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Volumn 15, Issue 11, 2010, Pages 3423-3434

Three analytical methods applied to Jeffery-Hamel flow

Author keywords

Differential Transformation Method (DTM); Homotopy Analysis Method (HAM); Homotopy Perturbation Method (HPM); Jeffery Hamel flows

Indexed keywords

NUMERICAL METHODS; PERTURBATION TECHNIQUES;

EID: 77952238986     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.12.023     Document Type: Article
Times cited : (67)

References (50)
  • 1
    • 0001083899 scopus 로고
    • The two-dimensional steady motion of a viscous fluid
    • Jeffery G.B. The two-dimensional steady motion of a viscous fluid. Philos Mag 6 (1915) 455-465
    • (1915) Philos Mag , vol.6 , pp. 455-465
    • Jeffery, G.B.1
  • 2
    • 0002347569 scopus 로고
    • Spiralformige Bewgungen, Zaher Flussigkeiten, Jahresbericht der Deutschen
    • Hamel G. Spiralformige Bewgungen, Zaher Flussigkeiten, Jahresbericht der Deutschen. Math Vereinigung 25 (1916) 34-60
    • (1916) Math Vereinigung , vol.25 , pp. 34-60
    • Hamel, G.1
  • 3
    • 0001375605 scopus 로고
    • The steady two-dimensional radial flow of viscous fluid between two inclined plane walls
    • Rosenhead L. The steady two-dimensional radial flow of viscous fluid between two inclined plane walls. Proc Roy Soc A 175 (1940) 436-467
    • (1940) Proc Roy Soc A , vol.175 , pp. 436-467
    • Rosenhead, L.1
  • 5
    • 0003187144 scopus 로고    scopus 로고
    • PhD thesis, Dept. Mechanical Engineering, the University of Western Ontario;
    • Sadri R. Channel entrance flow, PhD thesis, Dept. Mechanical Engineering, the University of Western Ontario; 1997.
    • (1997) Channel entrance flow
    • Sadri, R.1
  • 6
    • 0022925935 scopus 로고
    • Bifurcations of two-dimensional channel flows
    • Sobey I.J., and Drazin P.G. Bifurcations of two-dimensional channel flows. J Fluid Mech 171 (1986) 263-287
    • (1986) J Fluid Mech , vol.171 , pp. 263-287
    • Sobey, I.J.1    Drazin, P.G.2
  • 7
    • 0028446807 scopus 로고
    • Temporal stability of Jeffery-Hamel flow
    • Hamadiche M., Scott J., and Jeandel D. Temporal stability of Jeffery-Hamel flow. J Fluid Mech 268 (1994) 71-88
    • (1994) J Fluid Mech , vol.268 , pp. 71-88
    • Hamadiche, M.1    Scott, J.2    Jeandel, D.3
  • 8
    • 0000902512 scopus 로고
    • Laminar flow in symmetrical channels with slightly curved walls. I: On the Jeffery-Hamel solutions for flow between plane walls
    • Fraenkel L.E. Laminar flow in symmetrical channels with slightly curved walls. I: On the Jeffery-Hamel solutions for flow between plane walls. Proc Roy Soc A 267 (1962) 119-138
    • (1962) Proc Roy Soc A , vol.267 , pp. 119-138
    • Fraenkel, L.E.1
  • 9
    • 33750451236 scopus 로고    scopus 로고
    • Hermite-Pade' approximation approach to MHD Jeffery-Hamel flows
    • Makinde O.D., and Mhone P.Y. Hermite-Pade' approximation approach to MHD Jeffery-Hamel flows. Appl Math Comput 181 (2006) 966-972
    • (2006) Appl Math Comput , vol.181 , pp. 966-972
    • Makinde, O.D.1    Mhone, P.Y.2
  • 10
    • 0002734020 scopus 로고    scopus 로고
    • A review on some new recently developed nonlinear analytical techniques
    • He J.H. A review on some new recently developed nonlinear analytical techniques. Int J Non-linear Sci Numer Simul 1 (2000) 51-70
    • (2000) Int J Non-linear Sci Numer Simul , vol.1 , pp. 51-70
    • He, J.H.1
  • 11
