# Numerical solutions of boundary value problems; applications in ferrohydrodynamics and magnetohydrodynamics

2017
Şenel, Pelin
In this thesis, steady, laminar, fully developed flows in pipes subjected to a point magnetic source or uniform magnetic field are simulated by the dual reciprocity boundary element method (DRBEM). The Navier-Stokes and energy equations are solved in terms of the velocity, pressure and the temperature of the fluid which are all of the original variables of the problem. The missing pressure equation is derived and pressure boundary conditions are generated by a finite difference approximation and the DRBEM coordinate matrix. Fundamental solution of Laplace equation is made use of to convert the nonlinear partial differential equations into the boundary integral equations. The terms other than Laplacian are approximated by a series of radial basis functions. The nonlinearities in the governing equations are easily handled by the use of the DRBEM coordinate matrix. The influence of the point source magnetic field on the Ferrohydrodynamics (FHD) Stokes, incompressible, and forced convection flows are investigated first. The interaction between the buoyancy force, magnetization force and the viscous dissipation is discussed. Then, the effect of multiple point magnetic sources on the FHD incompressible flow is studied. DRBEM simulations of Magnetohydrodynamics (MHD) pipe flow and the flow between parallel infinite plates with slip velocity conditions are also presented. The coupled momentum and magnetic induction equations are combined and solved without an iteration. This process provides the nodal solutions in one stroke both on the boundary and inside the problem domain. The importance of the thesis study is in the fact that it is the first DRBEM application to FHD flow under point magnetic source and MHD flow with slip walls.

# Suggestions

 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...
 BEM solution to magnetohydrodynamic flow in a semi-infinite?duct Bozkaya, Canan; Tezer, Münevver (2012-09-30) 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 condu...
 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...
 Thermal convection in the presence of a vertical magnetic field Guray, E.; Tarman, H. I. (Springer Science and Business Media LLC, 2007-11-01) The interaction between thermal convection and an external uniform magnetic field in the vertical is numerically simulated within a computational domain of a horizontally periodic convective box between upper and lower rigid plates. The numerical technique is based on a spectral element method developed earlier to simulate natural thermal convection. In this work, it is extended to a magnetoconvection problem. Its main features are the use of rescaled Legendre-Lagrangian polynomial interpolants in expanding...
 Numerical Modeling of Electromagnetic Scattering from Periodic Structures by Transformation Electromagnetics ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2016-09-22) The transformation electromagnetics is applied to the modeling of electromagnetic scattering from periodic structures in conjunction with the finite element method with periodic boundary conditions. In a unit cell of periodic structure, a uniform mesh is used over a flat surface and the arbitrary periodic surface is modeled by a coordinate transformation. The major advantage of this approach is that arbitrary geometries can be handled by using a single and simple mesh. Therefore, repeated computations (such...
Citation Formats
P. Şenel, “Numerical solutions of boundary value problems; applications in ferrohydrodynamics and magnetohydrodynamics,” Ph.D. - Doctoral Program, Middle East Technical University, 2017. 