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Analytic Series Solution for Unsteady Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium

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Abstract

In this paper, we solve the unsteady mixed convection flow near the stagnation point on a heated vertical flat plate embedded in a Darcian fluid-saturated porous medium by means of an analytic technique, namely the Homotopy Analysis Method. Different from previous perturbation results, our analytic series solutions are accurate and uniformly valid for all dimensionless times and for all possible values of mixed convection parameter, and besides agree well with numerical results. This provides us with a new analytic approach to investigate related unsteady problems.

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References

  1. 1.

    G. Adomian (1976) ArticleTitleNonlinear stochastic differential equations J. Math. Anal. Appl. 55 441–452 Occurrence Handle10.1016/0022-247X(76)90174-8

  2. 2.

    E.H. Aly L. Elliott D.B. Ingham (2003) ArticleTitleMixed convection boundary-layer flow over a vertical surface embedded in a porous medium Eur J. Mech. B/Fluids 22 529–543 Occurrence Handle10.1016/S0997-7546(03)00059-1 Occurrence HandleMR2023860

  3. 3.

    M. Ayub A. Rasheed T. Hayat (2003) ArticleTitleExact flow of a third grade fluid past a porous plate using homotopy analysis method Int. J. Eng. Sci. 41 2091–2103 Occurrence Handle10.1016/S0020-7225(03)00207-6

  4. 4.

    A. Bejan I. Dincer S. Lorente A.F. Miguel A.H. Reis (2004) Porous and Complex Flow Structures in Modern Technologies Springer New York

  5. 5.

    A. Bejan A.D. Kraus (Eds) (2003) Heat Transfer Handbook Wiley New York

  6. 6.

    T. Cebeci P. Bradshaw (1984) Physcial and Computational Aspects of Convective Heat Transfer Springer New York

  7. 7.

    T. Hayat M. Khan S. Asghar (2004) ArticleTitleHomotopy analysis of MHD flows of an Oldroyd 8-constant fluid Acta Mech. 168 213–232 Occurrence Handle10.1007/s00707-004-0085-2

  8. 8.

    S.D. Harris D.B. Ingham I. Pop (1999) ArticleTitleUnsteady mixed convection boundary-layer flow on a vertical surface in a porous medium Int. J. Heat Mass Transfer. 42 357–372 Occurrence Handle10.1016/S0017-9310(98)00209-9 Occurrence Handle1:CAS:528:DyaK1MXivVylsA%3D%3D

  9. 9.

    D.B. Ingham A. Bejan E. Mamut I. Pop (Eds) (2004) Emerging Technologies and Techniques in Porous Media Kluwer Dordrecht

  10. 10.

    D.B. Ingham I. Pop (Eds) (1998) Transport Phenomena in Porous Media Pergamon Oxford

  11. 11.

    C.H. Johnson P. Cheng (1978) ArticleTitlePossible similarity solutions for free convection boundary layers adjacent to flat plates in porous media Int. J. Heat Mass Transfer. 21 709–718 Occurrence Handle10.1016/0017-9310(78)90032-7

  12. 12.

    Karmishin A.V., Zhukov A.T., Kolosov V.G. (1990). Methods of Dynamics Calculation and Testing for Thin-walled Structures, Mashinostroyenie, Moscow. (in Russian)

  13. 13.

    S.J. Liao (2003a) Beyond Perturbation: Introduction to Homotopy Analysis Method Chapman & Hall/CRC Press Boca Raton

  14. 14.

    S.J. Liao (2003b) ArticleTitleOn the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet J. Fluid Mech. 488 189–212 Occurrence Handle10.1017/S0022112003004865

  15. 15.

    S.J. Liao (2003c) ArticleTitleAn explicit analytic solution to the Thomas-Fermi equation Appl. Math. Comput. 144 495–506 Occurrence Handle10.1016/S0096-3003(02)00423-X

  16. 16.

    S.J. Liao (2004) ArticleTitleOn the homotopy analysis method for nonlinear problems Appl. Math. Comput. 147 499–513 Occurrence Handle10.1016/S0096-3003(02)00790-7

  17. 17.

    Liao S.J. in press, An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate, Commun. Nonlinear Sci. Numer. Simul

  18. 18.

    S.J. Liao K.F. Cheung (2003) ArticleTitleHomotopy analysis of nonlinear progressive waves in deep water J. Eng. Math. 45 IssueID2 105–116 Occurrence Handle10.1023/A:1022189509293

  19. 19.

    S.J. Liao I. Pop (2004) ArticleTitleExplicit analytic solution for similarity boundary layer equations Int. J. Heat Mass Transfer 47 IssueID1 75–85 Occurrence Handle10.1016/S0017-9310(03)00405-8

  20. 20.

    Lyapunov A.M. (1892). General Problem on Stability of Motion. Taylor & Francis, London, 1992. (English translation)

  21. 21.

    E. Magyari I. Pop B. Keller (2004) ArticleTitleAnalytic solutions for unsteady free convection in porous media J. Eng. Math. 48 93–104 Occurrence Handle10.1023/B:ENGI.0000011914.16863.06

  22. 22.

    J.H. Merkin (1980) ArticleTitleMixed convection boundary layer flow on a vertical surface in a saturated porous medium J. Eng. Math. 14 301–313 Occurrence Handle10.1007/BF00052913

  23. 23.

    R. Nazar N. Amin I. Pop (2004) ArticleTitleUnsteady mixed convection boundary layer flow near the stagnation point on a vertical surface embedded in a porous medium Int. J. Heat Mass Transfer. 47 2681–2688 Occurrence Handle10.1016/j.ijheatmasstransfer.2004.01.002

  24. 24.

    D.A. Nield A. Bejan (1999) Convection in Porous Media EditionNumber2 Springer New York

  25. 25.

    I. Pop D.B. Ingham (2001) Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media Pergamon Oxford

  26. 26.

    K. Vafai (Eds) (2000) Handbook of Porous Media Marcel Dekker New York

  27. 27.

    J.C. Williams T.H. Rhyne (1980) ArticleTitleBoundary layer development on a wedge impulsively set into motion SIAM J. Appl. Math. 38 215–224 Occurrence Handle10.1137/0138019

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Correspondence to Shijun Liao.

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Cheng, J., Liao, S. & Pop, I. Analytic Series Solution for Unsteady Mixed Convection Boundary Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium. Transp Porous Med 61, 365–379 (2005). https://doi.org/10.1007/s11242-005-0546-7

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Keywords

  • unsteady mixed convection
  • boundary layer flows
  • stagnation point
  • homotopy analysis method