Influence of the Prandtl number on the location of recirculation eddies in thermocapillary flows
Two-dimensional thermocapillary-driven flow in a horizontal cavity of large aspect ratio is considered. Of particular interest is the asymptotic matching between the known parallel core flow solution and the non-parallel flow near the ends of the cavity. The influence of the end regions on the core...
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| Veröffentlicht in: | International journal of heat and mass transfer 2002-02, Vol.45 (4), p.793-801 |
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| creator | Mercier, Jean-François Normand, Christiane |
| description | Two-dimensional thermocapillary-driven flow in a horizontal cavity of large aspect ratio is considered. Of particular interest is the asymptotic matching between the known parallel core flow solution and the non-parallel flow near the ends of the cavity. The influence of the end regions on the core flow is described by the superposition of spatial disturbances to the core flow solution. The stability analysis of this perturbed state leads to an eigenvalue problem for the complex wave number of the disturbances. The end flow structures are related to the nature of the lowest eigenvalue: when purely real it describes a boundary layer regime whereas a non-vanishing imaginary part reveals the existence of periodic structures known as recirculation rolls or eddies. It is found that, depending on the Prandtl number value,
Pr, recirculation eddies can exist either near the hot wall (
Pr≫1) or the cold wall (
Pr≪1). Our results provide a direct interpretation to the different behaviors observed in previous experimental and numerical studies. |
| doi_str_mv | 10.1016/S0017-9310(01)00185-5 |
| format | Article |
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Pr, recirculation eddies can exist either near the hot wall (
Pr≫1) or the cold wall (
Pr≪1). Our results provide a direct interpretation to the different behaviors observed in previous experimental and numerical studies.</description><identifier>ISSN: 0017-9310</identifier><identifier>EISSN: 1879-2189</identifier><identifier>DOI: 10.1016/S0017-9310(01)00185-5</identifier><identifier>CODEN: IJHMAK</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Aspect ratio ; Boundary layer flow ; Eigenvalues and eigenfunctions ; Exact sciences and technology ; Fluid dynamics ; Fundamental areas of phenomenology (including applications) ; Hydrodynamic stability ; Pattern selection; pattern formation ; Perturbation techniques ; Physics ; Prandtl number ; Recirculation eddies ; Surface-tension-driven instability ; Thermocapillary flows</subject><ispartof>International journal of heat and mass transfer, 2002-02, Vol.45 (4), p.793-801</ispartof><rights>2001 Elsevier Science Ltd</rights><rights>2002 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c486t-e39480a7b5d3e5680ba044c81a4d6660a0f5fdcbe05bb809e323db23b98034793</citedby><cites>FETCH-LOGICAL-c486t-e39480a7b5d3e5680ba044c81a4d6660a0f5fdcbe05bb809e323db23b98034793</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/S0017-9310(01)00185-5$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,780,784,885,3548,27923,27924,45994</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=13400546$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://ensta-paris.hal.science/hal-00990225$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Mercier, Jean-François</creatorcontrib><creatorcontrib>Normand, Christiane</creatorcontrib><title>Influence of the Prandtl number on the location of recirculation eddies in thermocapillary flows</title><title>International journal of heat and mass transfer</title><description>Two-dimensional thermocapillary-driven flow in a horizontal cavity of large aspect ratio is considered. Of particular interest is the asymptotic matching between the known parallel core flow solution and the non-parallel flow near the ends of the cavity. The influence of the end regions on the core flow is described by the superposition of spatial disturbances to the core flow solution. The stability analysis of this perturbed state leads to an eigenvalue problem for the complex wave number of the disturbances. The end flow structures are related to the nature of the lowest eigenvalue: when purely real it describes a boundary layer regime whereas a non-vanishing imaginary part reveals the existence of periodic structures known as recirculation rolls or eddies. It is found that, depending on the Prandtl number value,
Pr, recirculation eddies can exist either near the hot wall (
Pr≫1) or the cold wall (
