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Volumn 15, Issue 3, 2010, Pages 581-589

On the homotopy solution for Poiseuille flow of a fourth grade fluid

Author keywords

Analytic solution; Fourth grade fluid; Homotopy analysis method (HAM)

Indexed keywords

SHEAR FLOW;

EID: 70349796197     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.04.024     Document Type: Article
Times cited : (34)

References (40)
  • 1
    • 0042566518 scopus 로고
    • Rheological phenomena in focus
    • Elsevier, New York
    • Boger D.V., and Walter K. Rheological phenomena in focus. Rheology series vol. 4 (1993), Elsevier, New York
    • (1993) Rheology series , vol.4
    • Boger, D.V.1    Walter, K.2
  • 2
    • 36849138624 scopus 로고
    • Normal stress effects in second order fluids
    • Coleman B.D., and Markovitz H.F. Normal stress effects in second order fluids. J Appl Phys 35 (1964) 1-48
    • (1964) J Appl Phys , vol.35 , pp. 1-48
    • Coleman, B.D.1    Markovitz, H.F.2
  • 3
    • 0018681758 scopus 로고
    • Anomalous features in the model of second order fluids
    • Fosdick R.L., and Rajagopal K.R. Anomalous features in the model of second order fluids. Arch Rat Mech Anal 70 (1978) 145-152
    • (1978) Arch Rat Mech Anal , vol.70 , pp. 145-152
    • Fosdick, R.L.1    Rajagopal, K.R.2
  • 4
    • 0001526376 scopus 로고
    • Stress-deformation relations for isotropic materials
    • Rivlin R.S., and Ericksen J.L. Stress-deformation relations for isotropic materials. Js Rat Mech Anal 3 (1955) 323-425
    • (1955) Js Rat Mech Anal , vol.3 , pp. 323-425
    • Rivlin, R.S.1    Ericksen, J.L.2
  • 5
    • 0002565890 scopus 로고
    • The nonlinear field theories of mechanics
    • Springer, Berlin
    • Truesdell C., and Noll W. The nonlinear field theories of mechanics. Handbuch der Physik vol. III/3 (1965), Springer, Berlin
    • (1965) Handbuch der Physik , vol.III-3
    • Truesdell, C.1    Noll, W.2
  • 6
    • 0000762280 scopus 로고
    • On boundary conditions for fluids of the differential type
    • Sequeira A. (Ed), Plenum Press, New York
    • Rajagopal K.R. On boundary conditions for fluids of the differential type. In: Sequeira A. (Ed). Navier-Stokes equations and related nonlinear problems (1995), Plenum Press, New York
    • (1995) Navier-Stokes equations and related nonlinear problems
    • Rajagopal, K.R.1
  • 7
    • 0021127642 scopus 로고
    • An exact solution for the flow of non-Newtonian fluid past an infinite porous plate
    • Rajagoapl K.R., and Gupta A.S. An exact solution for the flow of non-Newtonian fluid past an infinite porous plate. Meccanica 19 (1984) 158-160
    • (1984) Meccanica , vol.19 , pp. 158-160
    • Rajagoapl, K.R.1    Gupta, A.S.2
  • 8
    • 0000392754 scopus 로고
    • Flow of a viscoelastic fluid between rotating disks
    • Rajagopal K.R. Flow of a viscoelastic fluid between rotating disks. Theor Comput Fluid Dyn 3 (1992) 185-206
    • (1992) Theor Comput Fluid Dyn , vol.3 , pp. 185-206
    • Rajagopal, K.R.1
  • 9
    • 53949109835 scopus 로고    scopus 로고
    • Stagnation point flow of a second grade fluid with slip
    • Labropulu F., and Li D. Stagnation point flow of a second grade fluid with slip. Int J Nonlinear Mech 43 (2008) 941-947
    • (2008) Int J Nonlinear Mech , vol.43 , pp. 941-947
    • Labropulu, F.1    Li, D.2
  • 10
    • 43649087862 scopus 로고    scopus 로고
    • Peristaltic mechanism of a Maxwell fluid in an asymmetrical channel
    • Hayat T., Alvi N., and Ali N. Peristaltic mechanism of a Maxwell fluid in an asymmetrical channel. Nonlinear Anal Real World Appl 9 (2008) 1474-1490
    • (2008) Nonlinear Anal Real World Appl , vol.9 , pp. 1474-1490
    • Hayat, T.1    Alvi, N.2    Ali, N.3
