{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23424"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23424","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Analytical investigations of convective effects on a solid-liquid interface","abstract":"A thin layer of a single-component Boussinesq fluid, contained between two rigid horizontal plates of low thermal conductivity, is cooled from above and heated from below. In the steady-static state, a heat flux traverses the system so that the temperature attained at the upper boundary of the layer is in the solid phase. An interface is planar in the conductive state, and corrugated in the convective regime. A small amplitude expansion study reveals that the critical Rayleigh number and the critical wavenumber for the onset of the interface deformation increase with the solid layer thickness. A weakly nonlinear stability analysis reveals that there is subcritical instability irrespective of the interface shape. The stable forms of the solidified front are then found. In the case of hexagonal pattern, the fluid motion is shown to be upward at the cells centers. Hexagons are also found to exhibit a higher heat flux than either rolls or squares. The non-planar interface is shown to have a cellular structure identical to the convection patterns which arise in this situation.","abstract_html":"A thin layer of a single-component Boussinesq fluid, contained between two rigid horizontal plates of low thermal conductivity, is cooled from above and heated from below. In the steady-static state, a heat flux traverses the system so that the temperature attained at the upper boundary of the layer is in the solid phase. An interface is planar in the conductive state, and corrugated in the convective regime. A small amplitude expansion study reveals that the critical Rayleigh number and the critical wavenumber for the onset of the interface deformation increase with the solid layer thickness. A weakly nonlinear stability analysis reveals that there is subcritical instability irrespective of the interface shape. The stable forms of the solidified front are then found. In the case of hexagonal pattern, the fluid motion is shown to be upward at the cells centers. Hexagons are also found to exhibit a higher heat flux than either rolls or squares. The non-planar interface is shown to have a cellular structure identical to the convection patterns which arise in this situation.","abstract_has_math":false,"creators":["Hadji, Layachi"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Applied Mechanics","degree_department":null,"school":null,"contributors":["Riahi, Daniel N."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:13:41Z","date_published":"2011-05-07T14:13:41Z","updated_at":"2026-07-22T22:25:21Z","subjects":["Applied Mechanics","Engineering, Mechanical","Physics, Fluid and Plasma"],"languages":["eng"],"rights":["Copyright 1989 Hadji, Layachi"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9010871","(UMI)AAI9010871"],"render_values":[{"text":"AAI9010871","href":null,"code":true},{"text":"(UMI)AAI9010871","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23424","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Riahi, Daniel N."]},{"key":"dc:creator","label":"Author","values":["Hadji, Layachi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:13:41Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mechanics","Engineering, Mechanical","Physics, Fluid and Plasma"]},{"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","Engineering, Mechanical","Physics, Fluid and Plasma"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Hadji, Layachi"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9010871","(UMI)AAI9010871","http://hdl.handle.net/2142/23424"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A thin layer of a single-component Boussinesq fluid, contained between two rigid horizontal plates of low thermal conductivity, is cooled from above and heated from below. In the steady-static state, a heat flux traverses the system so that the temperature attained at the upper boundary of the layer is in the solid phase. An interface is planar in the conductive state, and corrugated in the convective regime. A small amplitude expansion study reveals that the critical Rayleigh number and the critical wavenumber for the onset of the interface deformation increase with the solid layer thickness. A weakly nonlinear stability analysis reveals that there is subcritical instability irrespective of the interface shape. The stable forms of the solidified front are then found. In the case of hexagonal pattern, the fluid motion is shown to be upward at the cells centers. Hexagons are also found to exhibit a higher heat flux than either rolls or squares. The non-planar interface is shown to have a cellular structure identical to the convection patterns which arise in this situation.","A long wavelength approximation is used to derive a non-linear evolution equation for the leading order interface pertubation. This evolution equation is found to be ill-posed when the dimensionless thickness of the solid layer A exceeds 0.256. The equation is then solved numerically for A between 0 and 0.256. The curve shifts to the right as A approaches the value 0.256.","The linear stability analysis for the binary alloy case is performed. This part complements the work done by Caroli et al. (1985). The critical value for the pulling velocity V at which both the morphological and convective instabilities are excited at the same concentration level is determined numerically.","Made available in DSpace on 2011-05-07T14:13:41Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9010871.pdf: 2272506 bytes, checksum: 25587d554ca9d3e5ea5150e391ac5440 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:04:23Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:30:45-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Analytical investigations of convective effects on a solid-liquid interface"]}]}],"canonical_facts":{"dc:contributor":["Riahi, Daniel N."],"dc:creator":["Hadji, Layachi"],"dc:date":["2011-05-07T14:13:41Z","10000-01-01","1989"],"dc:description":["A thin layer of a single-component Boussinesq fluid, contained between two rigid horizontal plates of low thermal conductivity, is cooled from above and heated from below. In the steady-static state, a heat flux traverses the system so that the temperature attained at the upper boundary of the layer is in the solid phase. An interface is planar in the conductive state, and corrugated in the convective regime. A small amplitude expansion study reveals that the critical Rayleigh number and the critical wavenumber for the onset of the interface deformation increase with the solid layer thickness. A weakly nonlinear stability analysis reveals that there is subcritical instability irrespective of the interface shape. The stable forms of the solidified front are then found. In the case of hexagonal pattern, the fluid motion is shown to be upward at the cells centers. Hexagons are also found to exhibit a higher heat flux than either rolls or squares. The non-planar interface is shown to have a cellular structure identical to the convection patterns which arise in this situation.","A long wavelength approximation is used to derive a non-linear evolution equation for the leading order interface pertubation. This evolution equation is found to be ill-posed when the dimensionless thickness of the solid layer A exceeds 0.256. The equation is then solved numerically for A between 0 and 0.256. The curve shifts to the right as A approaches the value 0.256.","The linear stability analysis for the binary alloy case is performed. This part complements the work done by Caroli et al. (1985). The critical value for the pulling velocity V at which both the morphological and convective instabilities are excited at the same concentration level is determined numerically.","Made available in DSpace on 2011-05-07T14:13:41Z (GMT). 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