BEM SOLUTIONS OF MAGNETOHYDRODYNAMIC FLOW EQUATIONS UNDER THE TIME AND AXIAL-DEPENDENT MAGNETIC FIELD

Download

thesis.pdf

Date

2021-9-6

Author

Ebren Kaya, Elif

Metadata

Show full item record

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

Item Usage Stats

433
views

423
downloads

In the thesis, four different MHD duct flow problems are solved by using the Dual Reciprocity Boundary Element Method (DRBEM) with the suitable boundary conditions according to the physics of the problem. The two-dimensional, steady or unsteady, fully-developed MHD flow of a viscous, incompressible and electrically conducting fluid is considered in a long pipe of rectangular cross-section (duct) under the effect of an externally applied magnetic field which is either uniform or time-dependent or axially changing. The inductionless MHD flow with temperature dependent viscosity and heat transfer is the first considered problem. In this problem, the induced magnetic field is neglected due to the small magnetic Reynolds number assumption. Secondly, the MHD duct flow under a time-varied external magnetic field is studied. Then, we turn our concern to MHD flow problems under an axial-dependent magnetic field varying in the streamwise direction (pipe-axis direction) in the third and the fourth problems. Specifically, the inductionless MHD flow with electric potential is considered under the effect of the axially-changing magnetic field as the third problem. Adding the induced magnetic field to the velocity and electric potential equations as a triple is the last MHD flow problem considered in the thesis. The parametrix BEM implementation is also presented for the solution of the variable coefficient convection-diffusion type equations. The influence of the magnetic fields on the MHD flows is investigated and simulated in terms of the velocity, temperature, induced magnetic field and electric potential contours for several values of physical parameters.

Subject Keywords

Magnetohydrodynamics, Dual Reciprocity Boundary Element Method, Parametrix BEM, Time-varied Magnetic Field, Axial-depedent Magnetic Field

URI

https://hdl.handle.net/11511/92898

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

BEM solution of MHD flow in a pipe coupled with magnetic induction of exterior region Tezer, Münevver (2013-05-01) In this paper, numerical solutions are presented for the MHD flow in a pipe surrounded by an electrically conducting medium, and under the influence of a transverse magnetic field. The boundary element method is used which discretizes only the pipe wall and is suitable for the infinite exterior region. Coupled MHD equations for the velocity and induced magnetic field inside the pipe, and the induced magnetic field equation for the outside medium are solved simultaneously taking into account also coupled bou...
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...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems Bozkaya, Canan (2005-03-18) The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
BEM solution of transient magnetohydrodynamic flows in ducts Fendoğlu, Hande; Bozkaya, Canan; Tezer, Münevver (2017-09-30) The present study focuses on the boundary type method solution of the magnetohydrodynamic (MHD) ow which is governed by the nonlinear convection-diusion type equations coupled in velocity and magnetic eld. The numerical method is based on the use of boundary element method (BEM) with two dierent formulations, namely domain BEM (DBEM) and dual reciprocity BEM (DRBEM) in the spatial discretization; and a backward nite dierence scheme is adopted for the time integration. The obtained DBEM and DRBEM resul...
Dual reciprocity boundary element method for magnetohydrodynamic flow using radial basis functions Tezer, Münevver (2002-02-01) A dual reciprocity boundary element method is given to obtain the solution in terms of velocity and induced magnetic field for the study of MHD (magnetohydrodynamic) flow through a rectangular duct having insulating walls. The equations are transformed to two types of nonlinear Poisson equations and the right-hand sides in these equations are approximated using combinations of two classes of radial basis functions (the value of the function and its normal derivatives are utilized for approximation). Computa...

Citation Formats

E. Ebren Kaya, “BEM SOLUTIONS OF MAGNETOHYDRODYNAMIC FLOW EQUATIONS UNDER THE TIME AND AXIAL-DEPENDENT MAGNETIC FIELD,” Ph.D. - Doctoral Program, Middle East Technical University, 2021.