Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation

The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell–Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases of the temperature profile being continuous or having a jump...

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Detalles Bibliográficos
Autores: Hennessy, M.G., Calvo-Schwarzwälder, M., Myers, T.G.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/445768
Acceso en línea:http://hdl.handle.net/2072/445768
Access Level:acceso abierto
Palabra clave:51
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spelling Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equationHennessy, M.G.Calvo-Schwarzwälder, M.Myers, T.G.51The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell–Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases of the temperature profile being continuous or having a jump across the solid–liquid interface. The jump conditions are derived from the sharp-interface limit of a phase-field model that accounts for variations in the thermal properties between the solid and liquid. The Stefan problem is solved using asymptotic and numerical methods. The analysis reveals that the Fourier-based solution can be recovered from the classical limit of zero relaxation time when either boundary condition is used. However, only the jump condition avoids the onset of unphysical “supersonic” melting, where the speed of the melt front exceeds the finite speed of heat propagation. These results conclusively demonstrate that the jump condition, not the continuity condition, is the most suitable for use in models of phase change based on the Maxwell–Cattaneo equation. Numerical investigations show that thermal relaxation can increase the time required to melt a nanoparticle by more than a factor of ten. Thus, thermal relaxation is an important process to include in models of nanoparticle melting and is expected to be relevant in other rapid phase-change processes. © 2018 Elsevier Inc.Elsevier Inc.2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion36 p.application/pdfhttp://hdl.handle.net/2072/445768RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/semantics/openAccessoai:recercat.cat:2072/4457682026-05-29T05:05:01Z
dc.title.none.fl_str_mv Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation
title Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation
spellingShingle Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation
Hennessy, M.G.
51
title_short Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation
title_full Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation
title_fullStr Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation
title_full_unstemmed Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation
title_sort Modelling ultra-fast nanoparticle melting with the Maxwell–Cattaneo equation
dc.creator.none.fl_str_mv Hennessy, M.G.
Calvo-Schwarzwälder, M.
Myers, T.G.
author Hennessy, M.G.
author_facet Hennessy, M.G.
Calvo-Schwarzwälder, M.
Myers, T.G.
author_role author
author2 Calvo-Schwarzwälder, M.
Myers, T.G.
author2_role author
author
dc.subject.none.fl_str_mv 51
topic 51
description The role of thermal relaxation in nanoparticle melting is studied using a mathematical model based on the Maxwell–Cattaneo equation for heat conduction. The model is formulated in terms of a two-phase Stefan problem. We consider the cases of the temperature profile being continuous or having a jump across the solid–liquid interface. The jump conditions are derived from the sharp-interface limit of a phase-field model that accounts for variations in the thermal properties between the solid and liquid. The Stefan problem is solved using asymptotic and numerical methods. The analysis reveals that the Fourier-based solution can be recovered from the classical limit of zero relaxation time when either boundary condition is used. However, only the jump condition avoids the onset of unphysical “supersonic” melting, where the speed of the melt front exceeds the finite speed of heat propagation. These results conclusively demonstrate that the jump condition, not the continuity condition, is the most suitable for use in models of phase change based on the Maxwell–Cattaneo equation. Numerical investigations show that thermal relaxation can increase the time required to melt a nanoparticle by more than a factor of ten. Thus, thermal relaxation is an important process to include in models of nanoparticle melting and is expected to be relevant in other rapid phase-change processes. © 2018 Elsevier Inc.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/445768
url http://hdl.handle.net/2072/445768
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 36 p.
application/pdf
dc.publisher.none.fl_str_mv Elsevier Inc.
publisher.none.fl_str_mv Elsevier Inc.
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812455

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