Homotopy analysis for boundary layer flow of a micropolar fluid through a porous channel

Applied Mathematical Modelling

Volumn 33, Issue 11, 2009, Pages 4120-4125

  Sajid, M ^a   Abbas, Z ^b   Hayat, T ^b  

^a PAKISTAN INSTITUTE OF NUCLEAR SCIENCE AND TECHNOLOGY   (Pakistan)

^b QUAID I AZAM UNIVERSITY   (Pakistan)

Author keywords

HAM solutions; Micropolar fluid; Porous channel

Indexed keywords

HAM SOLUTIONS; HOMOTOPY ANALYSIS; HOMOTOPY ANALYSIS METHODS; MICROPOLAR FLUID; MICROPOLAR FLUIDS; MICROROTATION; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; POROUS CHANNEL; SERIES SOLUTIONS; SIMILARITY TRANSFORMATION;

AERODYNAMICS; BOUNDARY LAYERS; FLUIDS; MEATS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; ROTATION;

BOUNDARY LAYER FLOW;

EID: 67649588586     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2009.02.006     Document Type: Article

References (48)

1. Hayat T., Kara A.H., and Momoniat E. Exact flow of a third grade fluid on a porous wall. Int. J. Non-Linear Mech. 33 (2003) 1533-1537
2. Hayat T., and Kara A.H. Couette flow of a third grade fluid with variable magnetic field. Math. Comput. Modell. 43 (2006) 132-137
3. Hayat T., Khan S.B., and Khan M. The influence of Hall current on the rotating oscillating flows of an Oldroyd-B fluid in a porous medium. Nonlinear Dyn. 47 (2007) 353-362
4. Fetecau C., and Fetecau C. Decay of a potential vortex in an Oldroyd-B fluid. Int. J. Eng. Sci. 43 (2005) 340-351
5. Fetecau C., and Fetecau C. Unsteady flows of Oldroy-B fluids in a channel of rectangular cross-section. Int. J. Non-Linear Mech. 40 (2005) 1214-1219
6. Fetecau C., and Fetecau C. On some axial Couette flows of non-Newtonian fluids. Z. Angew. Math. Phys. C 56 (2005) 1098-1106
7. Fetecau C., and Fetecau C. Starting solutions for some unsteady unidirectional flows of a second grade fluid. Int. J. Eng. Sci. 43 (2005) 781-789
8. Tan W.C., and Masuoka T. Stokes first problem for a second grade fluid in a porous half-space with heated boundary. Int. J. Non-Linear Mech. 40 (2005) 515-522
9. Tan W.C., and Masuoka T. Stokes' first problem for an Oldroyd-B fluid in a porous half space. Phys. Fluids 17 (2005) 023101-023107
10. Chen C.I., Chen C.K., and Yang Y.T. Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate conditions. Heat Mass Transf. 40 (2004) 203-209
11. Eringen A.C. Simple microfluids. Int. J. Eng. Sci. 2 (1964) 205-217
12. Eringen A.C. Theory of micropolar fluids. J. Math. Mech. 16 (1966) 1-18
13. Ariman T., Turk M.A., and Sylvester N.D. Application of microcontinuum fluid mechanics- a review. Int. J. Eng. Sci. 12 (1973) 273-293
14. Eringen A.C. Microcontinuum Field Theories II: Fluent Media (2001), Springer, New York
15. Lukaszewicz G. Micropolar Fluids: Theory and Applications (1999), Birkhauser, Basel
16. Berman A.S. Laminar flow in a channel with porous walls. J. Appl. Phys. 24 (1953) 1232-1235
17. Yuan S.W. Further investigation of laminar flow in channels with porous walls. J. Appl. Phys. 27 (1956) 267-269
18. Robinson W.A. The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls. J. Eng. Math. 10 (1976) 23-40
19. Zaturska M.B., Drazin P.G., and Banks W.H.H. On the flow of a viscous fluid driven along a channel by suction at porous walls. Fluid Dyn. Res. 4 (1988) 151-178
20. Desseaus A. Influence of a magnetic field over a laminar viscous flow in a semi-porous channel. Int. J. Eng. Sci. 37 (1999) 1781-1794
21. Choi J.J., Rusak Z., and Tichy J.A. Maxwell fluid suction flow in a channel. J. Non-Newtonian Fluid Mech. 85 (1999) 165-187