    • 17844387391 scopus 로고    scopus 로고
    • Homotopy perturbation method for bifurcation on nonlinear problems
    • He J.H. Homotopy perturbation method for bifurcation on nonlinear problems. Int J Non-linear Sci Numer Simul 8 (2005) 207-208
    • (2005) Int J Non-linear Sci Numer Simul , vol.8 , pp. 207-208
    • He, J.H.1
  • 14
    • 0000615571 scopus 로고
    • An approximate solution technique not depending on small parameters: a special example
    • Liao S.J. An approximate solution technique not depending on small parameters: a special example. Int J Non-Linear Mech 30 3 (1995) 371-380
    • (1995) Int J Non-Linear Mech , vol.30 , Issue.3 , pp. 371-380
    • Liao, S.J.1
  • 15
    • 0031223353 scopus 로고    scopus 로고
    • Boundary element method for general nonlinear differential operators
    • Liao S.J. Boundary element method for general nonlinear differential operators. Eng Anal Bound Elem 20 2 (1997) 91-99
    • (1997) Eng Anal Bound Elem , vol.20 , Issue.2 , pp. 91-99
    • Liao, S.J.1
  • 16
    • 0000494305 scopus 로고    scopus 로고
    • An explicit, totally analytic approximate solution for Blasius' viscous flow problems
    • Liao S.J. An explicit, totally analytic approximate solution for Blasius' viscous flow problems. Int. J Non-Linear Mech. 34 (1999) 759-778
    • (1999) Int. J Non-Linear Mech. , vol.34 , pp. 759-778
    • Liao, S.J.1
  • 18
    • 0042354097 scopus 로고    scopus 로고
    • On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet
    • Liao S.J. On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. J Fluid Mech 488 (2003) 189-212
    • (2003) J Fluid Mech , vol.488 , pp. 189-212
    • Liao, S.J.1
  • 19
    • 0141961626 scopus 로고    scopus 로고
    • On the homotopy analysis method for nonlinear problems
    • Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 147 (2004) 499-513
    • (2004) Appl Math Comput , vol.147 , pp. 499-513
    • Liao, S.J.1
  • 20
    • 17944369480 scopus 로고    scopus 로고
    • A new branch of solutions of boundary-layer flows over an impermeable stretched plate
    • Liao S.J. A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Int J Heat Mass Transfer 48 12 (2005) 2529-2539
    • (2005) Int J Heat Mass Transfer , vol.48 , Issue.12 , pp. 2529-2539
    • Liao, S.J.1
  • 21
    • 0037300634 scopus 로고    scopus 로고
    • Homotopy analysis of nonlinear progressive waves in deep water
    • Liao S.J., and Cheung K.F. Homotopy analysis of nonlinear progressive waves in deep water. J Eng Math 45 2 (2003) 103-116
    • (2003) J Eng Math , vol.45 , Issue.2 , pp. 103-116
    • Liao, S.J.1    Cheung, K.F.2
  • 22
    • 0141961626 scopus 로고    scopus 로고
    • On the homotopy analysis method for nonlinear problems
    • Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 47 2 (2004) 499-513
    • (2004) Appl Math Comput , vol.47 , Issue.2 , pp. 499-513
    • Liao, S.J.1
  • 23
    • 0141927321 scopus 로고    scopus 로고
    • On the explicit analytic solutions of an Oldroyd 6-constant fluid
    • 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
    • (2004) Int J Eng Sci , vol.42 , pp. 123-135
    • Hayat, T.1    Khan, M.2    Ayub, M.3
  • 24
    • 85196178642 scopus 로고    scopus 로고
    • S. Nadeem, Noreen Sher Akbar, Influence of heat transfer on a peristaltic flow of Johnson Segalman fluid in a non uniform tube, Comm. Non-linear Sci. Num. Simul, doi: 10.1016/j.icheatmasstransfer.2009.07.012.
