Linear stability analysis for high-velocity boundary layers in liquid- metal magnetohydrodynamic flows
type: Item
instance of: scholarly article
title: Linear stability analysis for high-velocity boundary layers in liquid- metal magnetohydrodynamic flows
zbMATH Open document ID: 0757.76017
DOI: 10.1016/0020-7225(91)90167-2
author: A. L. Ting
author: C. B. Reed
author: B. F. Picologlou
author: J. S. Walker
author: Tess J. Moon
published in: International Journal of Engineering Science
publication date: 1993-01-16T00:00:00Z
review text: The paper is concerned with the linear stability analysis of the fully developed liquid-metal flow in a rectangular duct of uniform cross section with thin metal walls subjected to a strong, uniform, transverse magnetic field. For large Hartmann numbers the steady flow consists of a uniform core region and boundary layers adjacent to the sides of the duct. There exist large velocities in boundary layers which are parallel to the applied magnetic field. A small harmonic disturbance is superimposed on the basic flow and the resulting linearized equations are studied to reveal its stability characteristics. This is reduced to the solution of two independent eigenvalue problems. The first problem involves a disturbance vorticity perpendicular to the magnetic field and leads to always decaying solutions. In the second problem the disturbance velocity is parallel to the magnetic field and it is found that there is a critical Reynolds number equal to 313. This value is much lower than the experimental observations and it implies that a nonlinear stability analysis is, in fact, necessary.
Mathematics Subject Classification ID: 76E25
zbMATH DE Number: 91132
zbMATH Keywords: rectangular duct
zbMATH Keywords: small harmonic disturbance
zbMATH Keywords: disturbance vorticity
zbMATH Keywords: disturbance velocity
zbMATH Keywords: critical Reynolds number
reviewed by: Erdoğan S. Şuhubi
MaRDI profile type: Publication
full work available at URL: 0020-7225(91)90167-2
OpenAlex ID: W2064573341
cites work: Q3908714
cites work: Why, how, and when, MHD turbulence becomes two-dimensional
description: scientific article; zbMATH DE number 91132