Application of Homotopy Perturbation Method to Solve Steady Flow of Walter B Fluid A Vertical Channel In Porous Media

Authors: A.Memari

Abstract:

In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.

Keywords: Steady flow; Walter's B' Fluid;, vertical channel;porous media, Homotopy Perturbation Method (HPM), Numerical Solution (NS).

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079376

References:

[1] Berman, A.S. Laminar Flow in Channels with Porous Walls, J. Appl. Phys., 24 (1953) 1232-1235.
[2] Choi, J.J., Rusak, Z. and Tichy, J.A., Maxwell Fluid Suction Flow in a Channel, J. Non- Newtonian Fluid Mech., 85 (1999) 165-187.
[3] Cox, S.M., Two Dimensional Flow of a Viscous Fluid in a Channel with Porous Walls, J. Fluid Mech. 227 (1991) 1-33.
[4] J.H. He, Homotopy perturbation technique, Comp. Meth. App. Mech. Eng. 178, (1999) 257-262.
[5] J.H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, I. J. Non-Lin. Mech. 35 (2000) 37- 43.
[6] Z.Z. Ganji, D.D. Ganji, Approximate Solutions of Thermal Boundarylayer Problems in a Semi-infinite Flat Plate by using He-s Homotopy Perturbation Method, International Journal of Nonlinear Sciences and Numerical Simulation, 9(4), (2008) 415-422.
[7] Z.Z. Ganji, D.D. Ganji, M. Esmaeilpour, A Study on Nonlinear Jeffery- Hamel Flow by Two He-s Semi-Analytic Methods and Comparison with Numerical Results, Computers and Mathematics with Applications, 58 (2009) 2107-2116.
[8] E. Yusufo─ƒlu, Homotopy Perturbation Method for Solving a Nonlinear System of Second Order Boundary Value Problems, Int. J. Non-Lin. Sc. Num. Sim.8 (2007) 353-358.
[9] Z.Z. Ganji, D.D. Ganji, H. Jafari, M. Rostamian, Application of the HPM to Coupled system of PDE, Topological Methods in Nonlinear Analysis, 31, (2008) 341-348.
[10] A. A. Joneidi, G. Domairry, M. Babaelahi, Homotopy Analysis Method to Walter-s B fluid in a vertical channel with porous wall, Meccanica, DOI: 10.1007/s11012-010-9295-y.