Solution of the Jeffery–Hamel flow problem by optimal homotopy asymptotic method

Esmaeilpour, Mehdi; Ganji, D.D.

doi:10.1016/j.camwa.2010.03.024

Cited by 82 publications

(36 citation statements)

References 31 publications

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“…12 used the Adomian decomposition method to analytically investigate the Jeffery-Hamel flow with nanoparticles and high magnetic field. 13 introduced the optimal homotopy asymptotic solution of the problem. Recently, a massive attention has been directed towards the artificial intelligence techniques to numerically solve the nonlinear differential equations.…”

Section: Introductionmentioning

confidence: 99%

Haar wavelet solution of the MHD Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid

et al. 2016

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This study deals with the numerical investigation of Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid in the presence of an outer magnetic field by using Haar wavelet method. Jeffery-Hamel flows occur in various practical situations involving flow between two non-parallel walls. Applications of such fluids in biological and industrial sciences brought a great concern to the investigation of flow characteristics in converging and diverging channels. A suitable similarity transformation is applied to transform the nonlinear coupled partial differential equations (PDEs) into nonlinear coupled ordinary differential equations (ODEs), which govern the momentum and heat transfer properties of the fluid. Due to the high nonlinearity of resulting coupled ODEs, the exact solution is unlikely. Thus, the solution is approximated using a numerical scheme based on Haar wavelets and the results are verified by comparing with 4th order Runge-Kutta results.

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Section: Introductionmentioning

confidence: 99%

Haar wavelet solution of the MHD Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid

et al. 2016

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“…The classical Jeffery-Hamel problem was extended in [9] to include the effects of external magnetic field in a conducting fluid. The optimal homotopy asymptotic method is applied by Marinca and Herişanu [10] and by Esmaeilpour and Ganji [11]. The effect of magnetic field and nanoparticles on the Jeffery-Hamel flow are studied in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

Marinca

Ene

2017

Open Physics

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Abstract:In this paper, the Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solution for the nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell's electromagnetism and heat transfer, lead to two nonlinear ordinary differential equations. The results obtained by means of OHPM show very good agreement with numerical results and with Homotopy Perturbation Method (HPM) results.

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“…ADM also was used by several researchers to solve a wide range of physical problems in various engineering fields such as fluid flow and porous media simulation [21] and other nonlinear systems [22][23][24][25][26] . In recent years, some researchers used new methods to solve these kinds of problems [27][28][29][30][31][32][33][34][35][36][37][38][39][40] . In this paper, we apply the ADM to find the approximate solutions of nonlinear differential equations governing the MHD Jeffery-Hamel flow, and a comparison between the ADM and mumerical solution results is provided.…”

Section: Introductionmentioning

confidence: 99%

Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method

Sheikholeslami¹,

Ganji²,

Ashorynejad³

et al. 2012

Appl. Math. Mech.-Engl. Ed.

208

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In this study, the effects of magnetic field and nanoparticle on the JefferyHamel flow are studied using a powerful analytical method called the Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell's electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different α, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.

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Solution of the Jeffery–Hamel flow problem by optimal homotopy asymptotic method

Cited by 82 publications

References 31 publications

Haar wavelet solution of the MHD Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid

Haar wavelet solution of the MHD Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid

Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method

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