Stability of Unsteady MHD Flow in a Rectangular Duct

Date

2018-06-29

Author

Tezer, Münevver

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In this study, the time dependent and coupled magnetohydrodynamic (MHD) flow equations are solved in the cross-section of a rectangular pipe (duct) by using the radial basis function approximation (RBF). The MHD studies electrically conducting fluids in the presence of a magnetic field. It has wide range of industrial applications such as MHD generators, MHD pumps, plasma physics and nuclear fusion [1]. The velocity and the induced magnetic field are obtained by approximating the inhomogeneities using thin plate splines (r2 lnr) [2]. Then, particular solution is found satisfying both the MHD equations and the boundary conditions which are the no-slip and insulated wall conditions. The Euler time integration scheme is used for advancing the solution to steady-state together with a relaxation parameter for achieving stable solution. It is shown that, as Hartman number (M) increases the flow develops boundary layers of order M-1 and M-1/2 on the Hartmann walls (perpendicular to the applied magnetic field) and side walls (parallel to the magnetic field), respectively. The induced magnetic field also exhibits boundary layers at the Hartmann walls, and the flow flattens and becomes stagnant at the center of the duct with an increase in the Hartmann number. These are the well-known characteristics of the MHD flow. The stability analysis is carried in terms of spectral radius of the coefficient matrix in the final discretized system, requiring the boundedness of spectral radius by one. The implemented scheme “Euler in time - radial basis function approximation in space” gives stable solution by using quite large time increment and relaxation parameter although the Euler scheme is an explicit method.

Subject Keywords

MHD, RBF, Euler Time-Integration, Stability

URI

https://hdl.handle.net/11511/84805
http://icame.balikesir.edu.tr/icame18/ICAME18_Abstract_Book.pdf

Conference Name

International Conference on Applied Mathematics in Engineering (ICAME) (27-29 Haziran 2018)

Collections

Department of Mathematics, Conference / Seminar

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Citation Formats

M. Tezer, “Stability of Unsteady MHD Flow in a Rectangular Duct,” presented at the International Conference on Applied Mathematics in Engineering (ICAME) (27-29 Haziran 2018), Balıkesir, Türkiye, 2018, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/84805.