FINITE DIFFERENCE METHOD SOLUTION OF MAGNETOHYDRODYNAMIC FLOW IN CHANNELS WITH ELECTRICALLY CONDUCTING AND SLIPPING WALLS

Download

thesis.pdf

Date

2018-5-28

Author

Arslan, Sinem

Metadata

Show full item record

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

Item Usage Stats

276
views

177
downloads

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.

Subject Keywords

MHD flow, FDM, Slipping Velocity, Variable Conductivity

URI

https://hdl.handle.net/11511/99804

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Effect of boundary conditions on magnetohydrodynamics duct flow Bozkaya, Canan (2017-12-01) The magnetohydrodynamic flow of an incompressible, viscous and electrically conducting fluid is investigated numerically in a channel of either rectangular or semi-infinite cross-section with several types of boundary conditions involving walls of variable conductivity in the presence of hydrodynamic slip. The flow is fully developed and driven by a constant pressure gradient in the axial direction under a uniform external inclined magnetic field. The governing differential equations coupled in velocity and...
The BEM Solutions of MHD Flow and Heat Transfer in a Rectangular Duct with Temperature Dependent Viscosity Kaya, Elif Ebren; Tezer, Münevver (2019-01-01) The steady, laminar, fully developed magnetohydrodynamic (MHD) flow of an incompressible, electrically conducting fluid with temperature dependent viscosity is studied in a rectangular duct together with its heat transfer. Although the induced magnetic field is neglected due to the small Reynolds number, the Hall effect, viscous and Joule dissipations are taken into consideration. The momentum and the energy equations are solved iteratively. Firstly, the momentum equation is solved by using the boundary ele...
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...
The application of BEM to MHD flow and heat transfer in a rectangular duct with temperature dependent viscosity Ebren Kaya, Elif; Tezer, Münevver ( EC LTD.; 2018-07-11) The steady, laminar, fully developed MHD flow of an incompressible, electrically conducting fluid with temperature dependent viscosity is studied in a rectangular duct together with its heat transfer. Although the induced magnetic field is neglected due to the small Reynolds number, the Hall effect, viscous and Joule dissipations are taken into consideration. The momentum equation for the pipe-axis velocity and the energy equation are solved iteratively. Firstly, the momentum equation is solved by using the...
Magnetohydrodynamic Flow in a Rectangular Duct Bozkaya, Canan (2018-12-02) The magnetohydrodynamic (MHD) flow of an incompressible, viscous and electrically conducting fluid in a rectangular duct with insulated and perfectly conducting walls is investigated numerically in the presence of hydrodynamic slip. The flow is fully developed and driven by a constant pressure gradient in the axial direction under the effect of an externally applied uniform and inclined magnetic field. A direct boundary element method (BEM) using a fundamental solution which enables to treat the governing M...

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.