scholarly journals Liquid-metal flow in a rectangular duct with a non-uniform magnetic field

1986 ◽  
Author(s):  
J.S. Walker
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Uniform Magnetic Field ◽  
Metal Flow ◽  
Rectangular Duct ◽  
Liquid Metal Flow

scholarly journals Linear Stability Analysis of Liquid Metal Flow in an Insulating Rectangular Duct under External Uniform Magnetic Field

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 177 ◽  
Author(s):  
Tagawa
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Liquid Metal ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Uniform Magnetic Field ◽  
Metal Flow ◽  
Rectangular Duct ◽  
Liquid Metal Flow ◽  
External Uniform Magnetic Field

Linear stability analysis of liquid metal flow driven by a constant pressure gradient in an insulating rectangular duct under an external uniform magnetic field was carried out. In the present analysis, since the Joule heating and induced magnetic field were neglected, the governing equations consisted of the continuity of mass, momentum equation, Ohm’s law, and conservation of electric charge. A set of linearized disturbance equations for the complex amplitude was decomposed into real and imaginary parts and solved numerically with a finite difference method using the highly simplified marker and cell (HSMAC) algorithm on a two-dimensional staggered mesh system. The difficulty of the complex eigenvalue problem was circumvented with a Newton—Raphson method during which its corresponding eigenfunction was simultaneously obtained by using an iterative procedure. The relation among the Reynolds number, the wavenumber, the growth rate, and the angular frequency was successfully obtained for a given value of the Hartmann number as well as for a direction of external uniform magnetic field.

Liquid-metal flow in a rectangular duct with a strong non-uniform magnetic field

1984 ◽  
Vol 139 ◽  
pp. 309-324 ◽  
Author(s):  
John C. Petrykowski ◽  
John S. Walker
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Metal Flow ◽  
Velocity Profiles ◽  
Transverse Magnetic ◽  
Secondary Flows ◽  
Rectangular Duct ◽  
Liquid Metal Flow ◽  
Displacement Thickness ◽  
The Magnetic Field

Liquid-metal flows in rectangular ducts having electrically insulating tops and bottoms and perfectly conducting sides and in the presence of strong, polar, transverse magnetic fields are examined. Solutions are presented for the boundary layers adjacent to the sides that are parallel to the magnetic field. Overshoots in the radial velocity profiles show that the side layers have zero displacement thickness and do not perturb the inviscid core. Very weak secondary flows involve four significant vortices, as reflected in the polar velocity profiles.

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