{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/9707"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/9707","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Some theoretical aspects of fibre suspension flows","abstract":"This thesis is concerned with properties of equations governing fibre suspensions. Of particular interest is the extent to which solutions, and their properties, depend on the type of closure used. For this purpose two closure rules are investigated: the linear and the quadratic closures. We show that the equations are consistent with the second law of thermodynamics, or dissipation inequality, when the quadratic closure is used. When the linear closure is used, a sufficient condition for consistency is that the particle number Np satisfies Np ≤ 35/2. Likewise, flows are found to be monotonically stable for the quadratic closure, and for the linear closure with Np ≤ 35/2. The second part of the thesis is concerned with one-dimensional problems, and their solution by finite element. The hyperbolic nature of the evolution equation for the orientation tensor necessitates a modification of the standard Galerkin-based approach. We investigate the conditions under which convergence is obtained, for unidirectional flows, with the use of the Streamline Upwind (SU) method, and the Streamline upwind Petrov/Galerkin (SUPG) method.","abstract_html":"This thesis is concerned with properties of equations governing fibre suspensions. Of particular interest is the extent to which solutions, and their properties, depend on the type of closure used. For this purpose two closure rules are investigated: the linear and the quadratic closures. We show that the equations are consistent with the second law of thermodynamics, or dissipation inequality, when the quadratic closure is used. When the linear closure is used, a sufficient condition for consistency is that the particle number Np satisfies Np ≤ 35/2. Likewise, flows are found to be monotonically stable for the quadratic closure, and for the linear closure with Np ≤ 35/2. The second part of the thesis is concerned with one-dimensional problems, and their solution by finite element. The hyperbolic nature of the evolution equation for the orientation tensor necessitates a modification of the standard Galerkin-based approach. We investigate the conditions under which convergence is obtained, for unidirectional flows, with the use of the Streamline Upwind (SU) method, and the Streamline upwind Petrov/Galerkin (SUPG) method.","abstract_has_math":false,"creators":["Diatezua, Jacquie Kiangebeni"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Reddy, Daya"],"committee_chairs":[],"committee_members":[],"year":1999,"date_issued":"1999","date_published":"1999","updated_at":"2026-07-22T22:22:58Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/9707","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Reddy, Daya"]},{"key":"dc:creator","label":"Author","values":["Diatezua, Jacquie Kiangebeni"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-11-18T17:04:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-11-18T17:04:11Z"]},{"key":"dc:date.issued","label":"Date","values":["1999"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/9707"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: leaves 77-82."]},{"key":"dc:description.abstract","label":"Abstract","values":["This thesis is concerned with properties of equations governing fibre suspensions. Of particular interest is the extent to which solutions, and their properties, depend on the type of closure used. For this purpose two closure rules are investigated: the linear and the quadratic closures. We show that the equations are consistent with the second law of thermodynamics, or dissipation inequality, when the quadratic closure is used. When the linear closure is used, a sufficient condition for consistency is that the particle number Np satisfies Np ≤ 35/2. Likewise, flows are found to be monotonically stable for the quadratic closure, and for the linear closure with Np ≤ 35/2. The second part of the thesis is concerned with one-dimensional problems, and their solution by finite element. The hyperbolic nature of the evolution equation for the orientation tensor necessitates a modification of the standard Galerkin-based approach. We investigate the conditions under which convergence is obtained, for unidirectional flows, with the use of the Streamline Upwind (SU) method, and the Streamline upwind Petrov/Galerkin (SUPG) method."]},{"key":"dc:title","label":"Title","values":["Some theoretical aspects of fibre suspension flows"]}]}],"canonical_facts":{"dc:contributor.advisor":["Reddy, Daya"],"dc:creator":["Diatezua, Jacquie Kiangebeni"],"dc:date.accessioned":["2014-11-18T17:04:11Z"],"dc:date.available":["2014-11-18T17:04:11Z"],"dc:date.issued":["1999"],"dc:description":["Bibliography: leaves 77-82."],"dc:description.abstract":["This thesis is concerned with properties of equations governing fibre suspensions. Of particular interest is the extent to which solutions, and their properties, depend on the type of closure used. For this purpose two closure rules are investigated: the linear and the quadratic closures. We show that the equations are consistent with the second law of thermodynamics, or dissipation inequality, when the quadratic closure is used. When the linear closure is used, a sufficient condition for consistency is that the particle number Np satisfies Np ≤ 35/2. Likewise, flows are found to be monotonically stable for the quadratic closure, and for the linear closure with Np ≤ 35/2. The second part of the thesis is concerned with one-dimensional problems, and their solution by finite element. The hyperbolic nature of the evolution equation for the orientation tensor necessitates a modification of the standard Galerkin-based approach. We investigate the conditions under which convergence is obtained, for unidirectional flows, with the use of the Streamline Upwind (SU) method, and the Streamline upwind Petrov/Galerkin (SUPG) method."],"dc:identifier.uri":["http://hdl.handle.net/11427/9707"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Some theoretical aspects of fibre suspension flows"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:22:58Z"}