Exact and FDM solutions of 1D MHD flow between parallel electrically conducting and slipping plates

Date

2019-08-01

Author

Arslan, Sinem
Tezer, Münevver

Metadata

Show full item record

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

Item Usage Stats

290
views

0
downloads

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 and b are only with respect to y-coordinate. The finite difference method (FDM) is used to solve the governing MHD equations with the wall conditions which include both the slip and the conductivity of the plates. The numerical results obtained from FDM discretized equations are compared with the exact solution derived here for the 1D MHD flow with Robin's type boundary conditions. The fluid velocity and the induced magnetic field are simulated for each special case of boundary conditions on the plates including no-slip to highly slipping and insulated to perfectly conducting plates. The well-known characteristics of the MHD flow are observed. It is found that the increase in the slip length weakens the formation of boundary layers. Thus, the FDM which is simple to implement, enables one to depict the effects of Hartmann number, conductivity parameter, and the slip length on the behavior of both the velocity and the induced magnetic field at a small expense.

Subject Keywords

Applied Mathematics, Computational Mathematics

URI

https://hdl.handle.net/11511/46459

Journal

ADVANCES IN COMPUTATIONAL MATHEMATICS

DOI

https://doi.org/10.1007/s10444-019-09669-x

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on vortex formation modes Bozkaya, Canan; Mironova, L. A.; Gubanov, O. I. (Elsevier BV, 2011-06-15) A computational study of a viscous incompressible two-fluid model with an oscillating cylinder is investigated at a Reynolds number of 200 and at a dimensionless displacement amplitude of A = 0.13 and for the dimensionless forcing cylinder oscillation frequency-to-natural vortex shedding frequency ratios, f/f(0) = 1.5, 2.5, 3.5. Specifically, two-dimensional flow past a circular cylinder subject to forced in-line oscillations beneath a free surface is considered. The method is based on a finite volume discr...
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 ...
Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field Tezer, Münevver; Bozkaya, Canan (Springer Science and Business Media LLC, 2008-03-01) 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 ...
Accurate numerical bounds for the spectral points of singular Sturm-Liouville problems over 0 < x < infinity Taşeli, Hasan (Elsevier BV, 2004-03-01) The eigenvalues of singular Sturm-Liouville problems defined over the semi-infinite positive real axis are examined on a truncated interval 0<x<l as functions of the boundary point l. As a basic theoretical result, it is shown that the eigenvalues of the truncated interval problems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds to the eigenvalues of the original problem. Moreover, the unperturbed system in a perturbation problem, where l remains sufficient...
ELECTRICALLY DRIVEN FLOWS IN MHD WITH MIXED ELECTROMAGNETIC BOUNDARY-CONDITIONS Tezer, Münevver; ARIEL, PD (Wiley, 1988-01-01) Flow of viscous, incompressible, electrically conducting fluid, driven by imposed electric currents has been investigated in the presence of a transverse magnetic field. The boundary perpendicular to the magnetic field is perfectly conducting partly along its length. Three cases have been considered: a) flow in the upper half plane when the boundary to the right of origin is insulating and that to the left is perfectly conducting, b) flow in the upper half plane when a finite length of the boundary is perfe...

Citation Formats

S. Arslan and M. Tezer, “Exact and FDM solutions of 1D MHD flow between parallel electrically conducting and slipping plates,” ADVANCES IN COMPUTATIONAL MATHEMATICS, pp. 1923–1938, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46459.