New asymptotic heat transfer model in thin liquid films
•An improved Nusselt solution is derived, which takes into account heat transfer phenomena across the free surface.•This model is studied and validated numerically by comparing with 2D direct simulations of the heat transfer equation.•A dynamical system analysis of the proposed model is performed.•C...
Gespeichert in:
Veröffentlicht in: | Applied Mathematical Modelling 2017-08, Vol.48, p.844-859 |
---|---|
Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 859 |
---|---|
container_issue | |
container_start_page | 844 |
container_title | Applied Mathematical Modelling |
container_volume | 48 |
creator | Chhay, Marx Dutykh, Denys Gisclon, Marguerite Ruyer-Quil, Christian |
description | •An improved Nusselt solution is derived, which takes into account heat transfer phenomena across the free surface.•This model is studied and validated numerically by comparing with 2D direct simulations of the heat transfer equation.•A dynamical system analysis of the proposed model is performed.•Coupling between the heat transfer and the hydrodynamics is taken into account.•The proposed model is strictly hyperbolic and provides the predictions with improved accuracy.
In this article, we present a model of heat transfer occurring through a liquid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution is obtained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems. |
doi_str_mv | 10.1016/j.apm.2017.02.022 |
format | Article |
fullrecord | <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_01224182v2</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0307904X1730118X</els_id><sourcerecordid>1932120549</sourcerecordid><originalsourceid>FETCH-LOGICAL-c402t-e3fee621d3d4840763cc943a8cebfde2cb64cafe412d3eb9c7b696b00ee302523</originalsourceid><addsrcrecordid>eNp9UMtKw0AUHUTBWv0AdwFXLhLvPJo0uCrFFxTdKLgbJpMbOiGvzkwr_XsnRMSVcLkvzjncewi5ppBQoOldnaihTRjQLAEWgp2QGXDI4hzE5-mf_pxcOFcDwCJMM5K94lek3LEdfO-NjraofOSt6lyFNmr7EpvIdJHfhtSY3d6UUWWa1l2Ss0o1Dq9-6px8PD68r5_jzdvTy3q1ibUA5mPkFWLKaMlLsRSQpVzrXHC11FhUJTJdpEKrCgVlJcci11mR5mkBgMiBLRifk9tJd6saOVjTKnuUvTLyebWR4w4oY4Iu2WHE3kzYwfa7PTov635vu3CepDlnlMFC5AFFJ5S2vXMWq19ZCnL0UtYyeClHLyWwEKPy_cTB8OrBoJVOG-w0lsai9rLszT_sb_WOex4</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1932120549</pqid></control><display><type>article</type><title>New asymptotic heat transfer model in thin liquid films</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>EBSCOhost Business Source Complete</source><source>Access via ScienceDirect (Elsevier)</source><source>EBSCOhost Education Source</source><creator>Chhay, Marx ; Dutykh, Denys ; Gisclon, Marguerite ; Ruyer-Quil, Christian</creator><creatorcontrib>Chhay, Marx ; Dutykh, Denys ; Gisclon, Marguerite ; Ruyer-Quil, Christian</creatorcontrib><description>•An improved Nusselt solution is derived, which takes into account heat transfer phenomena across the free surface.•This model is studied and validated numerically by comparing with 2D direct simulations of the heat transfer equation.•A dynamical system analysis of the proposed model is performed.•Coupling between the heat transfer and the hydrodynamics is taken into account.•The proposed model is strictly hyperbolic and provides the predictions with improved accuracy.
