An analytical solution of the MHD Jeffery–Hamel flow by the modified Adomian decomposition method

Dib, A.; Haiahem, Ammar; Said, Benyebka Bou

doi:10.1016/j.compfluid.2014.06.026

Cited by 29 publications

(19 citation statements)

References 13 publications

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“…solution has full compatibility with [24], [28] and Dib et al [39]. The opposite extreme case where 0 m  or Fig.…”

Section: Resultsmentioning

confidence: 66%

Jeffery–Hamel Flow of Nano Fluid Influenced by Wall Slip Conditions

Nagler¹

2016

j nanofluids

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Combined MHD and electroosmotic Jeffery-Hamel flow of Nano fluid type inside a wedge (inclined walls) with non-linear viscosity and wall friction are investigated analytically. As a result of similarity relations, one nonlinear ordinary differential equation is obtained and solved analytically with the appropriate assumptions   2 0, 0 20 f f    . Moreover, excellent agreement was found between the obtained analytic solution and suggested simple parabolic approximation. Although it was found that in case where more effects are gradually being considered, a slight difference is emerged, but the most dramatic change between solutions occurs when solid to fluid ratio gets significant value. In addition, suitable match in the quantitatively and qualitatively aspects was found between literature results and obtained solution. In addition, analytical solution parametric investigation was performed for specific parameters choice. It was found that the normalized velocity was found to decrease gradually with the tangential direction progress and/or with friction coefficient increase. However, the normalized velocity profile gets higher values as long as the solid to fluid ratio increases. Additionally, Reynolds, Hartmann and solid volume fraction coefficient increase (separately or all together) have raised the normalized velocity function values. Finally, unprevail distinguished cases were introduced to understand flow complexity. It was found that the electrical field magnitude effect is significantly, especially for small friction coefficient values and for high wedge semi angle. Also, the combination between small friction coefficient values including small parameter flow values (Re and Ha numbers) and high electrically field may lead to unoptimized course of normalized velocity profile. The last case that was examined is concerned with friction coefficient variation effect on the normalized velocity profile for different values of wedge semi angle with high electric field for specific parameters choice. It was found that increasing friction coefficient leads to normalized velocity profile consolidation.

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“…solution has full compatibility with [24], [28] and Dib et al [39]. The opposite extreme case where 0 m  or Fig.…”

Section: Resultsmentioning

confidence: 66%

Jeffery–Hamel Flow of Nano Fluid Influenced by Wall Slip Conditions

Nagler¹

2016

j nanofluids

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“…Duan et al [25] have presented a new modification of the ADM that called Duan-Rach Approach (DRA), to solve a wide class of multi-order and multi-point nonlinear boundary value problems (BVP). Dib et al [26] applied Duan-Rach Approach (DRA) to solve the magneto hydrodynamic (MHD) Jeffery-Hamel flow. The results obtained show a good agreement with the numerical method and homotopy analysis method (HAM).…”

Section: Introductionmentioning

confidence: 99%

Investigation of heat transfer for cooling turbine disks with a non-Newtonian fluid flow using DRA

Dogonchi

Ganji

2015

Case Studies in Thermal Engineering

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a b s t r a c tA non-Newtonian viscoelastic fluid flow passes through the porous wall of an axisymmetric channel on a turbine disc for cooling application. The present article solves the couple equations (momentum and heat transfer) of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall for turbine cooling applications by using the Duan-Rach Approach (DRA). The precious achievement of the present work is introducing a new and efficient approximate analytical technique that this method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. The approximate analytical investigation is carried out for different values of the embedding parameters namely: Reynolds number, Prandtl number, injection Reynolds number and power law index. The DRA results indicate that Nusselt number has direct relationship with Reynolds number, Prandtl number and power law index. Also the results were compared with numerical solution in order to verify the accuracy of the proposed method. It is seen that the current results in comparison with the numerical ones are in excellent agreement.

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“…Various analytical approximations methods have also been proposed to solve this problem: the homotopy analysis method (HAM) [13,14,15,18,19,20,21,22], the homotopy perturbation method (HPM) [9,10], the optimal homotopy asymptotic method [9,10,11,16] and the Duan-Rach approach (DRA) [5], where the authors proposed a new modified recursion scheme for the resolution of such boundary value problems for nonlinear ordinary differential equations. They derived the following recursion scheme for the solutions components:…”

Section: Introductionmentioning

confidence: 99%

“…In Dib et al [5], they used a nocanonical variation of the Duan-Rach modified decomposition method to solve the nonlinear Jeffery-Hamel flow boundary value problem, wherein Dib et al selected a nocanonical partition of the nonlinear differential equation as Lf (η) + N f (η) = 0 by incorporating the linear remainder term Rf (η) into the nonlinear term N f (η), which unnecessarily complicates the automated generation of the Adomian polynomials that decompose the nonlinear term Rf (η). This degrades the efficiency of the subroutines used to calculate the Adomian polynomials tailored to the physical nonlinear term.…”

Section: Introductionmentioning

confidence: 99%

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

Bougoffa

Mziou

Rach

2016

Mathematical Modelling and Analysis

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This paper aims to find the exact solution in an implicit form for the wellknown nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).

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An analytical solution of the MHD Jeffery–Hamel flow by the modified Adomian decomposition method

Cited by 29 publications

References 13 publications

Jeffery–Hamel Flow of Nano Fluid Influenced by Wall Slip Conditions

Jeffery–Hamel Flow of Nano Fluid Influenced by Wall Slip Conditions

Investigation of heat transfer for cooling turbine disks with a non-Newtonian fluid flow using DRA

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

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