# DRBEM solutions of Stokes and Navier-Stokes equations in cavities under point source magnetic field

2016-03-01
Senel, P.
Tezer, Münevver
This paper describes an iterative dual reciprocity boundary element method (DRBEM) for the solutions of Stokes and Navier-Stokes equations in cavities under the effect of an external point source magnetic field placed very close to the bottom. The fluid is viscous, incompressible and electrically non-conducting but magnetizable, and the flow is steady, laminar and fully developed. Both the Stokes and Navier-Stokes equations are solved in terms of velocity and pressure of the fluid by using DRBEM. Pressure boundary conditions are obtained through momentum equations by approximating pressure gradients with finite differences. All the space derivatives are computed by using DRBEM coordinate matrix. The results of Stokes flow under point magnetic source in lid-driven square and circular cavities are presented and compared. The three-dimensional flow of an incompressible fluid is considered in the 2D rectangular cross-section of a long duct with and without a moving top-lid imposed to a point magnetic source. The axial velocity is also computed due to the pressure gradient given in the axial direction. The obtained results for varying magnetic number show that the flow is appreciably influenced by the presence of the magnetic field.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

# Suggestions

 DRBEM Solution of Incompressible MHD Flow with Magnetic Potential Pekmen, B.; Tezer, Münevver (2013-12-01) The dual reciprocity boundary element method (DRBEM) formulation is presented for solving incompressible magnetohydrodynamic (MHD) flow equations. The combination of Navier-Stokes equations of fluid dynamics and Maxwell's equations of electromagnetics through Ohm's law is considered in terms of stream function, vorticity and magnetic potential in 2D. The velocity field and the induced magnetic field can be determined through the relations with stream function and magnetic potential, respectively. The numeri...
 DRBEM Solution of MHD Flow and Electric Potential in a Rectangular Pipe with a Moving Lid Tezer, Münevver; Bozkaya, Canan (2015-09-18) We present the dual reciprocity boundary element method (DRBEM) solution of the system of equations which model magnetohydrodynamic (MHD) flow in a pipe with moving lid at low magnetic Reynolds number. The external magnetic field acts in the pipe-axis direction generating the electric potential. The solution is obtained in terms of stream function, vorticity and electric potential in the cross-section of the pipe, and the pipe axis velocity is also computed under a constant pressure gradient. It is found th...
 DRBEM solutions of cauchy problem for the magnetohydrodynamic duct flow Aydın, Cemre; Tezer-Sezgin, Münevver,; Department of Mathematics (2020) In this thesis, the direct and inverse problems of the MHD flow in rectangular ducts are solved in terms of the velocity of the fluid and the induced magnetic field by using the Dual Reciprocity Boundary Element Method (DRBEM). The two-dimensional, steady flow of a viscous, incompressible, and electrically conducting fluid is considered under the effect of an externally applied mangetic field. The duct wall conditions for the MHD flow ranges from the no-slip to slip and insulated to perfectly conducting. In...
 DRBEM applications in fluid dynamics problems and DQM solutions of hyperbolic equations Pekmen, Bengisen; Tezer Sezgin, Münevver; Department of Scientific Computing (2014) In this thesis, problems of fluid dynamics defined by the two-dimensional convection-diffusion type partial differential equations (PDEs) are solved using the dual reciprocity boundary element method (DRBEM). The terms other than the Laplacian are treated as inhomogeneous terms in the DRBEM application. Once the both sides are multiplied by the fundamental solution of Laplace equation, and then integrated over the domain, all the domain integrals are transformed to boundary integrals using the Green's ident...
 DRBEM solution of free convection in porous enclosures under the effect of a magnetic field Pekmen, B.; Tezer, Münevver (2013-01-01) The dual reciprocity boundary element method (DRBEM) is applied for solving steady free convection in special shape enclosures filled with a fluid saturated porous medium under the effect of a magnetic field. The left and right walls are maintained at constant or different temperatures while the top and bottom walls are kept adiabatic. The effect of the external magnetic field on the flow and temperature behavior is visualized with different Rayleigh numbers Ra, Hartmann numbers Ha and inclination angle phi...
Citation Formats
P. Senel and M. Tezer, “DRBEM solutions of Stokes and Navier-Stokes equations in cavities under point source magnetic field,” ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, pp. 158–175, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35944. 