BEM solution to magnetohydrodynamic flow in a semi‐infinite duct

Abstract

SUMMARY We consider the magnetohydrodynamic flow that is laminar and steady of a viscous, incompressible, and electrically conducting fluid in a semi‐infinite duct under an externally applied magnetic field. The flow is driven by the current produced by a pressure gradient. The applied magnetic field is perpendicular to the semi‐infinite walls that are kept at the same magnetic field value in magnitude but opposite in sign. The wall that connects the two semi‐infinite walls is partly non‐conducting and partly conducting (in the middle). A BEM solution was obtained using a fundamental solution that enables to treat the magnetohydrodynamic equations in coupled form with general wall conductivities. The inhomogeneity in the equations due to the pressure gradient was tackled, obtaining a particular solution, and the BEM was applied with a fundamental solution of coupled homogeneous convection–diffusion type partial differential equations. Constant elements were used for the discretization of the boundaries (y = 0, −a ⩽ x ⩽ a) and semi‐infinite walls at x = ±a, by keeping them as finite since the boundary integral equations are restricted to these boundaries due to the regularity conditions as y → ∞ . The solution is presented in terms of equivelocity and induced magnetic field contours for several values of Hartmann number (M), conducting length (l), and non‐conducting wall conditions (k). The effect of the parameters on the solution is studied. Flow rates are also calculated for these values of parameters. Copyright © 2011 John Wiley & Sons, Ltd.

Solving inhomogeneous magnetohydrodynamic flow equations in an infinite region using boundary element method

“…Tezer-Sezgin and Bozkaya in [6] and Malek and Morovati in [1] have used BEM to solve homogeneous MHD flow equations in an infinite region (the upper half plane). Also, Bozkaya and TezerSezgin used BEM for solving MHD flow equations in a semi-infinite duct [12] and in an infinite strip [10]. Because of the complexities of partial differential equations solving in infinite regions, only two articles [1,6] have been presented to solve the MHD flow equations in the infinite region (upper half plane) so far.…”