In this article, we present a model of heat transfer occurring through a liquid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution is obtained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.</description><identifier>ISSN: 0307-904X</identifier><identifier>ISSN: 1088-8691</identifier><identifier>EISSN: 0307-904X</identifier><identifier>EISSN: 1872-8480</identifier><identifier>DOI: 10.1016/j.apm.2017.02.022</identifier><language>eng</language><publisher>New York: Elsevier Inc</publisher><subject>Analysis of PDEs ; Asymptotic methods ; Asymptotic modeling ; Asymptotic properties ; Asymptotic series ; Computational Physics ; Fluid Dynamics ; Fluid mechanics ; Heat transfer ; Liquid films ; Long waves ; Marangoni effect ; Mathematical models ; Mathematics ; Mechanics ; Nonlinear Sciences ; Numerical Analysis ; Pattern Formation and Solitons ; Physics ; Steady state ; Studies ; Thermal dependency properties ; Thin films ; Thin liquid film ; Viscosity</subject><ispartof>Applied Mathematical Modelling, 2017-08, Vol.48, p.844-859</ispartof><rights>2017 Elsevier Inc.</rights><rights>Copyright Elsevier BV Aug 2017</rights><rights>Attribution - NonCommercial - NoDerivatives</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c402t-e3fee621d3d4840763cc943a8cebfde2cb64cafe412d3eb9c7b696b00ee302523</citedby><cites>FETCH-LOGICAL-c402t-e3fee621d3d4840763cc943a8cebfde2cb64cafe412d3eb9c7b696b00ee302523</cites><orcidid>0009-0004-4512-7774 ; 0000-0001-5247-2788</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.apm.2017.02.022$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,780,784,885,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttps://hal.science/hal-01224182$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Chhay, Marx</creatorcontrib><creatorcontrib>Dutykh, Denys</creatorcontrib><creatorcontrib>Gisclon, Marguerite</creatorcontrib><creatorcontrib>Ruyer-Quil, Christian</creatorcontrib><title>New asymptotic heat transfer model in thin liquid films</title><title>Applied Mathematical Modelling</title><description>•An improved Nusselt solution is derived, which takes into account heat transfer phenomena across the free surface.•This model is studied and validated numerically by comparing with 2D direct simulations of the heat transfer equation.•A dynamical system analysis of the proposed model is performed.•Coupling between the heat transfer and the hydrodynamics is taken into account.•The proposed model is strictly hyperbolic and provides the predictions with improved accuracy.
In this article, we present a model of heat transfer occurring through a liquid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution is obtained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.</description><subject>Analysis of PDEs</subject><subject>Asymptotic methods</subject><subject>Asymptotic modeling</subject><subject>Asymptotic properties</subject><subject>Asymptotic series</subject><subject>Computational Physics</subject><subject>Fluid Dynamics</subject><subject>Fluid mechanics</subject><subject>Heat transfer</subject><subject>Liquid films</subject><subject>Long waves</subject><subject>Marangoni effect</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mechanics</subject><subject>Nonlinear Sciences</subject><subject>Numerical Analysis</subject><subject>Pattern Formation and Solitons</subject><subject>Physics</subject><subject>Steady state</subject><subject>Studies</subject><subject>Thermal dependency properties</subject><subject>Thin films</subject><subject>Thin liquid film</subject><subject>Viscosity</subject><issn>0307-904X</issn><issn>1088-8691</issn><issn>0307-904X</issn><issn>1872-8480</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9UMtKw0AUHUTBWv0AdwFXLhLvPJo0uCrFFxTdKLgbJpMbOiGvzkwr_XsnRMSVcLkvzjncewi5ppBQoOldnaihTRjQLAEWgp2QGXDI4hzE5-mf_pxcOFcDwCJMM5K94lek3LEdfO-NjraofOSt6lyFNmr7EpvIdJHfhtSY3d6UUWWa1l2Ss0o1Dq9-6px8PD68r5_jzdvTy3q1ibUA5mPkFWLKaMlLsRSQpVzrXHC11FhUJTJdpEKrCgVlJcci11mR5mkBgMiBLRifk9tJd6saOVjTKnuUvTLyebWR4w4oY4Iu2WHE3kzYwfa7PTov635vu3CepDlnlMFC5AFFJ5S2vXMWq19ZCnL0UtYyeClHLyWwEKPy_cTB8OrBoJVOG-w0lsai9rLszT_sb_WOex4</recordid><startdate>20170801</startdate><enddate>20170801</enddate><creator>Chhay, Marx</creator><creator>Dutykh, Denys</creator><creator>Gisclon, Marguerite</creator><creator>Ruyer-Quil, Christian</creator><general>Elsevier Inc</general><general>Elsevier