Numerical Solution Of Magnetohydrodynamic
Flow Problems Using The Boundary Element
Method
Author(s)
M. Tezer-Sezgin & S. Han Aydın
Abstract
A boundary element solution is given for a magnetohydrodynamic (MHD) flow
problem in a rectangular duct having insulating walls, in terms of velocity and
induced magnetic field. The coupled velocity and magnetic field equations are first
transformed into decoupled nonhomogeneous convection-diffusion type equations
and then finding particular solutions, the homogeneous equations are solved using
the boundary elementmethod (BEM). The fundamental solutions of the decoupled
homogeneous equations themselves are used which contain the Hartmann number
through exponential and modified Bessel functions. Thus, it is possible to increase
the Hartmann number to moderate values in the calculations especially when the
singularities in the integrals are taken care of with the asymptotic expansions of
modified Bessel functions. The computations are carried out for the Hartmann
number M ≤ 50 using constant boundary elements. It is found that as the number
of boundary elements increases it is possible to increase the Hartmann number
although it is time consuming. This is not the case in the dual reciprocity boundary
element solution of MHD problems since the fundamental solution of the Laplace
equation is used, Tezer-Sezgin and Aydın [1]. The velocity and induced magnetic
field contours are illustrated in terms of graphics. It is observed that as the Hartmann
number increases boundary layers are formed near the boundaries which is
a well known behaviour of MHD flow.
Keywords: MHD flow, boundary element method.
Keywords
MHD flow, boundary element method
Related Book
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