Finite difference method solution of magnetohydrodynamic flow in channels with electrically conducting and slipping walls

Arslan, Sinem
In this thesis, the laminar, steady and fully developed magnetohydrodynamic (MHD) flow is considered in a pipe (channel) along with the z-axis under an external magnetic field applied perpendicular to the pipe. The velocity and the induced magnetic field depend only on the plane coordinates x and y on the cross-section of the pipe (duct) when the flow reaches to fully-developed case. This results in two-dimensional MHD duct flow. When the lateral channel walls are extended to infinity the flow is considered between two parallel plates (Hartmann flow). Then, the variations of the velocity and the induced magnetic field are only with respect to the coordinate y between the plates which are perpendicular to the external magnetic field and the problem becomes one-dimensional MHD flow between parallel plates. The finite difference method (FDM) is used to solve the governing equations of 1D and 2D MHD flow problems with the boundary conditions which include both the slip and the varying conductivity of the walls. The numerical results obtained from FDM discretized equations are compared with the exact solution derived for the 1D MHD flow between parallel plates with the most general case of slipping and variably conducting boundary conditions. On the other hand, for the validation of the numerical results obtained from the FDM for the 2D MHD flow in a square duct with the exact solution, the case of no-slip and insulated duct walls is considered and the agreement is obtained. Also, for both of the 1D and the 2D MHD flow problems, the velocity of the fluid and the induced magnetic field are simulated for each special case of boundary conditions including no-slip to highly slipping and insulated to perfectly conducting plates. The well-known characteristics of the MHD flow and the influences of slipping and electrically conducting plates on the flow and the induced magnetic field are observed. Thus, the FDM which is simple to implement, enables one to depict the effects of Hartmann number, conductivity parameter and the slip parameter on the behavior of both the velocity of the fluid and the induced magnetic field at a small expense.


Finite Difference Solutions of 2D Magnetohydrodynamic Channel Flow in a Rectangular Duct
Arslan, Sinem (2019-10-04)
In this study, the MHD flow of an electrically conducting fluid is considered in a long channel (pipe) of rectangular cross-section along with the z-axis. The fluid is driven by a pressure gradient along the z-axis. The flow is steady, laminar, fully-developed and is influenced by an external magnetic field applied perpendicular to the channel axis. So, the velocity field V=(0,0,V) and the magnetic field B=(0, B_{0}, B) have only channel-axis components V and B depending only on the plane coordinates x an...
Finite element analysis of a projection-based stabilization method for the Darcy-Brinkman equations in double-diffusive convection
Cibik, Aytekin; Kaya Merdan, Songül (2013-02-01)
This paper presents a projection-based stabilization method of the double-diffusive convection in Darcy-Brinkman flow. In particular, it is concerned with the convergence analysis of the velocity, temperature and concentration in the time dependent case. Numerical experiments are presented to verify both the theory and the effectiveness of the method. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.
Single discharge thermo-electrical modeling of micromachining mechanism in electric discharge machining
Sarikavak, Yasin; Cogun, Can (2012-05-01)
In this study, single discharge thermo-electrical model of workpiece material removal in electrical discharge machining (EDM) was developed. Developed model includes generation of energy in liquid media, variation of plasma channel radius and transfer of heat from the channel by the electrical discharge. Effect of generated energy in plasma channel on workpiece removal was theoretically investigated by using different experimental parameters used in literature. The developed model finds the temperature dist...
Finite element method solution of electrically driven magnetohydrodynamic flow
Nesliturk, AI; Tezer, Münevver (Elsevier BV, 2006-08-01)
The magnetohydrodynamic (MHD) flow in a rectangular duct is investigated for the case when the flow is driven by the current produced by electrodes, placed one in each of the walls of the duct where the applied magnetic field is perpendicular, The flow is steady, laminar and the fluid is incompressible, viscous and electrically conducting. A stabilized finite element with the residual-free bubble (RFB) functions is used for solving the governing equations. The finite element method employing the RFB functio...
Turbulent Combustion Modeling with Fully Coupled Fully Implicit Compressible Solver
Kalpakli, B.; Ozturkmen, M. O.; Akmandor, I. S. (2014-09-28)
The aim of this paper is to report on a recently developed fully coupled and fully implicit solver for turbulent combustion. All the equationsare written in terms of primitive variables (pressure, velocity, temperature, turbulent parameters and species mass fractions) and solved in a fully coupled manner. The coupled system of equations is solved using an unstructured collocated Finite Volume (FV) approach using a fully implicit temporal discretization. An all speed version of AUSM approach is used along wi...
Citation Formats
S. Arslan, “Finite difference method solution of magnetohydrodynamic flow in channels with electrically conducting and slipping walls,” M.S. - Master of Science, Middle East Technical University, 2018.