Unsteady contact melting of a rectangular cross-section material on a flat plate

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dc.contributor.authorMyers, T G
dc.contributor.authorMitchell, S L
dc.contributor.authorMuchatibaya, G
dc.date.accessioned2021-10-08T07:11:53Z
dc.date.available2021-10-08T07:11:53Z
dc.date.issued2008
dc.description.abstractThe work in this paper concerns a mathematical model of the contact melting process of a rectangular material in contact with a hot plate. The problem is described by a coupled system of heat equations in the solid and melt layer, fluid flow in the melt, a Stefan condition at the melt interface, and a force balance between the weight of the solid and the fluid pressure. Since the melt layer remains thin throughout the process, we use the lubrication approximation to the fluid equations and assume that the heat flow in the fluid is dominated by conduction across the thin film. In the solid we employ a heat balance integral method. Results show that the film height has initial and final rapid increases, whereas for intermediate times the height slowly increases. The quasisteady state of previous models is never attained: This is shown to be an effect of neglecting the change in mass and conduction in the solid. The previously observed initial infinite velocity of the melt is shown to be a result of the perfect thermal contact assumption. For a water-ice system the melting rate is shown to be approximately linear, this allows us to reduce the problem to solving a single first order differential equation for the liquid layer thickness. The main analysis is carried out in two dimensions, but we briefly highlight the extension to three dimensions. The method is verified by comparison with previously published experimental results on the melting of n -octadecane.
dc.identifier.apacitationMyers, T. G., Mitchell, S. L., & Muchatibaya, G. (2008). Unsteady contact melting of a rectangular cross-section material on a flat plate. <i>Physics of Fluids</i>, 20(10), 103101 - 177. http://hdl.handle.net/11427/34703en_ZA
dc.identifier.chicagocitationMyers, T G, S L Mitchell, and G Muchatibaya "Unsteady contact melting of a rectangular cross-section material on a flat plate." <i>Physics of Fluids</i> 20, 10. (2008): 103101 - 177. http://hdl.handle.net/11427/34703en_ZA
dc.identifier.citationMyers, T.G., Mitchell, S.L. & Muchatibaya, G. 2008. Unsteady contact melting of a rectangular cross-section material on a flat plate. <i>Physics of Fluids.</i> 20(10):103101 - 177. http://hdl.handle.net/11427/34703en_ZA
dc.identifier.issn1070-6631
dc.identifier.issn1089-7666
dc.identifier.issn1527-2435
dc.identifier.ris TY - Journal Article AU - Myers, T G AU - Mitchell, S L AU - Muchatibaya, G AB - The work in this paper concerns a mathematical model of the contact melting process of a rectangular material in contact with a hot plate. The problem is described by a coupled system of heat equations in the solid and melt layer, fluid flow in the melt, a Stefan condition at the melt interface, and a force balance between the weight of the solid and the fluid pressure. Since the melt layer remains thin throughout the process, we use the lubrication approximation to the fluid equations and assume that the heat flow in the fluid is dominated by conduction across the thin film. In the solid we employ a heat balance integral method. Results show that the film height has initial and final rapid increases, whereas for intermediate times the height slowly increases. The quasisteady state of previous models is never attained: This is shown to be an effect of neglecting the change in mass and conduction in the solid. The previously observed initial infinite velocity of the melt is shown to be a result of the perfect thermal contact assumption. For a water-ice system the melting rate is shown to be approximately linear, this allows us to reduce the problem to solving a single first order differential equation for the liquid layer thickness. The main analysis is carried out in two dimensions, but we briefly highlight the extension to three dimensions. The method is verified by comparison with previously published experimental results on the melting of n -octadecane. DA - 2008 DB - OpenUCT DP - University of Cape Town IS - 10 J1 - Physics of Fluids LK - https://open.uct.ac.za PY - 2008 SM - 1070-6631 SM - 1089-7666 SM - 1527-2435 T1 - Unsteady contact melting of a rectangular cross-section material on a flat plate TI - Unsteady contact melting of a rectangular cross-section material on a flat plate UR - http://hdl.handle.net/11427/34703 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/34703
dc.identifier.vancouvercitationMyers TG, Mitchell SL, Muchatibaya G. Unsteady contact melting of a rectangular cross-section material on a flat plate. Physics of Fluids. 2008;20(10):103101 - 177. http://hdl.handle.net/11427/34703.en_ZA
dc.language.isoeng
dc.publisher.departmentDepartment of Mathematics and Applied Mathematics
dc.publisher.facultyFaculty of Science
dc.sourcePhysics of Fluids
dc.source.journalissue10
dc.source.journalvolume20
dc.source.pagination103101 - 177
dc.source.urihttps://dx.doi.org/10.1063/1.2990751
dc.subject.otherDirect contact
dc.subject.otherHeat transfer
dc.subject.otherPCM material
dc.subject.otherModeling
dc.subject.otherIce
dc.subject.otherMelting
dc.subject.otherContact direct
dc.subject.otherTransfert chaleur
dc.subject.otherMatériau PCM
dc.subject.otherModélisation
dc.subject.otherGlace
dc.subject.otherFusion
dc.subject.otherOctadécane
dc.subject.otherContacto directo
dc.subject.otherTransferencia térmica
dc.subject.otherMaterial PCM
dc.subject.otherModelización
dc.subject.otherHielo
dc.subject.otherFusión
dc.titleUnsteady contact melting of a rectangular cross-section material on a flat plate
dc.typeJournal Article
uct.type.publicationResearch
uct.type.resourceJournal Article
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