    • S. Nadeem, Noreen Sher Akbar, Influence of heat transfer on a peristaltic flow of Johnson Segalman fluid in a non uniform tube, Comm. Non-linear Sci. Num. Simul, doi: 10.1016/j.icheatmasstransfer.2009.07.012.
  • 25
    • 73249149292 scopus 로고    scopus 로고
    • Thin film flow of a third grade fluid with variable viscosity
    • Nadeem S. Thin film flow of a third grade fluid with variable viscosity. Zeitschrift fur Naturforschung (2009) 553-559
    • (2009) Zeitschrift fur Naturforschung , pp. 553-559
    • Nadeem, S.1
  • 26
    • 28144444967 scopus 로고    scopus 로고
    • Homotopy solutions for generalized second-grade fluid past porous plate
    • Hayat T., and khan M. Homotopy solutions for generalized second-grade fluid past porous plate. Nonlinear Dyn 4 2 (2005) 395-405
    • (2005) Nonlinear Dyn , vol.4 , Issue.2 , pp. 395-405
    • Hayat, T.1    khan, M.2
  • 27
    • 56049108113 scopus 로고    scopus 로고
    • Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel's models of viscosities
    • Nadeem S., and Ali M. Analytical solutions for pipe flow of a fourth grade fluid with Reynold and Vogel's models of viscosities. Commun Non-linear Sci Numer Simul 5 (2009) 2073-2090
    • (2009) Commun Non-linear Sci Numer Simul , Issue.5 , pp. 2073-2090
    • Nadeem, S.1    Ali, M.2
  • 28
    • 70449643530 scopus 로고    scopus 로고
    • Effects of partial slip on a fourth grade fluid with variable viscosity: an analytic solution
    • 10.1016/j.nonrwa.2009.01.030
    • Nadeem S., Hayat T., Abbasbandy S., and Ali M. Effects of partial slip on a fourth grade fluid with variable viscosity: an analytic solution. Nonlinear Anal: Real World Appl (2009) 10.1016/j.nonrwa.2009.01.030
    • (2009) Nonlinear Anal: Real World Appl
    • Nadeem, S.1    Hayat, T.2    Abbasbandy, S.3    Ali, M.4
  • 29
    • 34547422837 scopus 로고    scopus 로고
    • Approximate explicit solutions of nonlinear BBMB equations by homotopy analysis method and comparison with the exact solution
    • Fakhari A., and Ebrahimpour G.D. Approximate explicit solutions of nonlinear BBMB equations by homotopy analysis method and comparison with the exact solution. Phys Lett A 36 8 (2007) 64-68
    • (2007) Phys Lett A , vol.36 , Issue.8 , pp. 64-68
    • Fakhari, A.1    Ebrahimpour, G.D.2
  • 30
    • 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 8 (2008) 2019-2026
    • (2008) Comput Math Appl , vol.56 , Issue.8 , pp. 2019-2026
    • Sajid, M.1    Awais, M.2    Nadeem, S.3    Hayat, T.4
  • 31
    • 85196181896 scopus 로고    scopus 로고
    • Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the homotopy analysis method
    • Rashidi M.M., Domairry G., and Dinarvand S. Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the homotopy analysis method. Commun Non-linear Sci Numer Simul 14 (2007) 708-717
    • (2007) Commun Non-linear Sci Numer Simul , vol.14 , pp. 708-717
    • Rashidi, M.M.1    Domairry, G.2    Dinarvand, S.3
  • 32
    • 46449124143 scopus 로고    scopus 로고
    • Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity
    • Nadeem S., and Awais M. Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity. Phys Lett A 372 30 (2008) 4965-4972
    • (2008) Phys Lett A , vol.372 , Issue.30 , pp. 4965-4972
    • Nadeem, S.1    Awais, M.2
  • 33
    • 35448951202 scopus 로고    scopus 로고
    • On explicit analytic solution for MHD pipe flow of a fourth grade fluid
