ANZIAM  J.  44 (2002), 305-322
The dual reciprocity boundary element method for magnetohydrodynamic channel flows

Huan-Wen Liu
  Department of Mathematics and Computer Science
  Guangxi University for Nationalities
  Nanning, Guangxi 530006
  P.R. China
Song-Ping Zhu
  School of Mathematics and Applied Statistics
  The University of Wollongong
  Wollongong, NSW 2522

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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