The ANZIAM Journal

Research Article

The dual reciprocity boundary element method for magnetohydrodynamic channel flows

Huan-Wen Liua1 and Song-Ping Zhua2

a1 Department of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, PR. China; e-mail: [email protected].

a2 School of Mathematics and Applied Statistics, The University of Wollongong, Wollongong, NSW 2522, Australia; e-mail: [email protected].


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 crosssections, 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).

(Received August 07 1998)

(Revised October 15 2002)