22. Abbas Z., Sajid M., and Hayat T. MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel. Theor. Comput. Fluid Dyn. 20 (2006) 229-238
23. Liao S.J. Beyond Perturbation: Introduction to Homotopy Analysis Method (2003), Chapman and Hall/CRC Press, Boca Raton
24. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147 (2004) 499-513
25. Liao S.J., and Cheung K.F. Homotopy analysis of nonlinear progressive waves in deep water. J. Eng. Math. 45 (2003) 105-116
26. Wu W., and Liao S.J. Solving solitary waves with discontinuity by means of homotopy analysis method. Chaos Solitons Fractals 26 (2005) 177-185
27. Liao S.J. A uniformly valid analytic solution of 2D viscous flow past a semi-infinite flat plate. J. Fluid Mech. 385 (1999) 101-128
28. Tan Y., Xu H., and Liao S.J. Explicit series solution of travelling waves with a front of Fisher equation. Chaos Solitons Fractals 31 (2007) 462-472
29. Liao S.J. An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate. Commun. Non-Linear Sci. Numer. Simm. 11 (2006) 326-339
30. Liao S.J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl. Math. Comput. 169 (2005) 1186-1194
31. Abbasbandy S. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys. Lett. A 361 (2007) 478-483
32. Zhu S.P. An exact and explicit solution for the valuation of american put options. Quant. Finance 6 (2006) 229-242
33. Zhu S.P. A closed-form analytical solution for the valuation of convertable bonds with constant dividend yield. Anziam J. 47 (2006) 477-494
34. Wu Y., Wang C., and Liao S.J. Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos Solitons Fractals 26 (2005) 177-185
35. Hayat T., and Khan M. Homotopy solution for a generalized second grade fluid past a porous plate. Nonlinear Dyn. 42 (2005) 395-405
36. Hayat T., Khan M., and Asghar S. Magnetohydrodynamic flow of an Oldroyd 6-constant fluid. Appl. Math. Comput. 155 (2004) 417-425
37. Hayat T., Khan M., Siddiqui A.M., and Asghar S. Transient flows of a second grade fluid. Int. J. Non-Linear Mech. 39 (2004) 1621-1633
38. Hayat T., Khan M., and Asghar S. Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid. Acta Mech. 168 (2004) 213-232
39. Hayat T., Khan M., and Ayub M. On the explicit analytic solutions of an Oldroyd 6-constant fluid. Int. J. Eng. Sci. 42 (2004) 123-135
40. Hayat T., Khan M., and Ayub M. Couette and Poiseuille flows of an Oldroyd 6-constant fluid with magnetic field. J. Math. Anal. Appl. 298 (2004) 225-244
41. 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
42. Hayat T., and Sajid M. On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder. Phys. Lett. A 361 (2007) 316-322
43. Sajid M., Hayat T., and Asghar S. On the analytic solution of the steady flow of a fourth grade fluid. Phys. Lett. A 355 (2006) 18-26
44. Sajid M., Hayat T., and Asghar S. Comparison of the HAM and HPM solutions of thin film flow of non-Newtonian fluids on a moving belt. Nonlinear Dyn. 50 (2007) 27-35
45. Rees D.A.S., and Pop I. Free convection boundary layer flow of a micropolar fluid from a vertical flat plate. IMA J. Appl. Math. 61 (2001) 179-191
46. Ahmadi G. Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite flat plate. Int. J. Eng. Sci. 14 (1976) 639-646
47. Jena S.K., and Mathur M.N. Similarity solutions for laminar free convection flow of a thermo-micropolar fluid past a nonisothermal flat plate. Int. J. Eng. Sci. 19 (1981) 1431-1439
48. Guram G.S., and Smith A.C. Stagnation flows of micropolar fluids with strong and weak interactions. Comput. Math. Appl. 6 (1980) 213-233