BV</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0009-0004-4512-7774</orcidid><orcidid>https://orcid.org/0000-0001-5247-2788</orcidid></search><sort><creationdate>20170801</creationdate><title>New asymptotic heat transfer model in thin liquid films</title><author>Chhay, Marx ; Dutykh, Denys ; Gisclon, Marguerite ; Ruyer-Quil, Christian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c402t-e3fee621d3d4840763cc943a8cebfde2cb64cafe412d3eb9c7b696b00ee302523</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Analysis of PDEs</topic><topic>Asymptotic methods</topic><topic>Asymptotic modeling</topic><topic>Asymptotic properties</topic><topic>Asymptotic series</topic><topic>Computational Physics</topic><topic>Fluid Dynamics</topic><topic>Fluid mechanics</topic><topic>Heat transfer</topic><topic>Liquid films</topic><topic>Long waves</topic><topic>Marangoni effect</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mechanics</topic><topic>Nonlinear Sciences</topic><topic>Numerical Analysis</topic><topic>Pattern Formation and Solitons</topic><topic>Physics</topic><topic>Steady state</topic><topic>Studies</topic><topic>Thermal dependency properties</topic><topic>Thin films</topic><topic>Thin liquid film</topic><topic>Viscosity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chhay, Marx</creatorcontrib><creatorcontrib>Dutykh, Denys</creatorcontrib><creatorcontrib>Gisclon, Marguerite</creatorcontrib><creatorcontrib>Ruyer-Quil, Christian</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Applied Mathematical Modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chhay, Marx</au><au>Dutykh, Denys</au><au>Gisclon, Marguerite</au><au>Ruyer-Quil, Christian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New asymptotic heat transfer model in thin liquid films</atitle><jtitle>Applied Mathematical Modelling</jtitle><date>2017-08-01</date><risdate>2017</risdate><volume>48</volume><spage>844</spage><epage>859</epage><pages>844-859</pages><issn>0307-904X</issn><issn>1088-8691</issn><eissn>0307-904X</eissn><eissn>1872-8480</eissn><abstract>•An improved Nusselt solution is derived, which takes into account heat transfer phenomena across the free surface.•This model is studied and validated numerically by comparing with 2D direct simulations of the heat transfer equation.•A dynamical system analysis of the proposed model is performed.•Coupling between the heat transfer and the hydrodynamics is taken into account.•The proposed model is strictly hyperbolic and provides the predictions with improved accuracy.
In this article, we present a model of heat transfer occurring through a liquid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution is obtained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.</abstract><cop>New York</cop><pub>Elsevier Inc</pub><doi>10.1016/j.apm.2017.02.022</doi><tpages>16</tpages><orcidid>https://orcid.org/0009-0004-4512-7774</orcidid><orcidid>https://orcid.org/0000-0001-5247-2788</orcidid><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0307-904X |
ispartof | Applied Mathematical Modelling, 2017-08, Vol.48, p.844-859 |
issn | 0307-904X 1088-8691 0307-904X 1872-8480 |
language | eng |
recordid | cdi_hal_primary_oai_HAL_hal_01224182v2 |
source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; EBSCOhost Business Source Complete; Access via ScienceDirect (Elsevier); EBSCOhost Education Source |
subjects | Analysis of PDEs Asymptotic methods Asymptotic modeling Asymptotic properties Asymptotic series Computational Physics Fluid Dynamics Fluid mechanics Heat transfer Liquid films Long waves Marangoni effect Mathematical models Mathematics Mechanics Nonlinear Sciences Numerical Analysis Pattern Formation and Solitons Physics Steady state Studies Thermal dependency properties Thin films Thin liquid film Viscosity |
title | New asymptotic heat transfer model in thin liquid films |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-04T04%3A18%3A47IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=New%20asymptotic%20heat%20transfer%20model%20in%20thin%20liquid%20films&rft.jtitle=Applied%20Mathematical%20Modelling&rft.au=Chhay,%20Marx&rft.date=2017-08-01&rft.volume=48&rft.spage=844&rft.epage=859&rft.pages=844-859&rft.issn=0307-904X&rft.eissn=0307-904X&rft_id=info:doi/10.1016/j.apm.2017.02.022&rft_dat=%3Cproquest_hal_p%3E1932120549%3C/proquest_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1932120549&rft_id=info:pmid/&rft_els_id=S0307904X1730118X&rfr_iscdi=true |