Analytical solution of viscous flow in porous media using ADM and comparison with the numerical Runge-Kutta method

Transport in Porous Media

Volumn 81, Issue 3, 2010, Pages 527-546

  Ganji, Z Z ^a   Ganji, D D ^a  

^a BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Adomian decomposition method (ADM); Laminar viscous flow; Numerical method (NM); Semi porous channel; Uniform magnetic field

Indexed keywords

ADOMIAN DECOMPOSITION METHOD; ADOMIAN DECOMPOSITION METHODS; ANALYTICAL SOLUTIONS; DIMENSIONLESS NUMBER; DYNAMIC FORCES; HARTMANN NUMBERS; HOMOTOPY PERTURBATION METHOD; ITERATION METHOD; LAMINAR VISCOUS FLOW; MAGNETIC FORCE; NONLINEAR PROBLEMS; POROUS CHANNEL; SEMI-POROUS CHANNEL; SYSTEM OF NONLINEAR DIFFERENTIAL EQUATIONS; TRANSVERSE MAGNETIC FIELD;

DIFFERENTIAL EQUATIONS; LINEARIZATION; MAGNETIC FIELDS; NONLINEAR EQUATIONS; NUMERICAL METHODS; OPERATIONS RESEARCH; PERTURBATION TECHNIQUES; POROUS MATERIALS; RADIOMETERS; REYNOLDS NUMBER; RUNGE KUTTA METHODS; VISCOSITY; VISCOUS FLOW;

NUMBER THEORY;

ANALYTICAL FRAMEWORK; COMPARATIVE STUDY; CONSTITUTIVE EQUATION; DECOMPOSITION ANALYSIS; LAMINAR FLOW; MAGNETIC FIELD; NONLINEARITY; PERTURBATION; POROUS MEDIUM; REYNOLDS NUMBER; STOCHASTICITY; VISCOUS FLOW;

EID: 76149145009     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-009-9421-2     Document Type: Article

References (28)

1. Adomian G.: A review of the decomposition method in applied mathematics. J. Math. Anal. Appl. 135(2), 501-544 (1988). doi: 10. 1016/0022-247X(88)90170-9.
2. Adomian G.: A review of the decomposition method and some recent results for nonlinear equations. Math. Comput. Model. 13(7), 17-43 (1992). doi: 10. 1016/0895-7177(90)90125-7.
3. Allan F. M., Syam M. I.: On the analytic solutions of the non-homogeneous Blasius problem. J. Comput. Appl. Math. 182(2), 362-371 (2005). doi: 10. 1016/j. cam. 2004. 12. 017.
4. Bulut H., Ergut M., Asil V., Bokor R. H.: Numerical solution of a viscous incompressible flow problem through an orifice by Adomian decomposition method. Appl. Math. Comput. 153(3), 733-741 (2004). doi: 10. 1016/S0096-3003(03)00667-2.
5. Desseaux A.: Influence of a magnetic field over a laminar viscous flow in a semi-porous channel. Int. J. Eng. Sci. 37, 1781-1794 (1999). doi: 10. 1016/S0020-7225(99)00003-8.
6. Esmaeilpour M., Ganji D. D.: Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate. Phys. Lett. A 372(1), 33-38 (2007). doi: 10. 1016/j. physleta. 2007. 07. 002.
7. Ganji D. D.: The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer. Phys. Lett. A 355(4-5), 337-341 (2006). doi: 10. 1016/j. physleta. 2006. 02. 056.
8. Ganji D. D., Sadighi A: Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations. Int. J. Nonlinear Sci. Numer. Simul. 7, 411-418 (2006).
9. Ganji Z. Z., Ganji DD: 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), 422 (2008).
10. Ganji D. D., Sadighi A.: Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods. Int. J. Nonlinear Sci. Numer. Simul. 8, 435-444 (2007).
11. Ganji D. D., Sadighi A.: Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations. J. Comput. Appl. Math. 207(1), 24-34 (2007). doi: 10. 1016/j. cam. 2006. 07. 030.
12. Ganji D. D., Afrouzi G. A., Hosseinzadeh H., Talarposhti R. A.: Application of homotopy-perturbation method to the second kind of nonlinear integral equations. Phys. Lett. A 371(1-2), 20-25 (2007). doi: 10. 1016/j. physleta. 2007. 06. 003.
13. Ganji D. D., Tari H., Bakhshi Jooybari M.: Variational iteration method and homotopy perturbation method for nonlinear evolution equations. Comput. Math. Appl. 54(7-8), 1018-1027 (2007). doi: 10. 1016/j. camwa. 2006. 12. 070.
14. Ganji D. D., Nourollahi M., Mohseni E.: Application of He's methods to nonlinear chemistry problems. Comput. Math. Appl. 54(7-8), 1122-1132 (2007). doi: 10. 1016/j. camwa. 2006. 12. 078.
15. Ghosh S., Roy A., Roy D.: An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators. Commun. Methods Appl. Mech. Eng. 196(4-6), 1133-1153 (2007). doi: 10. 1016/j. cma. 2006. 08. 010.
16. Hashim I.: Adomian decomposition method for solving BVPs for fourth-order integro-differential equations. J. Comput. Appl. Math. 193(2), 658-664 (2006). doi: 10. 1016/j. cam. 2004. 12. 017.
17. He J. H.: Variational iteration method-a kind of non-linear analytical technique: some examples. Int. J. Non-linear Mech. 34(4), 699-708 (1999). doi: 10. 1016/S0020-7462(98)00048-1.
18. He J. H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20(10), 1141-1199 (2006). doi: 10. 1142/S0217979206034819.
19. He J. H., Abdou M. A.: New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos Sol. Fractals 34(5), 1421-1429 (2007). doi: 10. 1016/j. chaos. 2006. 05. 072.
20. He J. H., Zhang L.-N.: Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method. Phys. Lett. A 372(7), 1044-1047 (2008). doi: 10. 1016/j. physleta. 2007. 08. 059.
21. Jafari H., Daftardar-Gejji V.: Revised Adomian decomposition method for solving a system of nonlinear equations. Appl. Math. Comput. 175(1), 1-7 (2006). doi: 10. 1016/j. amc. 2005. 07. 010.
22. Liao, S. J.: Proposed homotopy analysis techniques for the solution of nonlinear problems. PhD thesis, Shanghai Jiao Tong University (1992).
23. Liao S. J.: Beyond Perturbation: Introduction to Homotopy Analysis method. Chapman and Hall/CRC, Boca Raton (2003).
24. Nayfeh A. H.: Perturbation Methods. Wiley, New York (2000).
25. Osterle J. F., Young F. J.: Natural convection between heated vertical plates in a horizontal magnetic field. J. Fluid Mech. 1, 512-518 (1961). doi: 10. 1017/S002211206100069X.
26. Soh C. W.: Non-perturbative semi-analytical source-type solutions of thin-film equation. Appl. Math. Comput. 174(2), 1576-1585 (2006). doi: 10. 1016/j. amc. 2005. 07. 006.
27. Umavathi J. C.: A note on magnetoconvection in a vertical enclosure. Int. J. Non-linear Mech. 31, 371-376 (1996). doi: 10. 1016/0020-7462(96)00061-3.
28. Wang L.: A new algorithm for solving classical Blasius equation. Appl. Math. Comput. 157(1), 1-9 (2004). doi: 10. 1016/j. amc. 2003. 06. 011.