    • Hayat T., Sajid M., and Ayub M. On explicit analytic solution for MHD pipe flow of a fourth grade fluid. Commun Non-linear Sci Numer Simul 13 4 (2008) 745-751
    • (2008) Commun Non-linear Sci Numer Simul , vol.13 , Issue.4 , pp. 745-751
    • Hayat, T.1    Sajid, M.2    Ayub, M.3
  • 34
    • 53549130019 scopus 로고    scopus 로고
    • The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid
    • Nadeem S., Asghar S., Hayat T., and Hussain M. The Rayleigh Stokes problem for rectangular pipe in Maxwell and second grade fluid. Meccanica 43 5 (2008)
    • (2008) Meccanica , vol.43 , Issue.5
    • Nadeem, S.1    Asghar, S.2    Hayat, T.3    Hussain, M.4
  • 35
    • 34249669720 scopus 로고    scopus 로고
    • A note on series solution for generalized Couette flow
    • Hayat T., Sajid M., and Ayub M. A note on series solution for generalized Couette flow. Commun Non-linear Sci Numer Simul 12 8 (2007) 1481-1487
    • (2007) Commun Non-linear Sci Numer Simul , vol.12 , Issue.8 , pp. 1481-1487
    • Hayat, T.1    Sajid, M.2    Ayub, M.3
  • 36
    • 34848880798 scopus 로고    scopus 로고
    • Homotopy analysis method for quadratic Riccati differential equation
    • Abbasbandy S. Homotopy analysis method for quadratic Riccati differential equation. Commun Non-linear Sci Numer Simul 13 3 (2008) 539-546
    • (2008) Commun Non-linear Sci Numer Simul , vol.13 , Issue.3 , pp. 539-546
    • Abbasbandy, S.1
  • 37
    • 37549038299 scopus 로고    scopus 로고
    • Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method
    • Abbasbandy S. Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method. Chaos Solitons Fractals 36 3 (2008) 581-591
    • (2008) Chaos Solitons Fractals , vol.36 , Issue.3 , pp. 581-591
    • Abbasbandy, S.1
  • 38
    • 85196196733 scopus 로고    scopus 로고
    • Analytical treatment on magnetohydrodynamic (MHD) flow and heat transfer due to a stretching hollow cylinder
    • doi. 10.1002/fld.208
    • Joneidi A.A., Domairry G., Babaelahi M., and Mozaffari M. Analytical treatment on magnetohydrodynamic (MHD) flow and heat transfer due to a stretching hollow cylinder. Int J Numer Meth Fluids (2009) doi. 10.1002/fld.208
    • (2009) Int J Numer Meth Fluids
    • Joneidi, A.A.1    Domairry, G.2    Babaelahi, M.3    Mozaffari, M.4
  • 39
    • 72149115945 scopus 로고    scopus 로고
    • Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction
    • 10.1016/j.jtice.2009.05.008
    • Joneidi A.A., Domairry G., and Babaelahi M. Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction. J Taiwan Inst Chem Eng (2009) 10.1016/j.jtice.2009.05.008
    • (2009) J Taiwan Inst Chem Eng
    • Joneidi, A.A.1    Domairry, G.2    Babaelahi, M.3
  • 40
    • 51749106558 scopus 로고    scopus 로고
    • Approximate solutions of thermal boundary-layer problems in a semi-infinite flat plate by using He's homotopy perturbation method
    • Ganji Z.Z., and Ganji D.D. Approximate solutions of thermal boundary-layer problems in a semi-infinite flat plate by using He's homotopy perturbation method. Int J Nonlinear Sci Numer Simul 9 4 (2008) 415-422
    • (2008) Int J Nonlinear Sci Numer Simul , vol.9 , Issue.4 , pp. 415-422
    • Ganji, Z.Z.1    Ganji, D.D.2
  • 41
    • 33144478462 scopus 로고    scopus 로고
    • Assessment of homotopy-perturbation and perturbation methods in heat radiation equations
    • Ganji D.D., and Rajabi A. Assessment of homotopy-perturbation and perturbation methods in heat radiation equations. Int Commun Heat Mass Transfer 33 (2006) 391-400