  • 11
    • 34548433485 scopus 로고    scopus 로고
    • Time-dependent magnetohydrodynamic flow induced by non-coaxial rotations of a non-torsionally oscillating porous plate and a third order fluid at infinity
    • Wang Y., and Wu W. Time-dependent magnetohydrodynamic flow induced by non-coaxial rotations of a non-torsionally oscillating porous plate and a third order fluid at infinity. Math Comput Model 46 (2007) 1277-1293
    • (2007) Math Comput Model , vol.46 , pp. 1277-1293
    • Wang, Y.1    Wu, W.2
  • 12
    • 43049159228 scopus 로고    scopus 로고
    • Flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate
    • Vieru D., Fetecau C., and Fetecau C. Flow of a viscoelastic fluid with the fractional Maxwell model between two side walls perpendicular to a plate. Appl Math Comput 200 (2008) 459-469
    • (2008) Appl Math Comput , vol.200 , pp. 459-469
    • Vieru, D.1    Fetecau, C.2    Fetecau, C.3
  • 13
    • 44649157180 scopus 로고    scopus 로고
    • Flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate
    • Vieru D., Fetecau C., and Fetecau C. Flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate. Appl Math Comput 201 (2008) 834-842
    • (2008) Appl Math Comput , vol.201 , pp. 834-842
    • Vieru, D.1    Fetecau, C.2    Fetecau, C.3
  • 14
    • 51349143639 scopus 로고    scopus 로고
    • Exact solutions for the flow of an Oldroyd-B fluid due to an infinite flat plate
    • Vieru D., Fetecau C., and Fetecau C. Exact solutions for the flow of an Oldroyd-B fluid due to an infinite flat plate. Z Angew Math Phys 59 (2008) 834-847
    • (2008) Z Angew Math Phys , vol.59 , pp. 834-847
    • Vieru, D.1    Fetecau, C.2    Fetecau, C.3
  • 15
    • 45349109022 scopus 로고    scopus 로고
    • An exact solution for start-up flow for the fractional generalized Burgers' fluid in a porous half space
    • Xue C.F., Nie J.X., and Tan W.C. An exact solution for start-up flow for the fractional generalized Burgers' fluid in a porous half space. Nonlinear Anal Theory Meth Appl 69 (2008) 2086-2094
    • (2008) Nonlinear Anal Theory Meth Appl , vol.69 , pp. 2086-2094
    • Xue, C.F.1    Nie, J.X.2    Tan, W.C.3
  • 16
    • 41349116524 scopus 로고    scopus 로고
    • Stability analysis of double diffusive convection of Maxwell fluid in a porous medium heated from below
    • Wang S.W., and Tan W.C. Stability analysis of double diffusive convection of Maxwell fluid in a porous medium heated from below. Phys Lett A 372 (2008) 3046-3050
    • (2008) Phys Lett A , vol.372 , pp. 3046-3050
    • Wang, S.W.1    Tan, W.C.2
  • 18
    • 55549111597 scopus 로고    scopus 로고
    • Travelling wave solutions to Stokes' problem for fourth grade fluid
    • Hayat T., Kara A.H., and Momoniat E. Travelling wave solutions to Stokes' problem for fourth grade fluid. Appl Math Model 33 (2009) 1613-1619
    • (2009) Appl Math Model , vol.33 , pp. 1613-1619
    • Hayat, T.1    Kara, A.H.2    Momoniat, E.3
  • 19
    • 45249101557 scopus 로고    scopus 로고
    • Exact solution of a thin film flow of an Oldroyd 6-constant fluid over a moving belt
    • Hayat T., Ellahi R., and Mahomed F.M. Exact solution of a thin film flow of an Oldroyd 6-constant fluid over a moving belt. Comm Nonlinear Sci Numer Simul 14 (2008) 133-139
    • (2008) Comm Nonlinear Sci Numer Simul , vol.14 , pp. 133-139
    • Hayat, T.1    Ellahi, R.2    Mahomed, F.M.3
  • 20
    • 10644241795 scopus 로고    scopus 로고
    • Invariant solutions of the unidirectional flow of an electrically charged power law magnetic field
    • Wafo Soh C. Invariant solutions of the unidirectional flow of an electrically charged power law magnetic field. Comm Nonlinear Sci Numer Simul 10 (2005) 537-548
    • (2005) Comm Nonlinear Sci Numer Simul , vol.10 , pp. 537-548
