ANZIAM J.
44 (2002), 305-322
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The dual reciprocity boundary element method for magnetohydrodynamic channel flows
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Huan-Wen Liu
Department of Mathematics and Computer Science
Guangxi University for Nationalities
Nanning, Guangxi 530006
P.R. China
huanwenliu@hotmail.com
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Song-Ping Zhu
School of Mathematics and Applied Statistics
The University of Wollongong
Wollongong, NSW 2522
Australia
spz@uow.edu.au
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Abstract
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In this paper, we consider the problem of the
steady-state fully developed magnetohydrodynamic
(MHD) flow of a conducting fluid through a
channel with arbitrary wall conductivity in the
presence of a transverse external magnetic field
with various inclined angles. The coupled
governing equations for both axial velocity and
induced magnetic field are firstly transformed
into decoupled Poisson-type equations with
coupled boundary conditions. Then the dual
reciprocity boundary element method (DRBEM)
[20] is used to solve the Poisson-type
equations. As testing examples, flows in channels
of three different cross-sections, rectangular,
circular and triangular, are calculated. It is
shown that solutions obtained by the DRBEM with
constant elements are accurate for Hartmann
number up to 8
and for large conductivity parameters comparing
to exact solutions and solutions by the finite
element method (FEM).
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