{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/68518"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/68518","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A Three-Dimensional Magnetohydrodynamic Duct Flow in A Non-Uniform Magnetic Field","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Petrykowski, John Claud"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Theoretical and Applied Mechanics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-14T14:42:23Z","date_published":"2014-12-14T14:42:23Z","updated_at":"2026-07-22T22:25:59Z","subjects":["Applied Mechanics","Energy"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8127669"],"render_values":[{"text":"(UMI)AAI8127669","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/68518","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Petrykowski, John Claud"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-14T14:42:23Z","10000-01-01","1981"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Theoretical and Applied Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mechanics","Energy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/68518","(UMI)AAI8127669"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2014-12-14T14:42:23Z (GMT). No. of bitstreams: 1 8127669.pdf: 2222579 bytes, checksum: 759ed90c36fa7d4358e1e1ccca431e96 (MD5) Previous issue date: 1981","Embargo set by: Seth Robbins for item 68696 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","105 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981."]},{"key":"dc:title","label":"Title","values":["A Three-Dimensional Magnetohydrodynamic Duct Flow in A Non-Uniform Magnetic Field"]}]}],"canonical_facts":{"dc:creator":["Petrykowski, John Claud"],"dc:date":["2014-12-14T14:42:23Z","10000-01-01","1981"],"dc:description":["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.","Made available in DSpace on 2014-12-14T14:42:23Z (GMT). No. of bitstreams: 1 8127669.pdf: 2222579 bytes, checksum: 759ed90c36fa7d4358e1e1ccca431e96 (MD5) Previous issue date: 1981","Embargo set by: Seth Robbins for item 68696 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","105 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981."],"dc:identifier":["http://hdl.handle.net/2142/68518","(UMI)AAI8127669"],"dc:language":["eng"],"dc:subject":["Applied Mechanics","Energy"],"dc:title":["A Three-Dimensional Magnetohydrodynamic Duct Flow in A Non-Uniform Magnetic Field"],"dc:type":["text"],"thesis:degree_discipline":["Theoretical and Applied Mechanics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:59Z"}