Accuracy of VIM, HPM and ADM in Solving Nonlinear Equations for the Steady Three-Dimensional Flow of a Walter’s B Fluid in Vertical Channel

Davood Domiri GANJI; Mehdi FAKOUR; Azadeh VAHABZADEH; Sayyid Habibollah Hashemi KACHAPI

Authors

Davood Domiri GANJI Department of Mechanical Engineering, Babol University of Technology, Babol
Mehdi FAKOUR Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari
Azadeh VAHABZADEH Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari
Sayyid Habibollah Hashemi KACHAPI Department of Mechanical Engineering, Babol University of Technology, Babol

Keywords:

Flow of a Walter’s B fluid, Adomian decomposition method (ADM), Variational iteration method (VIM), Homotopy perturbation method (HPM)

Abstract

In this paper, the steady three-dimensional flow of a Walter's B fluid in a vertical channel is investigated. It is assumed that the fluid is injected into the passage through one side of the channel. The combined effects of viscoelasticity and inertia are considered. By using the appropriate similarity transformations for the velocity components and temperature, the basic equations governing flow and heat transfer are reduced to a set of ordinary differential equations. These equations are solved approximately, subject to the relevant boundary conditions, with a numerical technique. In the present study, three powerful analytical methods of Variational iteration method (VIM), Homotopy perturbation method (HPM) and Adomian decomposition method (ADM) are introduced to overcome this shortcoming. Then, VIM, HPM and ADM are used to solve nonlinear equations in fluids. These methods are useful and practical for solving the nonlinear equation in fluids. Comparison of the results obtained by all three methods and exact solutions reveals that all three methods are tremendously effective.

doi:10.14456/WJST.2014.12

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