The application of the boundary element method to the magnetohydrodynamic duct flow

Carabineanu, Adrian; Dinu, Adrian; Oprea, Iuliana

doi:10.1007/bf00917881

Cited by 29 publications

(18 citation statements)

References 6 publications

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“…The approximating functions f j (x; y) are linked with the particular solutionsû j of the equation ∇ 2û j = f j . Substituting f j 's into Equation (10) and then applying Green's second identity to both sides of Equation (9) we obtain the matrix-vector equation…”

Section: Drbem Applicationmentioning

confidence: 99%

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Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme

Bozkaya

Tezer‐Sezgin

2005

Numerical Methods in Fluids

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SUMMARYA numerical scheme which is a combination of the dual reciprocity boundary element method (DRBEM) and the di erential quadrature method (DQM), is proposed for the solution of unsteady magnetohydrodynamic (MHD) ow problem in a rectangular duct with insulating walls. The coupled MHD equations in velocity and induced magnetic ÿeld are transformed ÿrst into the decoupled time-dependent convection-di usion-type equations. These equations are solved by using DRBEM which treats the time and the space derivatives as nonhomogeneity and then by using DQM for the resulting system of initial value problems. The resulting linear system of equations is overdetermined due to the imposition of both boundary and initial conditions. Employing the least square method to this system the solution is obtained directly at any time level without the need of step-by-step computation with respect to time. Computations have been carried out for moderate values of Hartmann number (M 6 50) at transient and the steady-state levels. As M increases boundary layers are formed for both the velocity and the induced magnetic ÿeld and the velocity becomes uniform at the centre of the duct. Also, the higher the value of M is the smaller the value of time for reaching steady-state solution.

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Section: Drbem Applicationmentioning

confidence: 99%

“…The boundary element method application of the steady MHD ow in channels was considered by Singh and Agarwal [9] in terms of a singular integral equation. Carabineanu et al [10], Tezer-Sezgin [11] and Liu and Zhu [12] have solved steady MHD duct ow problem for small and moderate values of Hartmann number.…”

Section: Introductionmentioning

confidence: 98%

Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme

Bozkaya

Tezer‐Sezgin

2005

Numerical Methods in Fluids

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“…The importance of the fluid motion through ducts under a magnetic field lies in these practical applications. Several numerical methods such as FDM [12,13], FEM [1,6,[14][15][16] and BEM [5,8,[17][18][19] produced physical numerical results in several configuration of interest. The Galerkin FEM with linear polynomials enriched by residual-free bubble functions is used to solve MHD flow problem in channels with partly insulated and partly conducting walls under oblique magnetic field by Neslitürk and Tezer-Sezgin [10] for large values of Hartmann number.…”

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confidence: 99%

Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field

Tezer‐Sezgin

Bozkaya

2007

Comput Mech

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The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct with one conducting and one insulating pair of opposite walls under an external magnetic field parallel to the conducting walls, is investigated. The MHD equations are coupled in terms of velocity and magnetic field and cannot be decoupled with conducting wall boundary conditions since then boundary conditions are coupled and involve an unknown function. The boundary element method (BEM) is applied here by using a fundamental solution which enables to treat the MHD equations in coupled form with the most general form of wall conductivities. Also, with this fundamental solution it is possible to obtain BEM solution for values of Hartmann number (M) up to 300 which was not available before. The equivelocity and induced magnetic field contours which show the well-known characteristics of MHD duct flow are presented for several values of M.

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“…The exact solution of the problem can be obtained only for some special cases [1,2]. Therefore, there are many numerical methods applied to the solution of the MHD pipe flow (see [3][4][5][6][7][8][9] and references there in).…”

Section: Introductionmentioning

confidence: 99%

FEM-BEM Coupling for the MHD Pipe Flow in an Exterior Region

Aydın¹

2013

OJFD

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In this study, the magnetohydrodynamic (MHD) flow through a circular pipe under the influence of a transverse magnetic field when the outside medium is also electrically conducting is solved numerically by using FEM-BEM coupling approach. The coupled partial differential equations defined for the interior medium are transformed into homogenous modified Helmholtz equations. For the exterior medium on an infinite region, the Laplace equation is considered for the exterior magnetic field. Unknowns in the equations are also related with the corresponding Dirichlet and Neumann type coupled boundary conditions. Unknown values of the magnetic field on the boundary and for the exterior region are obtained by using BEM, and the unknown velocity and magnetic field inside the pipe are obtained by using SUPG type stabilized FEM. Computations are carried for very high values of magnetic Reynolds numbers Rm 1 , Reynolds number Re and magnetic pressure Rh of the fluid. The results show that using stabilized method enables us to get stable and accurate numerical approximations consistent with the physical configuration of the problem over rough mesh which also results a cheap computational cost.

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The application of the boundary element method to the magnetohydrodynamic duct flow

Cited by 29 publications

References 6 publications

Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme

Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme

Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field

FEM-BEM Coupling for the MHD Pipe Flow in an Exterior Region

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