Influence of a magnetic field over a laminar viscous flow in a semi-porous channel

Desseaux, André

doi:10.1016/s0020-7225(99)00003-8

Cited by 31 publications

(19 citation statements)

References 9 publications

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“…Recalling the condition N 3 > | |N 1,2 (discussed in Section 3), we note that the results presented in Figure 2(a) and 2(b) correspond to N 3 /(| |N 1,2 ) = 2 and 5, respectively. In both cases, the first order analytic solution is in very good agreement with the corresponding computed profile, and the totality of our numerical results for injection indicate that this is always observed provided that the condition N 3 /(| |N 1,2 ) > 1 is met.…”

Section: Resultsmentioning

confidence: 66%

“…The corresponding Newtonian fluid model was first studied by Berman [1], who described an exact solution of the Navier-Stokes equations by assuming a self-similar solution and reducing the governing partial differential equations to a nonlinear ordinary differential equation of fourth order. The solution is of potential value in understanding more realistic flows in channels and pipes, and study of Berman's exact solution and generalisations of it have attracted numerous studies subsequently, for example Yuan [15], Robinson [14], Zaturska et al [16], Desseaux [2].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Micropolar flow in a porous channel with high mass transfer

Kelson¹,

Desseaux²,

Farrell³

2003

ANZIAMJ

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Two dimensional flow of a micropolar fluid in a porous channel is investigated. The flow is driven by suction or injection at the channel walls, and the micropolar model due to Eringen is used to describe the working fluid. An extension of Berman's similarity transform is used to reduce the governing equations to a set of non-linear coupled ordinary differential equations. The latter are solved for large mass transfer via a perturbation analysis where the inverse of the cross-flow Reynolds number is used as the perturbing parameter. Complementary numerical solutions for strong injection are also obtained using a quasilinearisation scheme, and good agreement is observed between the solutions obtained from the perturbation analysis and the computations.

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Section: Resultsmentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Micropolar flow in a porous channel with high mass transfer

Kelson¹,

Desseaux²,

Farrell³

2003

ANZIAMJ

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“…Then, we consider two dimensionless numbers, the Hartman number (Ha) for the description of the magnetic forces (Desseaux 1999) and the Reynolds number (Re) for the dynamic forces:…”

Section: Governing Equationsmentioning

confidence: 99%

“…On the other hand, the influence of an induction on the dynamic and thermodynamic fields has been highly investigated in the past years and many studies have been published: Osterle and Young (1961) and Umavathi (1996) considered the natural convection between two parallel plates. More recently, Desseaux (1999) analyzed the influence of a magnetic field over a laminar viscous flow in a semi-porous channel. All these problems and phenomena are modeled by ordinary or partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Viscous Flow in Porous Media Using ADM and Comparison with the Numerical Runge–Kutta Method

Ganji

2009

Transp Porous Med

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In this article, the problem of laminar viscous flow in a semi-porous channel in the presence of a transverse magnetic field is presented, and the Adomian decomposition method is employed to compute an approximation for the solution of the system of nonlinear differential equations governing on the problem. Then, we consider the influence of the two dimensionless numbers: the Hartmann number (Ha) for the description of the magnetic forces and the Reynolds number (Re) for the dynamic forces. The results of the Adomian decomposition method (ADM) were compared with the numerical method (NM) solution, homotopy perturbation method (HPM), and variation iteration method (VIM). The results reveal that this method is very effective and simple and can be applied for other nonlinear problems.Keywords Adomian decomposition method (ADM) · Numerical method (NM) · Laminar viscous flow · Semi-porous channel · Uniform magnetic field Abbreviations ADM Adomian decomposition method VIM Variational iteration method NM Numerical method HPM Homotopy perturbation method List of symbols P Pressure q Rate of mass transfer Re Reynolds number

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“…All these problems and phenomena are modeled by ordinary or partial differential equations. [12] The present work focuses on presenting an analytical approximate solution based on differential transformation method for the problem of slip flow in a micro-channel packed with Darcy-BrinkmanForchheimer hyper-porous media, in order to consider the effect of inertia effects on hydrodynamic aspects. The merit of obtaining an analytical approximate is that we can easily integrate or derivate the solution easily which is different from numerical one.…”

Section: Introductionmentioning

confidence: 99%

A numerical study on slip flow in packed hyper-porous media inside micro-channels using differential transformation method

et al. 2016

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Velocity slip boundary condition in parallel-plate micro-channels filled with hyper-porous media is studied using differential transformation method (DTM) in order to find an analytical approximate solution. The results focus on slip flow regime (i.e., for Knudsen numbers in the range 10 −3 < Kn < 10 −1 ). The Darcy-Brinkman-Forchheimer model is applied to study the effect of nonlinear drag term further boundary-friction effects on hydrodynamic of gas flow in micro-channels. The results show that DTM results are in good agreement with numerical ones. Also, it is observed that decreasing the value of Darcy number flattens the velocity profile while this trend is opposite for decreasing the Forchheimer number. Also, increasing the value of  causes to increase the velocity slip at the wall.

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Influence of a magnetic field over a laminar viscous flow in a semi-porous channel

Cited by 31 publications

References 9 publications

Micropolar flow in a porous channel with high mass transfer

Micropolar flow in a porous channel with high mass transfer

Analytical Solution of Viscous Flow in Porous Media Using ADM and Comparison with the Numerical Runge–Kutta Method

A numerical study on slip flow in packed hyper-porous media inside micro-channels using differential transformation method

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