Exact and Approximate Analytic Solutions of the Jeffery-Hamel Flow Problem by the Duan-Rach Modified Adomian Decomposition Method

Bougoffa, Lazhar; Mziou, Samy; Rach, Randolph

doi:10.3846/13926292.2016.1145152

Cited by 11 publications

(7 citation statements)

References 23 publications

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“…In this study, a perturbation iterative scheme has been applied to find approximate analytical solutions to the nonlinear differential problems that govern Jeffrey-Hamel flow regarding heat transfer and viscous dissipation in nanofluids. The effect of active parameters such as nanoparticle volume friction, opening angle, Reynolds number, Prandtl number and Eckert number on velocity and temperature boundary layer thicknesses [31] have been examined [24]. Analytical approximate solutions are given and compared with Range-Kutta of fourth order scheme(RK4S), Differential Transformation method (DTM) [7], Homotopy Perturbation method (HPM) [8], Optimal Homotopy Asymptotic method (OHAM) [9], Spectral-Homotopy Analysis method (SHAM) [10], and Homotopy Analysis method(HAM) [11].…”

Section: Introductionmentioning

confidence: 99%

Computational Analysis of Metallic- Nonmetallic Nanoparticle on Jeffery Hamel Nanofluid Flow Problem

Abdulridah,

Jasim

2023

Iraqi Journal of Science

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In this article, we investigate the heat transfer on nanoparticles Jeffrey Hamel flow problem between two rigid plane walls. Water is used as a main fluid using four different types of nanoparticles, namely aluminum, cuprous, titanium, and silver. The results of nonlinear transformational equations with boundary conditions are solved analytically and numerically. The perturbation iteration scheme (PIS) is used for the analytic solution, while for determining the numerical results, the Rang-Kutta of the four-order scheme (RK4S) is used. The effects on the behavior of non-dimensional velocity and temperature distributions are presented in the form of tables and graphs for different values of emerging physical parameters (Reynolds number, Prandtl number, Eckert number and open angles).The solid component of nanoparticles has an influence on the heat transfer and flow characteristics that is more visible when compared to other types of particles. The temperature distribution increases with the increase of the Reynolds number, Bruntel number, Eckert number, but the velocity distribution decreases with the increase of the Reynolds number. Finally, the obtained findings demonstrate PIS efficacy, accuracy, and convenience in solving the problem of nanofluid flow.

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Section: Introductionmentioning

confidence: 99%

Computational Analysis of Metallic- Nonmetallic Nanoparticle on Jeffery Hamel Nanofluid Flow Problem

Abdulridah,

Jasim

2023

Iraqi Journal of Science

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“…Recently, these types of problems have been resolved with known semianalytical or numerical methods. These problems contain the Lattice-Boltzmann method, 20 He's variational iteration method (VIM) with the HPM, 21 the homotopy analysis method (HAM) with the homotopy perturbation method (HPM), and the differential transformation method (DTM), 22 the Adomian-decomposition method (ADM), [23][24][25][26][27] the Sumudu transform method, 28 Haar wavelet method. 29 The MHD Jeffery-Hamel flow with nanoparticle problem solved by using different numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Jeffery–Hamel flow with high magnetic field and nanoparticle by DTM

Raghunatha

Siddanagowdru

2022

Heat Trans

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In this article, the special properties of the magnetic field and nanoparticles on the Jeffery-Hamel flow are considered via an influential numerical differential transform method (DTM). The proposed technique is very helpful and appropriate for solving highly nonlinear differential equations.Furthermore, the outcomes are compared with those of other techniques such as HPM, HAM, ADM, and a numerical method (Rung-Kutta method) in the literature revealing that the current method solution is better than other methods. Also, the properties of Reynolds number, Hartmann number, and angle of the channel on applications of the MHD Jeffery-Hamel flow are discussed.

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“…The existence and uniqueness of the solution of (1.4) subject to (1.2) have been proved in [49]. Also, the numerical solutions to problems related to Blasius equations using the Adomian decomposition method can be found in [50,51]. The authors in [52] demonstrated that the solution for an arbitrary value of a can be obtained from the classical Blasius equation with a = 1 after a transformation.…”

Section: Introductionmentioning

confidence: 99%

Analytic Approximate Solution of the Extended Blasius Equation with Temperature-Dependent Viscosity

Khanfer

Bougoffa

Bougouffa

2022

J Nonlinear Math Phys

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An explicit approximate solution is obtained for the extended Blasius equation subject to its well-known classical boundary conditions, where the viscosity coefficient is assumed to be positive and temperature-dependent, which arises in several important boundary layer problems in fluid dynamics. This problem extends a previous problem by Cortell (Appl Math Comput 170:706–710, 2005) when the viscosity is constant, in which a numerical solution was obtained. A comparison with other numerical solutions demonstrates that our approximate solution shows an enhancement over some of the existing numerical techniques. Moreover, highly accurate estimates for the skin-friction were calculated and found to be in good agreement with the numerical values obtained by Howarth (Proc R Soc A: Math Phys Eng Sci 164(919):547–579, 1938), Töpfer (Z Math Phys 60:397–398, 1912), and Cortell [34] when the viscosity is equal to 1, and when it is equal to 2.

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Exact and Approximate Analytic Solutions of the Jeffery-Hamel Flow Problem by the Duan-Rach Modified Adomian Decomposition Method

Cited by 11 publications

References 23 publications

Computational Analysis of Metallic- Nonmetallic Nanoparticle on Jeffery Hamel Nanofluid Flow Problem

Computational Analysis of Metallic- Nonmetallic Nanoparticle on Jeffery Hamel Nanofluid Flow Problem

Investigation of Jeffery–Hamel flow with high magnetic field and nanoparticle by DTM

Analytic Approximate Solution of the Extended Blasius Equation with Temperature-Dependent Viscosity

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