The boundary element solution of the magnetohydrodynamic flow in an infinite region

Abstract

a b s t r a c tWe consider the magnetohydrodynamic (MHD) flow which is laminar, steady and incompressible, of a viscous and electrically conducting fluid on the half plane (y ≥ 0). The boundary y = 0 is partly insulated and partly perfectly conducting. An external circuit is connected so that current enters the fluid at discontinuity points through external circuits and moves up on the plane. The flow is driven by the interaction of imposed electric currents and a uniform, transverse magnetic field applied perpendicular to the wall, y = 0.The MHD equations are coupled in terms of the velocity and the induced magnetic field. The boundary element method (BEM) is applied here by using a fundamental solution which enables treating the MHD equations in coupled form with general wall conditions. Constant elements are used for the discretization of the boundary y = 0 only since the boundary integral equation is restricted to this boundary due to the regularity conditions at infinity. The solution is presented for the values of the Hartmann number up to M = 700 in terms of equivelocity and induced magnetic field contours which show the wellknown characteristics of the MHD flow. Also, the thickness of the parabolic boundary layer propagating in the field from the discontinuity points in the boundary conditions, is calculated.

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

“…After that, in 2014, Malek and Morovati [1] generalized the homogeneous MHD flow equations solving in the infinite region (upper half plane) for the high Hartmann numbers (up to 10 4 ) and arbitrary angles of magnetic field radiation on the fluid surface. In this article, it is intended to generalize the conducted works in articles [1,6] to a status in which the numerical pressure gradient is a non-zero constant. In other words, it is intended to solve the inhomogeneous MHD flow equations in the infinite region (upper half plane) for the high Hartmann numbers (up to 10 4 ) and arbitrary angles of magnetic field radiation on the fluid surface.…”

“…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. In 2009, TezerSezgin and Bozkaya [6] solved the MHD flow equations in the status that pressure gradient is zero (homogeneous form).…”

“…In this case computational domain is infinite and therefore domain integral is not calculable. For this reason, Sezgin and Bozkaya [6] and Malek and Morovati [1] have solved only homogeneous part of MHD flow equations in an infinite region. In 2013, Hosseinzadeh et al [5] could solve the above-mentioned problems (inhomogeneous MHD flow equations) in a duct.…”

“…The boundary element method is a technique that offers a great advantage to solve the MHD flow equations in an infinite region. 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. In 2009, TezerSezgin and Bozkaya [6] solved the MHD flow equations in the status that pressure gradient is zero (homogeneous form). They solved these homogeneous equations only for Hartmann numbers less than 700 (There are some valuable works in the MHD literature [21,22] which confirm that the important range of the Hartmann number in industrial applications is the values between 10 2 and 10 5 ) and a special angle of magnetic field radiation on the fluid surface.…”