Finite element method solution of electrically driven magnetohydrodynamic flow

Abstract

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 functions is capable of resolving high gradients near the layer regions without refining the mesh. Thus, it is possible to obtain solutions consistent with the physical configuration of the problem even for high values of the Hartmann number. Before employing the bubble functions in the global problem, we have to find them inside each element by means of a local problem. This is achieved by approximating the bubble functions by a nonstandard finite element method based on the local problem. Equivelocity and current lines are drawn to show the well-known behaviours of the MHD flow. Those are the boundary layer formation close to the insulated walls for increasing values of the Hartmann number and the layers emanating from the endpoints of the electrodes. The changes in direction and intensity with respect to the values of wall inductance are also depicted in terms of level curves for both the velocity and the induced magnetic field

Solution of magnetohydrodynamic flow in a rectangular duct by Chebyshev collocation method

“…But he indicated the method is computationally very memory intensive and therefore time consuming. Neslitürk and Tezer-Sezgin [8,9] solved MHD flow equations in rectangular ducts by using stabilized FEM with residual free bubble functions, but their method is also time and memory consuming for large H .…”

A DRBEM solution for MHD pipe flow in a conducting medium

“…Some numerical methods have been used for MHD flow in ducts and pipes for several configurations of interest such as mixed wall conditions when the outside medium is insulating. Among them we can count the works by Sheu and Lin [9] with the finite difference method (FDM), Singh and Lal [10], Barrett [11] and Neslitürk and Tezer-Sezgin [12] with the FEM, and Liu and Zhu [13], Tezer-Sezgin and Aydin [14], and Tezer-Sezgin and Bozkaya [15] with the boundary element method (BEM). Some meshless methods have also been used for solving MHD flow equations in channels for arbitrary cross-section and arbitrary wall conductivities in [16,17].…”

Two‐level finite element method with a stabilizing subgrid for the incompressible MHD equations

“…Verardi and Cardoso [14,15], Krzeminski et al [16], Tezer-Sezgin and Köksal [17] have given FE solutions of MHD equations in rectangular ducts. A stabilized FEM using the residual-free bubble (RFB) functions has been proposed by Neslitürk and Tezer-Sezgin [18,19] for solving steady MHD duct flow problems at high Hartmann numbers.…”