A Three-Dimensional Magnetohydrodynamic Duct Flow in A Non-Uniform Magnetic Field

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical and Applied Mechanics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Petrykowski, John Claud

• Applied Mechanics
• Energy

Language dc:language

eng

Identifier

(UMI)AAI8127669

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/68518