Stability of Unsteady MHD Flow in a Rectangular Duct

2018-06-29
In this study, the time dependent and coupled magnetohydrodynamic (MHD) flow equations are solved in the cross-section of a rectangular pipe (duct) by using the radial basis function approximation (RBF). The MHD studies electrically conducting fluids in the presence of a magnetic field. It has wide range of industrial applications such as MHD generators, MHD pumps, plasma physics and nuclear fusion [1]. The velocity and the induced magnetic field are obtained by approximating the inhomogeneities using thin plate splines (r2 lnr) [2]. Then, particular solution is found satisfying both the MHD equations and the boundary conditions which are the no-slip and insulated wall conditions. The Euler time integration scheme is used for advancing the solution to steady-state together with a relaxation parameter for achieving stable solution. It is shown that, as Hartman number (M) increases the flow develops boundary layers of order M-1 and M-1/2 on the Hartmann walls (perpendicular to the applied magnetic field) and side walls (parallel to the magnetic field), respectively. The induced magnetic field also exhibits boundary layers at the Hartmann walls, and the flow flattens and becomes stagnant at the center of the duct with an increase in the Hartmann number. These are the well-known characteristics of the MHD flow. The stability analysis is carried in terms of spectral radius of the coefficient matrix in the final discretized system, requiring the boundedness of spectral radius by one. The implemented scheme “Euler in time - radial basis function approximation in space” gives stable solution by using quite large time increment and relaxation parameter although the Euler scheme is an explicit method.
International Conference on Applied Mathematics in Engineering (ICAME) (27-29 Haziran 2018)

Suggestions

Numerical Solution and Stability Analysis of Transient MHD Duct Flow
Tezer, Münevver (2018-11-01)
This paper simulates the 2D transient magnetohydrodynamic (MHD) flow in a rectangular duct in terms of the velocity of the fluid and the induced magnetic field by using the radial basis function (RBF) approximation. The inhomogeneities in the Poisson’s type MHD equations are approximated using the polynomial functions (1+r) and the particular solution is found satisfying both the equations and the boundary conditions (no-slip and insulated walls). The Euler scheme is used for advancing the solution to ste...
Stabilizing subgrid FEM solution of the natural convection flow under high magnitude magnetic field on sinusoidal corrugated enclosure
Aydın, S. H.; Tezer, Münevver (Informa UK Limited, 2019-7-7)
This study deals with the stabilized finite element solution of the steady, natural convection flow in an enclosure under a magnetic field applied perpendicular to the sinusoidal corrugated vertical walls of the enclosure, in terms of primitive variables. Several vertical sinusoidal functions are selected for the comparison. A stabilized FEM scheme called SSM is proposed in order to obtain a stable solution for the high values of problem parameters with a cheap computational cost. Proposed numerical scheme ...
Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method
Tezer, Münevver (2004-05-01)
The polynomial based differential quadrature and the Fourier expansion based differential quadrature method are applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of a transverse external oblique magnetic field. Numerical solution for velocity and induced magnetic field is obtained for the steady-state, fully developed, incompressible flow of a conducting fluid inside of the duct. Equal and unequal grid point discretizations are both used in the domain and it is ...
Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number
Evcin, Cansu; Uğur, Ömür; Tezer, Münevver (2018-10-01)
The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms ...
Controlling the power law fluid flow and heat transfer under the external magnetic field using the flow index and the Hartmann number
Evcin, Cansu; Uğur, Ömür; Tezer, Münevver (2018-10-01)
The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms ...
Citation Formats
M. Tezer, “Stability of Unsteady MHD Flow in a Rectangular Duct,” presented at the International Conference on Applied Mathematics in Engineering (ICAME) (27-29 Haziran 2018), Balıkesir, Türkiye, 2018, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/84805.