Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow

Date

2014-12-01

Author

Sellier, A.
AYDIN, SELÇUK HAN
Tezer, Münevver

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

114
views

0
downloads

The fundamental free-space 2D steady creeping MHD flow produced by a concentrated point force of strength g located at a so-called source point x(0) in an unbounded conducting Newtonian liquid with uniform viscosity mu and conductivity sigma > 0 subject to a prescribed uniform ambient magnetic field B = Be-1 is analytically obtained. More precisely, not only the produced flow pressure p and velocity u but also the resulting stress tensor field sigma are expressed at any observation point x not equal x(0) in terms of usual modified Bessel functions, the vectors g, x - x(0) and the so-called Hartmann layer thickness d = (root mu/sigma)/B (see Hartmann (1937)). The resulting basic flows obtained for g either parallel with or normal to the magnetic field B are examined and found to exhibit quite different properties.

Subject Keywords

Modified Bessel functions, Hartmann layer thickness, Green tensor, Fundamental solution, Stokes flow, Two-dimensional flow, MagnetoHydroDynamics

URI

https://hdl.handle.net/11511/54230

Journal

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

A numerical solution of the steady MHD flow through infinite strips with BEM Bozkaya, Canan; Tezer, Münevver (2012-04-01) The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in infinite channels in the presence of a magnetic field is investigated. The fluid is driven either by a pressure gradient or by the currents produced by electrodes placed parallel in the middle of the walls. The applied magnetic field is perpendicular to the infinite walls which are combined from conducting and insulated parts. A boundary element method (BEM) solution has been obtained by using a fundamental so...
A direct BEM solution to MHD flow in electrodynamically coupled rectangular channels Bozkaya, Canan; Tezer, Münevver (2012-08-15) Magnetohydrodynamic flows in coupled rectangular channels are numerically investigated under an external, horizontally applied magnetic field. The flows are driven by constant pressure gradients in the channels, which are separated with a thin partly insulating and partly conducting barrier. A direct boundary element formulation is utilized to solve these two-dimensional steady, convection-diffusion type coupled partial differential equations in terms of velocity and induced magnetic fields. The resulting s...
Radial basis function and dual reciprocity boundary element solutions of fluid dynamics problems Gürbüz, Merve; Tezer Sezgin, Münevver; Department of Mathematics (2017) In this thesis, the two-dimensional, laminar steady or unsteady flow of a viscous, incompressible, electrically conducting fluid is considered in channels of several geometries under the impact of a uniform magnetic field with different orientations. Magnetohydrodynamic (MHD) flow governed by the hydrodynamic and electromagnetic equations is solved numerically with or without Stokes approximation and with or without magnetic induction due to the large or small values of Reynolds and magnetic Reynolds number...
Two-way Fourier Split Step Algorithm over Variable Terrain with Narrow and Wide Angle Propagators Ozgun, Ozlem; Apaydin, Gökhan; Kuzuoğlu, Mustafa; Sevgi, Levent (2010-07-17) Helmholtz's wave equation can be approximated by means of two differential equations, corresponding to forward and backward propagating waves each of which is in parabolic wave equation (PWE) form. The standard PWE is very suitable for marching-type numerical solutions. The one-way Fourier split-step parabolic equation algorithm (SSPE) is highly effective in modeling electromagnetic (EM) wave propagation above the Earth's irregular surface through inhomogeneous atmosphere. The two drawbacks of the standard ...
Numerical solution of buoyancy MHD flow with magnetic potential Pekmen, B.; Tezer, Münevver (2014-04-01) In this study, dual reciprocity boundary element method (DRBEM) is applied for solving the unsteady flow of a viscous, incompressible, electrically conducting fluid in channels under the effect of an externally applied magnetic field and buoyancy force. Magnetohydrodynamics (MHD) equations are coupled with the energy equation due to the heat transfer by means of the Boussinessq approximation. Then, the 20 non-dimensional full MHD equations in terms of stream function, temperature, magnetic potential, curren...

Citation Formats

A. Sellier, S. H. AYDIN, and M. Tezer, “Free-Space Fundamental Solution of a 2D Steady Slow Viscous MHD Flow,” CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, pp. 393–406, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54230.