48 (2005) 4557-4561
14. Chung-Liu I. Flow and heat transfer of an electrically-conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field. Int. J. Non-Linear Mech. 40 (2005) 465-474
15. Takhar H.S., Chamkha A.J., and Nath G. Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species. Internat. J. Engrg. Sci. 38 (2003) 1303-1314
16. Chung-Liu I. A note on heat and mass transfer for a hydromagnetic flow over a stretching sheet. Int. Commun. Heat Mass Transfer 32 (2005) 1075-1084
17. Fosdick R.L., and Rajagopal K.R. Anomalous features in the model of second-order fluids. Arch. Ration. Mech. Anal. 70 (1979) 145-152
18. Dunn J.E., and Rajagopal K.R. Fluids of differential type: critical review and thermodynamic analysis. Internat. J. Engrg. Sci. 33 (1995) 689-729
19. Hayat T., Abbas Z., and Sajid M. Series solution for the upper-convected Maxwell fluid over a porous stretching plate. Phys. Lett. A 358 (2006) 396-403
20. Alizadeh-Pahlavan A., Aliakbar V., Vakili-Farahani F., and Sadeghy K. MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 473-488
21. Hillermeier C. Generalized homotopy approach to multiobjective optimization. Int. J. Optim. Theory Appl. 110 3 (2001) 557-583
22. Liao S.J. Boundary element method for general nonlinear differential operators. Eng. Anal. Bound. Elem. 20 2 (1997) 91-99
23. He J.H. An approximate solution technique depending upon an artificial parameter. Commun. Nonlinear Sci. Numer. Simul. 3 2 (1998) 92-97
24. He J.H. Newton-like iteration method for solving algebraic equations. Commun. Nonlinear Sci. Numer. Simul. 3 2 (1998) 106-109
25. Yildirim A. On the solution of the nonlinear Kortewegde Vries equation by the homotopy perturbation method. Commun. Numer. Methods Eng. (2008) 10.1002/cnm.1146
26. Ganji D.D., and Rajabi A. Assessment of homotopyperturbation and perturbation methods in heat radiation equations. Int. Commun. Heat Mass Transfer 33 (2006) 391-400
27. Domairry G., and Nadim N. Assessment of homotopy analysis method and homotopy perturbation method in non-linear heat transfer equation. Int. Commun. Heat Mass Transfer 35 (2008) 93-102
28. Rajabi A. Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Phys. Lett. A 364 (2007) 33-37
29. Xu L. He's homotopy perturbation method for a boundary layer equation in unbounded domain. Comput. Math. Appl. 54 (2007) 1067-1070
30. He J.H. Periodic solutions and bifurcations of delay-differential equations. Phys. Lett. A 347 (2005) 228-230
31. Ganji D.D. The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer. Phys. Lett. A 355 (2006) 337-341
32. Yildirim A. Application of He's homotopy perturbation method for solving the Cauchy reaction-diffusion problem. Comput. Math. Appl. 57 4 (2009) 612-618
33. Yildirim A. Homotopy perturbation method to obtain exact special solutions with solitary patterns for Boussinesq-like B (m, n) equations with fully nonlinear dispersion. J. Math. Phys. 50 2 (2009) 023510/1-10
34. Yildirim A., and Koçak H. Homotopy perturbation method for solving the space-time fractional advection-dispersion equation. Adv. Water Resour. 32 12 (2009) 1711-1716
35. Yildirim A. Exact solitary-wave solutions for the nonlinear dispersive K (2, 2, 1) and K (3, 3, 1) equations by the homotopy perturbation method. Modern Phys. Lett. B 23 30 (2009) 3667-3675
36. A. Yildirim, Analysis of fractional heat-like and wave-like equations with variable coefficients using the homotopy perturbation method, Internat. J. Modern Phys. B (2009) (in press).
37. Raftari B. Application of He's homotopy perturbation method and variational iteration method for nonlinear partial integro-differential equations. World Appl. Sci. J. 7 4 (2009) 399-404
38. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simul. 6 2 (2005) 207-208
39. He J.H. Homotopy perturbation method for solving boundary value problems. Phys. Lett. A 350 (2006) 87-88
40. H. Bararnia, E. Ghasemi, S. Soleimani, A. Barari, D.D. Ganji, HPM-Padé method on natural convection of Darcian fluid about a vertical full cone embedded in porous media, J. Porous Med. (2010) (in press).
41. Barari A., Ghotbi A.R., Farrokhzad F., and Ganji D.D. Variational iteration method and homotopy-perturbation method for solving different types of wave equations. J. Appl. Sci. 8 1 (2008) 120-126
42. Geng F., Cui M., and Zhang B. Method for solving nonlinear initial value problems by combining homotopy perturbation and reproducing kernel Hilbert space methods. Nonlinear Anal. RWA 11 2 (2010) 637-644
43. Barari A., Omidvar M., Ghotbi A.R., and Ganji D.D. Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations. Acta Appl. Math. 104 2 (2008) 161-171
44. Biazar J., Ayati Z., and Ebrahimi H. Homotopy perturbation method for general form of porous medium equation. J. Porous Med. 12 11 (2009) 1121-1127
45. Sadeghy K., Najafi A.H., and Saffaripour M. Sakiadis flow of an upper-convected Maxwell fluid. Int. J. Non-Linear Mech. 40 (2005) 1220-1228
46. Schlichting H. Boundary Layer Theory. sixth ed. (1964), McGraw-Hill, New York