Application of homotopy perturbation method to deformable channel with wall suction and injection in a porous medium

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 9, Issue 2, 2008, Pages 195-206

  Mahmood, M ^a   Hossain, M A ^a   Asghar, S ^a   Hayat, T ^b  

^a COMSATS Institute of Information Technology ^*  (Pakistan)

^b QUAID I AZAM UNIVERSITY   (Pakistan)

Author keywords

Deformable channel; Porous medium; Porous walls

Indexed keywords

EID: 47049105318     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2008.9.2.195     Document Type: Article

References (25)

1. Herman, A.S. Laminar flow in channels with porous walls, Journal of Applied Physics, 24 (1953):1232-1235
2. Dauenhauer, B.C., Majdalani, J. Exact self-similarity solution of the Navier-Stokes equations for a deformable channel with wall suction or injection, AIAA 3588 (2001):1-11
3. Majdalan, J., Zhou, C., Dawson, C.A. Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability, Journal of Bio Mechanics, 35(2002):1399-1403
4. Boutros, Y.Z., Abd-el-Malek, M.B., Badran, N.A., Hassan, H.S. Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability, Applied Mathematical Modeling (in press)
5. Liao, S.J. The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. thesis, Shanghai Jio Tong University, 1992
6. Liao, S.J. On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation, 147(2004):499-513
7. Liao, S.J. Beyond Perturbation: Introduction to homotopy analysis method, Boca Raton: Chapman & Hall/CRC press, 2003
8. He, J.H. Newton like method for solving algebraic equations, Communication in Nonlinear Science and Numerical Simulation, 3(1998):106-109
9. He, J.H. Homotopy perturbation technique, Computational Methods in Applied Mechanical Engineering, 178(1999):257-262
10. He, J.H. A coupling method of homotopy and perturbation technique for nonlinear problems, International Journal of Nonlinear Mechanics, 35(2000):37-43
11. He, J.H. Homotopy perturbation method: A new nonlinear analytic technique, Applied Mathematics and Computation, 135(2003):73-79
12. He, J.H. A new approach to nonlinear partial differential equation, Communication in Nonlinear Science Numerical Simulation, 2(1997):230-235
13. He, J.H. Comparison of homotopy perturbation and homotopy analysis method, Applied Mathematics and Computation, 156(2004):527-539
14. He, J.H. Some asymptotic methods for strongly nonlinear equations, International Journal of Modern Physics B, 20(2006):1141-1199
15. Ariel, P.D., Hayat, T., Asghar, S., Homotopy perturbation method for axisymmetric flow over a stretching sheet, International Journal of Nonlinear Sciences and Numerical Simulation, 7(4),2006:399-406
16. Beléndez, A., Hernández, A., Beléndez, T. et al., Application of He's homotopy perturbation method to Duffing-Harmonic Oscillator, International Journal of Nonlinear Sciences and Numerical Simulation, 8(1),2007:79-88
17. Ganji, D.D., Sadighi, A., Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, International Journal of Nonlinear Sciences and Numerical Simulation, 7(4),2006:411-418
18. Rafei, M., Ganji, D.D., Explicit solutions of Helmholtz equation and Fifth-order KdV equation using homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 7(3),2006:321-328
19. Siddiqui, A.M., Mahmood , R., Ghori, Q.K., Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method, International Journal of Nonlinear Sciences and Numerical Simulation, 7(1),2006:7-14
20. Siddiqui, A.M., Ahmed, M., Ghori, Q.K., Couette and Poiseuille flows for non-Newtonian fluids, International Journal of Nonlinear Sciences and Numerical Simulation, 7(1),2006:15-26
21. Özis, T., Yidirim, A., Determination of limit cycles by a modified straightforward expansion for nonlinear oscillators, Chaos, Solitons and Fractals, 32(2),2007:445-448
22. He, J.H., Modified Lindstedt-Poincare method for some strongly non-linear oscillations. Part I: expansion of a constant, International Journal of Nonlinear Mechanics, 37(2),2002: 309-314
23. He, J.H., Modified Lindstedt-Poincare method for some strongly non-linear oscillations. Part II: a new transformation, International Journal of Nonlinear Mechanics, 37(2),2002:315-320
24. He, J.H., Modified Lindstedt-Poincare method for some strongly non-linear oscillations. Part III: double series expansion, International Journal of Nonlinear Science and Numerical Simulation, 2(4),2001:317-320
25. Abbasbandy, S., Homotopy perturbation method for quadratic Ricatti differential equation and comparison with Adomian Decomposition method, Applied Mathematics and Computation, 172(2006):485-490