Solution of magnetohydrodynamic flow problems using the boundary element method

Date

2006-05-01

Author

Tezer, Münevver

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A boundary element solution is implemented for magnetohydrodynamic (MHD) flow problem in ducts with several geometrical cross-section with insulating walls when a uniform magnetic field is imposed perpendicular to the flow direction. The coupled velocity and induced magnetic field equations are first transformed into uncoupled inhomogeneous convection-diffusion type equations. After introducing particular solutions, only the homogeneous equations are solved by using boundary element method (BEM). The fundamental solutions of the uncoupled equations themselves (convection-diffusion type) involve the Hartmann number (M) through exponential and modified Bessel functions. Thus, it is possible to obtain results for large values of M (M <= 300) using only the simplest constant boundary elements. It is found that as the Hartmann number increases, boundary layer formation starts near the walls and there is a flattening tendency for both the velocity and the induced magnetic field. Also, velocity becomes uniform at the center of the duct. These are the well-known behaviours of MHD flow. The velocity and the induced magnetic field contours are graphically visualized for several values of At and for different geometries of the duct cross-section.

Subject Keywords

General Engineering, Applied Mathematics, Analysis, Computational Mathematics

URI

https://hdl.handle.net/11511/44617

Journal

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

DOI

https://doi.org/10.1016/j.enganabound.2005.12.001

Collections

Department of Mathematics, Article

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Citation Formats

M. Tezer, “Solution of magnetohydrodynamic flow problems using the boundary element method,” ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, pp. 411–418, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44617.