The boundary element solution of the magnetohydrodynamic flow in an infinite region

Date

2009-03-15

Author

Tezer, Münevver
Bozkaya, Canan

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

209
views

0
downloads

We consider the magnetohydrodynamic (MHD) flow which is laminar, steady and incompressible, of a viscous and electrically conducting fluid on the half plane (y >= 0). The boundary y = 0 is partly insulated and partly perfectly conducting. An external circuit is connected so that current enters the fluid at discontinuity points through external circuits and moves up on the plane. The flow is driven by the interaction of imposed electric currents and a uniform, transverse magnetic field applied perpendicular to the wall, y = 0. The MHD equations are coupled in terms of the velocity and the induced magnetic field. The boundary element method (BEM) is applied here by using a fundamental solution which enables treating the MHD equations in coupled form with general wall conditions. Constant elements are used for the discretization of the boundary y = 0 only since the boundary integral equation is restricted to this boundary due to the regularity conditions at infinity. The solution is presented for the values of the Hartmann number up to M = 700 in terms of equivelocity and induced magnetic field contours which show the well-known characteristics of the MHD flow. Also, the thickness of the parabolic boundary layer propagating in the field from the discontinuity points in the boundary conditions, is calculated.

Subject Keywords

Applied Mathematics, Computational Mathematics

URI

https://hdl.handle.net/11511/37267

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2008.08.016

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Finite element study of biomagnetic fluid flow in a symmetrically stenosed channel Turk, O.; Tezer, Münevver; Bozkaya, Canan (Elsevier BV, 2014-03-15) The two-dimensional unsteady, laminar flow of a viscous, Newtonian, incompressible and electrically conducting biofluid in a channel with a stenosis, under the influence of a spatially varying magnetic field, is considered. The mathematical modeling of the problem results in a coupled nonlinear system of equations and is given in stream function-vorticity-temperature formulation for the numerical treatment. These equations together with their appropriate boundary conditions are solved iteratively using the ...
Finite element method solution of electrically driven magnetohydrodynamic flow Nesliturk, AI; Tezer, Münevver (Elsevier BV, 2006-08-01) The magnetohydrodynamic (MHD) flow in a rectangular duct is investigated for the case when the flow is driven by the current produced by electrodes, placed one in each of the walls of the duct where the applied magnetic field is perpendicular, The flow is steady, laminar and the fluid is incompressible, viscous and electrically conducting. A stabilized finite element with the residual-free bubble (RFB) functions is used for solving the governing equations. The finite element method employing the RFB functio...
A finite element variational multiscale method for the Navier-Stokes equations Volker, John; Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01) This paper presents a variational multiscale method (VMS) for the incompressible Navier-Stokes equations which is defined by a large scale space L-H for the velocity deformation tensor and a turbulent viscosity nu(T). The connection of this method to the standard formulation of a VMS is explained. The conditions on L-H under which the VMS can be implemented easily and efficiently into an existing finite element code for solving the Navier - Stokes equations are studied. Numerical tests with the Smagorinsky ...
Exact and FDM solutions of 1D MHD flow between parallel electrically conducting and slipping plates Arslan, Sinem; Tezer, Münevver (Springer Science and Business Media LLC, 2019-08-01) In this study, the steady, laminar, and fully developed magnetohydrodynamic (MHD) flow is considered in a long channel along with the z-axis under an external magnetic field which is perpendicular to the channel axis. The fluid velocity u and the induced magnetic field b depend on the plane coordinates x and y on the cross-section of the channel. When the lateral channel walls are extended to infinity, the problem turns out to be MHD flow between two parallel plates (Hartmann flow). Now, the variations of u...
Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement Manguoğlu, Murat; Sameh, Ahmed H.; Tezduyar, Tayfun E. (Springer Science and Business Media LLC, 2010-06-01) Computation of incompressible flows in arterial fluid mechanics, especially because it involves fluid-structure interaction, poses significant numerical challenges. Iterative solution of the fluid mechanics part of the equation systems involved is one of those challenges, and we address that in this paper, with the added complication of having boundary layer mesh refinement with thin layers of elements near the arterial wall. As test case, we use matrix data from stabilized finite element computation of a b...

Citation Formats

M. Tezer and C. Bozkaya, “The boundary element solution of the magnetohydrodynamic flow in an infinite region,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 510–521, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37267.