Analysis of velocity equation of steady flow of a viscous incompressible fluid in channel with porous walls

International Journal for Numerical Methods in Fluids

Volumn 63, Issue 9, 2010, Pages 1048-1059

  Babaelahi, M ^a   Ganji, D D ^b   Joneidi, A A ^c  

^a K N TOOSI UNIVERSITY OF TECHNOLOGY   (Iran)

^b BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

^c SHAHROOD UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Differential transformation method (DTM); He's variational iteration method (VIM); Injection; Numerical solution (NS); Suction; Velocity equation; Viscous incompressible fluid

Indexed keywords

DIFFERENTIAL TRANSFORMATION METHODS; NUMERICAL SOLUTION; SUCTION VELOCITY; VARIATIONAL ITERATION METHOD; VISCOUS INCOMPRESSIBLE FLUIDS;

BOUNDARY CONDITIONS; DIFFERENTIATION (CALCULUS); FLUIDS; INITIAL VALUE PROBLEMS; ITERATIVE METHODS; ORDINARY DIFFERENTIAL EQUATIONS; STEADY FLOW; VELOCITY; VISCOUS FLOW;

NONLINEAR EQUATIONS;

EID: 77954596517     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2114     Document Type: Article

References (30)

1. Berman AS. Laminar flow in channels with porous walls. Journal of Applied Physics 1953; 24:1232-1235.
2. Yuan SW. Further investigation of laminar flow in channels with porous walls. Journal of Applied Physics 1956; 27:267-269.
3. Terrill RM. Laminar flow in a uniformly porous channel with large injection. Aeronautical Quarterly 1965; 16:323-332.
4. Terrill RM. Laminar flow in a uniformly porous channel. Aeronautical Quarterly 1964; 15:299-310.
5. Robinson RWA. The existence of multiple solutions for the laminar flow in a uniformly porous channel with suction at both walls. Journal of Engineering Mathematics 1976; 10:23-40.
6. MacGillivray AD, Lu C. Asymptotic solution of a laminar flow in a porous channel with large suction: a nonlinear turning point problem. Methods and Applications of Analysis 1994; 1:229-248.
7. Zhou JK. Differential Transformation and its Applications for Electrical Circuits. Huarjung University Press: Wuuhahn, China, 1986 (in Chinese).
8. Chiou JS, Tzeng JR. Application of the Taylor transform to nonlinear vibration problems. Transaction of the American Society of Mechanical Engineers, Journal of Vibration and Acoustics 1996; 118:83-87.
9. Jang MJ, Chen CL, Liu YC. Two-dimensional differential transform for partial differential equations. Applied Mathematics and Computation 2001; 121:261-270.
10. Hassan IHA-H. On solving some eigenvalue-problems by using a differential transformation. Applied Mathematics and Computation 2002; 127:1-22.
11. Chen CL, Liu YC. Differential transformation technique for steady nonlinear heat conduction problems. Applied Mathematics and Computation 1998; 95:155-164.
12. Chen CK, Chen SS. Application of the differential transformation method to a non-linear conservative system. Applied Mathematics and Computation 2004; 154:431-441.
13. Chen CK, Ju SP. Application of differential transformation to transient advective-dispersive transport equation. Applied Mathematics and Computation 2004; 155:25-38.
14. Yeh YL, Wang CC, Jang MJ. Using finite difference and differential transformation method to analyze of large deflections of orthotropic rectangular plate problem. Applied Mathematics and Computation 2007; 190:1146-1156.
15. Catal S. Solution of free vibration equations of beam on elastic soil by using differential transform method. Applied Mathematics and Computation 2008; 32:1744-1757.
16. Al-Sawalha MM, Noorani MSM. Application of the differential transformation method for the solution of the hyperchaotic Rossler system. Communications in Nonlinear Science and Numerical Simulation 2008; DOI: 10.1016/j.cnsns.2008.02.002.
17. He JH. Variational iteration method-some recent results and new interpretations. Journal of Computational and Applied Mathematics 2007; 207(1):3-17.
18. He JH. An Elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. International Journal of Modern Physics B (IJMPB) 2008; 22(21):3487-3578.
19. He JH. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B (IJMPB) 2006; 20(10):1141-1199.
20. He JH. Variational iteration method-a kind of non-linear analytical technique: some examples. International Journal of Non-Linear Mechanics 1999; 34(4):699-708.
21. He JH. Variational iteration method for autonomous ordinary differential systems. Applied Mathematics and Computation 2000; 114:115-123.
22. Abdou MA, Soliman AA. Variational iteration method for solving Burger's and coupled Burger's equations. Journal of Computational and Applied Mathematics 2005; 181(2):245-251.
23. Wazwaz AM. A comparison between the variational iteration method and Adomian decomposition method. Journal of Computational and Applied Mathematics 2006; 207(1):129-136.
24. Wazwaz AM. A study on linear and nonlinear Schrödinger equations by the variational iteration method. Chaos, Solitons and Fractals 2008; 37(4):1136-1142.
25. Wazwaz AM. The variational iteration method for solving two forms of Blasius equation on a half-infinite domain. Applied Mathematics and Computation 2007; 188(1):485-491.
26. Ganji DD, Tari H, Jooybari BM. Exact solutions of nonlinear diffusion equations by variational iteration method. Computers and Mathematics with Applications 2007; 54(7-8):1112-1121.
27. Ganji DD, Afrouzi GA, Talarposhti RA. Application of He's variational iteration method for solving the reaction-diffusion equation with ecological parameters. Computers and Mathematics with Applications 2007; 54(7, 8):1010-1017.
28. Ganji DD, Afrouzi GA, Talarposhti RA. Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations. Physics Letters A 2007; 368(6):450-457.
29. Abbasbandy S, Shirzadi A. The variational iteration method for a family of fifth-order boundary value differential equations. International Journal of Nonlinear Dynamics in Engineering and Sciences 2009; 1(1):39-46.
30. Bildik N, Konuralp A. The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations. International Journal of Nonlinear Science and Numerical Simulation 2006; 7:65-70.