    • (2006) Int Commun Heat Mass Transfer , vol.33 , pp. 391-400
    • Ganji, D.D.1    Rajabi, A.2
  • 42
    • 33748919061 scopus 로고    scopus 로고
    • Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations
    • Ganji D.D., and Sadighi A. Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. Int J Nonlinear Sci Numer Simul 7 4 (2006) 411-418
    • (2006) Int J Nonlinear Sci Numer Simul , vol.7 , Issue.4 , pp. 411-418
    • Ganji, D.D.1    Sadighi, A.2
  • 43
    • 0006035689 scopus 로고    scopus 로고
    • Solving partial differential equations by two dimensional differential transform method
    • Chen C.K., and Ho S.H. Solving partial differential equations by two dimensional differential transform method. Appl Math Comput 106 (1999) 171-179
    • (1999) Appl Math Comput , vol.106 , pp. 171-179
    • Chen, C.K.1    Ho, S.H.2
  • 44
    • 0141961581 scopus 로고    scopus 로고
    • Solutions of the systems of differential equations by differential transform method
    • Ayaz F. Solutions of the systems of differential equations by differential transform method. Appl Math Comput 147 (2004) 547-567
    • (2004) Appl Math Comput , vol.147 , pp. 547-567
    • Ayaz, F.1
  • 45
    • 35348853810 scopus 로고    scopus 로고
    • Comparison differential transformation technique with adomian decomposition method for linear and nonlinear initial value problems
    • Abdel-Halim Hassan I.H. Comparison differential transformation technique with adomian decomposition method for linear and nonlinear initial value problems. Chaos, Solitons Fractals 36 (2008) 53-65
    • (2008) Chaos, Solitons Fractals , vol.36 , pp. 53-65
    • Abdel-Halim Hassan, I.H.1
  • 46
    • 44449088392 scopus 로고    scopus 로고
    • Solution of singular two-point boundary value problems using differential transformation method
    • Ravi Kanth A.S.V., and Aruna K. Solution of singular two-point boundary value problems using differential transformation method. Phys Lett A 372 (2008) 4671-4673
    • (2008) Phys Lett A , vol.372 , pp. 4671-4673
    • Ravi Kanth, A.S.V.1    Aruna, K.2
  • 47
    • 33749517865 scopus 로고    scopus 로고
    • Solution of differential-difference equations by using differential transform method
    • Arikoglu A., and Ozkol I. Solution of differential-difference equations by using differential transform method. Appl Math Comput 181 (2006) 153-162
    • (2006) Appl Math Comput , vol.181 , pp. 153-162
    • Arikoglu, A.1    Ozkol, I.2
  • 48
    • 67649095208 scopus 로고    scopus 로고
    • Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity
    • Joneidi A.A., Ganji D.D., and Babaelahi M. Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity. Int Commun Heat Mass Transfer 36 (2009) 757-762
    • (2009) Int Commun Heat Mass Transfer , vol.36 , pp. 757-762
    • Joneidi, A.A.1    Ganji, D.D.2    Babaelahi, M.3
  • 49
    • 85196189146 scopus 로고    scopus 로고
    • Analysis of velocity equation of steady flow of a viscous incompressible fluid in channel with porous walls
    • doi.:10.1002/fld.211
    • Babaelahi M., Ganji D.D., and Joneidi A.A. Analysis of velocity equation of steady flow of a viscous incompressible fluid in channel with porous walls. Int J Numer Meth Fluids (2009) doi.:10.1002/fld.211
    • (2009) Int J Numer Meth Fluids
    • Babaelahi, M.1    Ganji, D.D.2    Joneidi, A.A.3


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