    • Wafo Soh, C.1
  • 21
    • 42549163315 scopus 로고    scopus 로고
    • Two dimensional stagnation point flow of an elastico-viscous fluid with partial slip
    • Ariel P.D. Two dimensional stagnation point flow of an elastico-viscous fluid with partial slip. Z Angew Math Mech 88 (2008) 320-324
    • (2008) Z Angew Math Mech , vol.88 , pp. 320-324
    • Ariel, P.D.1
  • 22
    • 34247857668 scopus 로고    scopus 로고
    • Numerical simulations of shear dependent viscoelastic flows with a combined finite element-finite volume method
    • Nadau L., and Sequeira A. Numerical simulations of shear dependent viscoelastic flows with a combined finite element-finite volume method. Comput Math Appl 53 (2007) 547-568
    • (2007) Comput Math Appl , vol.53 , pp. 547-568
    • Nadau, L.1    Sequeira, A.2
  • 23
    • 53949123352 scopus 로고    scopus 로고
    • Analytic and numerical solutions of electro-osmotically driven flow of a third grade fluid between micro-parallel plates
    • Akgul M.B., and Pakdemirli M. Analytic and numerical solutions of electro-osmotically driven flow of a third grade fluid between micro-parallel plates. Int J Nonlinear Mech 43 (2008) 985-992
    • (2008) Int J Nonlinear Mech , vol.43 , pp. 985-992
    • Akgul, M.B.1    Pakdemirli, M.2
  • 24
    • 51049099572 scopus 로고    scopus 로고
    • Flow of incompressible fluids subject to Navier's slip on the boundary
    • Hron J., Roux J., Malek J., and Rajagopal K.R. Flow of incompressible fluids subject to Navier's slip on the boundary. Comput Math Appl 56 (2008) 2128-2143
    • (2008) Comput Math Appl , vol.56 , pp. 2128-2143
    • Hron, J.1    Roux, J.2    Malek, J.3    Rajagopal, K.R.4
  • 25
    • 46449121531 scopus 로고    scopus 로고
    • Finite element solution for flow of a third grade fluid past a porous plate with partial slip
    • Sajid M., Mahmood R., and Hayat T. Finite element solution for flow of a third grade fluid past a porous plate with partial slip. Comput Math Appl 56 (2008) 1236-1244
    • (2008) Comput Math Appl , vol.56 , pp. 1236-1244
    • Sajid, M.1    Mahmood, R.2    Hayat, T.3
  • 27
    • 35348910139 scopus 로고    scopus 로고
    • Series solution of three-dimensional unsteady laminar viscous flow due to a stretching surface in a rotating fluid
    • Tan Y., and Liao S.J. Series solution of three-dimensional unsteady laminar viscous flow due to a stretching surface in a rotating fluid. J Appl Mech 74 (2007) 1011-1018
    • (2007) J Appl Mech , vol.74 , pp. 1011-1018
    • Tan, Y.1    Liao, S.J.2
  • 28
    • 41449097382 scopus 로고    scopus 로고
    • Series solutions of nano boundary layer flows by means of the homotopy analysis method
    • Cheng J., Liao S.J., Mohapatra R.N., and Vajravelu K. Series solutions of nano boundary layer flows by means of the homotopy analysis method. J Math Anal Appl 343 (2008) 233-245
    • (2008) J Math Anal Appl , vol.343 , pp. 233-245
    • Cheng, J.1    Liao, S.J.2    Mohapatra, R.N.3    Vajravelu, K.4
  • 29
    • 33845466309 scopus 로고    scopus 로고
    • Series solutions of unsteady three dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate
    • Xu H., Liao S.J., and Pop I. Series solutions of unsteady three dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate. Eur J Mech B 26 (2007) 15-27
    • (2007) Eur J Mech B , vol.26 , pp. 15-27
    • Xu, H.1    Liao, S.J.2    Pop, I.3
  • 31
    • 38649139314 scopus 로고    scopus 로고
    • Approximate solution of the nonlinear model of diffusion and reaction catalysts by means of the homotopy analysis method
    • Abbasbandy S. Approximate solution of the nonlinear model of diffusion and reaction catalysts by means of the homotopy analysis method. Chem Eng J 136 (2008) 144-150
