A Three-Dimensional Magnetohydrodynamic Duct Flow in A Non-Uniform Magnetic Field
Petrykowski, John Claud
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https://hdl.handle.net/2142/68518
Description
Title
A Three-Dimensional Magnetohydrodynamic Duct Flow in A Non-Uniform Magnetic Field
Author(s)
Petrykowski, John Claud
Issue Date
1981
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Energy
Language
eng
Abstract
The theory of three-dimensional magnetohydrodynamic duct flows in uniform magnetic fields is well developed. A corresponding theory for non-uniform magnetic fields does not exist. This study represents the first analysis of a three-dimensional MHD duct flow in which the magnetic field has spatial variations. A magnetic field of the type B = r('-1)e(,(theta)) is considered because it resembles the fringing field associated with a magnet's poles. In this way, the important problem of end effects can be modeled. The duct is an expansion with parallel, perfectly-conducting side walls and diverging, electrically insulating top and bottom walls. The problem is solved using boundary layer techniques via matched asymptotic expansions. Solutions for the core, Hartmann layer, intersection layer and side layer are determined. In particular, the analysis of the side layer problem centers on solving a formidable pair of coupled Fredholm integral equations. The complexity of these equations requires that numerical quadrature technique be used. The velocity field in the side layer has two notable features. A weak secondary flow exists which is driven by a correspondingly weak transverse electromagnetic force. The curvature of the field lines and the duct geometry conspire to produce this weak force. Secondly, the non-uniform generates a radial velocity profile with multiple overshoots of the core value. Several divergence angles are considered.
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