A threedimensional magnetohydrodynamic duct flow in a nonuniform magnetic yield
Abstract
The theory of three dimensional magnetohydrodynamic duct flows in uniform magnetic fields is well developed. A corresponding theory for nonuniform 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 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, perfectlyconducting 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 1981
 Bibcode:
 1981PhDT........37P
 Keywords:

 Magnetohydrodynamic Flow;
 Nonuniform Magnetic Fields;
 Boundary Layers;
 Ducts;
 Integral Equations;
 Fluid Mechanics and Heat Transfer