    • (2008) Chem Eng J , vol.136 , pp. 144-150
    • Abbasbandy, S.1
  • 32
    • 35448933724 scopus 로고    scopus 로고
    • Soliton solution for the fifth-order Kdv equation with the homotopy analysis method
    • Abbasbandy S., and Zakaria F.S. Soliton solution for the fifth-order Kdv equation with the homotopy analysis method. Nonlinear Dyn 51 (2008) 83-87
    • (2008) Nonlinear Dyn , vol.51 , pp. 83-87
    • Abbasbandy, S.1    Zakaria, F.S.2
  • 33
    • 47749118739 scopus 로고    scopus 로고
    • Modified homotopy analysis method for solving systems of second-order BVPs
    • Bataineh A.S., Noorani M.S.M., and Hashim I. Modified homotopy analysis method for solving systems of second-order BVPs. Comm Nonlinear Sci Numer Simul 14 (2009) 430-442
    • (2009) Comm Nonlinear Sci Numer Simul , vol.14 , pp. 430-442
    • Bataineh, A.S.1    Noorani, M.S.M.2    Hashim, I.3
  • 34
    • 85196205374 scopus 로고    scopus 로고
    • Numerical results of flow in a third grade fluid between two porous walls, ZNA
    • in press
    • Abbasbandy S, Hayat T, Ellahi R, Asghar S. Numerical results of flow in a third grade fluid between two porous walls, ZNA, in press.
    • Abbasbandy, S.1    Hayat, T.2    Ellahi, R.3    Asghar, S.4
  • 35
    • 43649103293 scopus 로고    scopus 로고
    • Three dimensional flow over a stretching surface in a viscoelastic fluid
    • Sajid M., Hayat T., and Pop I. Three dimensional flow over a stretching surface in a viscoelastic fluid. Nonlinear Anal Real World Appl 9 (2008) 1811-1822
    • (2008) Nonlinear Anal Real World Appl , vol.9 , pp. 1811-1822
    • Sajid, M.1    Hayat, T.2    Pop, I.3
  • 36
    • 42949170894 scopus 로고    scopus 로고
    • Heat transfer analysis on MHD flow of a second grade fluid in a channel with porous medium
    • Hayat T., and Abbas Z. Heat transfer analysis on MHD flow of a second grade fluid in a channel with porous medium. Chaos, Solitons & Fractals 38 (2008) 556-567
    • (2008) Chaos, Solitons & Fractals , vol.38 , pp. 556-567
    • Hayat, T.1    Abbas, Z.2
  • 37
    • 42949165898 scopus 로고    scopus 로고
    • The application of homotopy analysis method to thin film flows of a third order fluid
    • Sajid M., and Hayat T. The application of homotopy analysis method to thin film flows of a third order fluid. Chaos, Solitons & Fractals 38 (2008) 506-515
    • (2008) Chaos, Solitons & Fractals , vol.38 , pp. 506-515
    • Sajid, M.1    Hayat, T.2
  • 38
    • 35448953657 scopus 로고    scopus 로고
    • MHD rotating flow of a viscous fluid over a shrinking surface
    • Sajid M., Javed T., and Hayat T. MHD rotating flow of a viscous fluid over a shrinking surface. Nonlinear Dyn 51 (2008) 259-265
    • (2008) Nonlinear Dyn , vol.51 , pp. 259-265
    • Sajid, M.1    Javed, T.2    Hayat, T.3
  • 39
    • 51049122143 scopus 로고    scopus 로고
    • The influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method
    • Sajid M., Awais M., Nadeem S., and Hayat T. The influence of slip condition on thin film flow of a fourth grade fluid by the homotopy analysis method. Comput Math Appl 56 (2008) 2019-2026
    • (2008) Comput Math Appl , vol.56 , pp. 2019-2026
    • Sajid, M.1    Awais, M.2    Nadeem, S.3    Hayat, T.4
  • 40
    • 45249084759 scopus 로고    scopus 로고
    • Unsteady flow and heat transfer of a second grade fluid over a stretching sheet
    • Sajid M., Ahmad I., Hayat T., and Ayub M. Unsteady flow and heat transfer of a second grade fluid over a stretching sheet. Comm Nonlinear Sci Numer Simul 14 (2009) 96-108
    • (2009) Comm Nonlinear Sci Numer Simul , vol.14 , pp. 96-108
    • Sajid, M.1    Ahmad, I.2    Hayat, T.3    Ayub, M.4


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