Abstract
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.
Highlights
Magnetohydrodynamics is a discipline that deals with the interaction between electromagnetic fields and fluid flows, and its application encompasses a wide range of subjects, such as astrophysics, geodynamo phenomena, metallurgy, and electromagnetic pumps [1,2,3]
The most basic system is that a vertical uniform magnetic field is applied to the liquid metal flow between parallel plates, the so-called Hartmann flow, in which a sufficiently long container in the span direction is used [4,5]
The velocity distribution of the Hartmann flow is divided into a core region where viscosity is negligible and boundary layers formed near the wall perpendicular to the imposed magnetic field
Summary
Magnetohydrodynamics is a discipline that deals with the interaction between electromagnetic fields and fluid flows, and its application encompasses a wide range of subjects, such as astrophysics, geodynamo phenomena, metallurgy, and electromagnetic pumps [1,2,3]. We carried out a linear stability analysis of liquid metal parallel flow in a duct with metal parallel flow in a duct with rectangular cross-section whoseThis wallsconfiguration were electrically rectangular cross-section whose walls were electrically insulating. This configuration was similar to the recent study presented in a conference by Tagawa [31], and we the recent study presented in a conference by Tagawa [31], and we extended this study in general, extended this study in general, focusing on the explanation of the numerical method.
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