Pr≪1). Our results provide a direct interpretation to the different behaviors observed in previous experimental and numerical studies.</description><subject>Aspect ratio</subject><subject>Boundary layer flow</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Exact sciences and technology</subject><subject>Fluid dynamics</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Hydrodynamic stability</subject><subject>Pattern selection; pattern formation</subject><subject>Perturbation techniques</subject><subject>Physics</subject><subject>Prandtl number</subject><subject>Recirculation eddies</subject><subject>Surface-tension-driven instability</subject><subject>Thermocapillary flows</subject><issn>0017-9310</issn><issn>1879-2189</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><recordid>eNqFkUtv1TAQhSNEJS4tPwEpGx5dpIzjR-wVqiqgla4EErA2jj1RjXzji50U9d_jJFXZwWp0Rt_MHM2pqpcELggQ8e4rAOkaRQm8BXJehOQNf1LtiOxU0xKpnla7R-RZ9Tznn4sEJnbVj5txCDOOFus41NMt1l-SGd0U6nE-9JjqOK7dEK2ZfBGFSmh9snPYGuicx1z7lUuHwh19CCbd10OIv_NZdTKYkPHFQz2tvn_88O3qutl__nRzdblvLJNiapAqJsF0PXcUuZDQG2DMSmKYE0KAgYEPzvYIvO8lKKQtdX1LeyWBsk7R0-p823trgj4mfygOdDReX1_u9dIDUAralt-Rwr7Z2GOKv2bMkz74bLG4HjHOWXeMC6bIuvX1P8m24x1l7QLyDbQp5pxwePRAQC8p6TUlvUSggeg1Jc3L3KuHAyZbE4byfOvz32HKADgThXu_cVh-eOcx6Wz9EpvzJY5Ju-j_c-kPGZullQ</recordid><startdate>20020201</startdate><enddate>20020201</enddate><creator>Mercier, Jean-François</creator><creator>Normand, Christiane</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>7TC</scope><scope>1XC</scope></search><sort><creationdate>20020201</creationdate><title>Influence of the Prandtl number on the location of recirculation eddies in thermocapillary flows</title><author>Mercier, Jean-François ; Normand, Christiane</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c486t-e39480a7b5d3e5680ba044c81a4d6660a0f5fdcbe05bb809e323db23b98034793</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>Aspect ratio</topic><topic>Boundary layer flow</topic><topic>Eigenvalues and eigenfunctions</topic><topic>Exact sciences and technology</topic><topic>Fluid dynamics</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Hydrodynamic stability</topic><topic>Pattern selection; pattern formation</topic><topic>Perturbation techniques</topic><topic>Physics</topic><topic>Prandtl number</topic><topic>Recirculation eddies</topic><topic>Surface-tension-driven instability</topic><topic>Thermocapillary flows</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mercier, Jean-François</creatorcontrib><creatorcontrib>Normand, Christiane</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Mechanical Engineering Abstracts</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>International journal of heat and mass transfer</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mercier, Jean-François</au><au>Normand, Christiane</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Influence of the Prandtl number on the location of recirculation eddies in thermocapillary flows</atitle><jtitle>International journal of heat and mass transfer</jtitle><date>2002-02-01</date><risdate>2002</risdate><volume>45</volume><issue>4</issue><spage>793</spage><epage>801</epage><pages>793-801</pages><issn>0017-9310</issn><eissn>1879-2189</eissn><coden>IJHMAK</coden><abstract>Two-dimensional thermocapillary-driven flow in a horizontal cavity of large aspect ratio is considered. Of particular interest is the asymptotic matching between the known parallel core flow solution and the non-parallel flow near the ends of the cavity. The influence of the end regions on the core flow is described by the superposition of spatial disturbances to the core flow solution. The stability analysis of this perturbed state leads to an eigenvalue problem for the complex wave number of the disturbances. The end flow structures are related to the nature of the lowest eigenvalue: when purely real it describes a boundary layer regime whereas a non-vanishing imaginary part reveals the existence of periodic structures known as recirculation rolls or eddies. It is found that, depending on the Prandtl number value,
Pr, recirculation eddies can exist either near the hot wall (
Pr≫1) or the cold wall (
Pr≪1). Our results provide a direct interpretation to the different behaviors observed in previous experimental and numerical studies.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/S0017-9310(01)00185-5</doi><tpages>9</tpages></addata></record> |
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| ispartof | International journal of heat and mass transfer, 2002-02, Vol.45 (4), p.793-801 |
| issn | 0017-9310 1879-2189 |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Aspect ratio Boundary layer flow Eigenvalues and eigenfunctions Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) Hydrodynamic stability Pattern selection pattern formation Perturbation techniques Physics Prandtl number Recirculation eddies Surface-tension-driven instability Thermocapillary flows |
| title | Influence of the Prandtl number on the location of recirculation eddies in thermocapillary flows |
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