{"id":{"repo_id":"city-london","oai_identifier":"oai:openaccess.city.ac.uk:7995"},"canonical_url":"https://search.dev.ndltd.org/etd/city-london/oai:openaccess.city.ac.uk:7995","repository":{"repo_id":"city-london","name":"City University of London","base_url":"https://openaccess.city.ac.uk/cgi/oai2"},"display":{"title":"Thermal convection in slender laterally-heated cavities","abstract":"Two-dimensional convective flows in shallow and tall cavities with adiabatic or conducting horizontal boundaries and driven by differential heating of the two vertical end walls, are studied numerically over a range of Rayleigh numbers and Prandtl numbers. As the Rayleigh number increases, nonlinearity first affects the flow structure in the turning regions near the ends of the cavity. These `end-zone problems' have been investigated by a combined computational and analytical approach. Numerical solutions are found using a DuFort-Frankel-Multigrid method, and appear to be in good agreement with theoretical predictions of a boundary-layer structure at high values of the Rayleigh number. For time-dependent shallow cavity flows, new theoretical solutions and numerical solutions are obtained by both analytical and computational methods. A numerical scheme for finding thermal convective flows in a finite laterally heated cavity is described in detail in Chapter 2. The end-zone problems for tall cavities with conducting and adiabatic horizontal boundaries are considered in Chapters 3 and 4 respectively. For shallow cavities, the end-zone problems for these two thermal boundary conditions are considered in Chapters 5 and 6. Finally, timedependent shallow cavity flows for insulated horizontal boundaries are investigated using both analytical and computational methods in Chapter 7.","abstract_html":"Two-dimensional convective flows in shallow and tall cavities with adiabatic or conducting horizontal boundaries and driven by differential heating of the two vertical end walls, are studied numerically over a range of Rayleigh numbers and Prandtl numbers. As the Rayleigh number increases, nonlinearity first affects the flow structure in the turning regions near the ends of the cavity. These `end-zone problems' have been investigated by a combined computational and analytical approach. Numerical solutions are found using a DuFort-Frankel-Multigrid method, and appear to be in good agreement with theoretical predictions of a boundary-layer structure at high values of the Rayleigh number. For time-dependent shallow cavity flows, new theoretical solutions and numerical solutions are obtained by both analytical and computational methods. A numerical scheme for finding thermal convective flows in a finite laterally heated cavity is described in detail in Chapter 2. The end-zone problems for tall cavities with conducting and adiabatic horizontal boundaries are considered in Chapters 3 and 4 respectively. For shallow cavities, the end-zone problems for these two thermal boundary conditions are considered in Chapters 5 and 6. Finally, timedependent shallow cavity flows for insulated horizontal boundaries are investigated using both analytical and computational methods in Chapter 7.","abstract_has_math":false,"creators":["Wang, P."],"institution":"City University London","degree_name":"phd","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1992,"date_issued":"1992-10","date_published":"1992-10","updated_at":"2026-07-24T01:39:08Z","subjects":["QA Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wang, P."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1992-10"]},{"key":"dc:date.issued","label":"Date","values":["1992-10"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics","Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["City University London"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://openaccess.city.ac.uk/id/eprint/7995/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["phd"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["QA Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://openaccess.city.ac.uk/id/eprint/7995/1/Thermal_convection_in_slender_laterally-heated_cavities.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Two-dimensional convective flows in shallow and tall cavities with adiabatic or conducting horizontal boundaries and driven by differential heating of the two vertical end walls, are studied numerically over a range of Rayleigh numbers and Prandtl numbers. As the Rayleigh number increases, nonlinearity first affects the flow structure in the turning regions near the ends of the cavity. These `end-zone problems' have been investigated by a combined computational and analytical approach. Numerical solutions are found using a DuFort-Frankel-Multigrid method, and appear to be in good agreement with theoretical predictions of a boundary-layer structure at high values of the Rayleigh number. For time-dependent shallow cavity flows, new theoretical solutions and numerical solutions are obtained by both analytical and computational methods. A numerical scheme for finding thermal convective flows in a finite laterally heated cavity is described in detail in Chapter 2. The end-zone problems for tall cavities with conducting and adiabatic horizontal boundaries are considered in Chapters 3 and 4 respectively. For shallow cavities, the end-zone problems for these two thermal boundary conditions are considered in Chapters 5 and 6. Finally, timedependent shallow cavity flows for insulated horizontal boundaries are investigated using both analytical and computational methods in Chapter 7."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Thermal convection in slender laterally-heated cavities"]}]}],"canonical_facts":{"dc:creator":["Wang, P."],"dc:date":["1992-10"],"dc:date.issued":["1992-10"],"dc:description.abstract":["Two-dimensional convective flows in shallow and tall cavities with adiabatic or conducting horizontal boundaries and driven by differential heating of the two vertical end walls, are studied numerically over a range of Rayleigh numbers and Prandtl numbers. As the Rayleigh number increases, nonlinearity first affects the flow structure in the turning regions near the ends of the cavity. These `end-zone problems' have been investigated by a combined computational and analytical approach. Numerical solutions are found using a DuFort-Frankel-Multigrid method, and appear to be in good agreement with theoretical predictions of a boundary-layer structure at high values of the Rayleigh number. For time-dependent shallow cavity flows, new theoretical solutions and numerical solutions are obtained by both analytical and computational methods. A numerical scheme for finding thermal convective flows in a finite laterally heated cavity is described in detail in Chapter 2. The end-zone problems for tall cavities with conducting and adiabatic horizontal boundaries are considered in Chapters 3 and 4 respectively. For shallow cavities, the end-zone problems for these two thermal boundary conditions are considered in Chapters 5 and 6. Finally, timedependent shallow cavity flows for insulated horizontal boundaries are investigated using both analytical and computational methods in Chapter 7."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://openaccess.city.ac.uk/id/eprint/7995/1/Thermal_convection_in_slender_laterally-heated_cavities.pdf"],"dc:publisher.department":["Department of Mathematics","Mathematics"],"dc:publisher.institution":["City University London"],"dc:relation.isreferencedby":["https://openaccess.city.ac.uk/id/eprint/7995/"],"dc:subject":["QA Mathematics"],"dc:title":["Thermal convection in slender laterally-heated cavities"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T01:39:08Z"}