Effects of second diffusing component and cross diffusion on primary and secondary thermoconvective instabilities in couple stress liquids
Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation....
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| Veröffentlicht in: | Applied mathematics and mechanics 2017-11, Vol.38 (11), p.1579-1600 |
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| creator | Ravi, R. Kanchana, C. Siddheshwar, P. G. |
| description | Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient. |
| doi_str_mv | 10.1007/s10483-017-2280-9 |
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G.</creator><creatorcontrib>Ravi, R. ; Kanchana, C. ; Siddheshwar, P. G.</creatorcontrib><description>Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.</description><edition>English ed.</edition><identifier>ISSN: 0253-4827</identifier><identifier>EISSN: 1573-2754</identifier><identifier>DOI: 10.1007/s10483-017-2280-9</identifier><language>eng</language><publisher>Shanghai: Shanghai University</publisher><subject>Applications of Mathematics ; Classical Mechanics ; Convection ; Diffusion effects ; Fluid- and Aerodynamics ; Hopf bifurcation ; Hopf分岔 ; Liquids ; Mass transport ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Nonlinear analysis ; Partial Differential Equations ; Soret coefficient ; 交叉扩散 ; 偶应力 ; 分岔现象 ; 对流不稳定性 ; 液体 ; 组件 ; 非线性分析</subject><ispartof>Applied mathematics and mechanics, 2017-11, Vol.38 (11), p.1579-1600</ispartof><rights>Shanghai University and Springer-Verlag GmbH Germany 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><rights>Copyright © Wanfang Data Co. Ltd. All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c378t-8d827ca10b4e87eeea33fc8244fd8a639c4aaab0014bf5b2e22583fb6bc6da863</citedby><cites>FETCH-LOGICAL-c378t-8d827ca10b4e87eeea33fc8244fd8a639c4aaab0014bf5b2e22583fb6bc6da863</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/86647X/86647X.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10483-017-2280-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10483-017-2280-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Ravi, R.</creatorcontrib><creatorcontrib>Kanchana, C.</creatorcontrib><creatorcontrib>Siddheshwar, P. G.</creatorcontrib><title>Effects of second diffusing component and cross diffusion on primary and secondary thermoconvective instabilities in couple stress liquids</title><title>Applied mathematics and mechanics</title><addtitle>Appl. Math. Mech.-Engl. Ed</addtitle><addtitle>Applied Mathematics and Mechanics（English Edition）</addtitle><description>Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.</description><subject>Applications of Mathematics</subject><subject>Classical Mechanics</subject><subject>Convection</subject><subject>Diffusion effects</subject><subject>Fluid- and Aerodynamics</subject><subject>Hopf bifurcation</subject><subject>Hopf分岔</subject><subject>Liquids</subject><subject>Mass transport</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear analysis</subject><subject>Partial Differential Equations</subject><subject>Soret coefficient</subject><subject>交叉扩散</subject><subject>偶应力</subject><subject>分岔现象</subject><subject>对流不稳定性</subject><subject>液体</subject><subject>组件</subject><subject>非线性分析</subject><issn>0253-4827</issn><issn>1573-2754</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9Uc1q3DAQFiWBbjd5gN5Mews41a8lH0NI2kKgl-YsZHm0q-CVdiU7zb5CnrraeNP0FBCImfl-pG8Q-kzwJcFYfssEc8VqTGRNqcJ1-wEtiJCsplLwE7TAVLCaKyo_ok85P2CMueR8gZ5vnAM75iq6KoONoa9679yUfVhVNm62MUAYK1P6NsWcX6cxVOVsk9-YtH8Zz-xDNa4hbWKpHouyf4TKhzyazg9-9JBLVYSn7QBVHhMUycHvJt_nM3TqzJDh_Hgv0f3tze_rH_Xdr-8_r6_uasukGmvVl19YQ3DHQUkAMIw5qyjnrlemYa3lxpgOY8I7JzoKlArFXNd0tumNatgSXcy6f0xwJqz0Q5xSKI56v89P6-FJAy05kpLrAfx1Bm9T3E2Qxzc0aYUQLSFMFBSZUS8ZJXD6mIwmWB_2o-f96KKrD_vRbeHQmZMLNqwg_af8DunL0Wgdw2pXeP-cGlke0jLF2V8IOqKQ</recordid><startdate>20171101</startdate><enddate>20171101</enddate><creator>Ravi, R.</creator><creator>Kanchana, C.</creator><creator>Siddheshwar, P. G.</creator><general>Shanghai University</general><general>Springer Nature B.V</general><general>Department of Humanities and Sciences, National Institute of Technology Goa, Goa 403401, India%Department of Mathematics, Jnana Bharathi Campus, Bangalore University,Bangalore 560056, India</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20171101</creationdate><title>Effects of second diffusing component and cross diffusion on primary and secondary thermoconvective instabilities in couple stress liquids</title><author>Ravi, R. ; Kanchana, C. ; Siddheshwar, P. G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c378t-8d827ca10b4e87eeea33fc8244fd8a639c4aaab0014bf5b2e22583fb6bc6da863</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Applications of Mathematics</topic><topic>Classical Mechanics</topic><topic>Convection</topic><topic>Diffusion effects</topic><topic>Fluid- and Aerodynamics</topic><topic>Hopf bifurcation</topic><topic>Hopf分岔</topic><topic>Liquids</topic><topic>Mass transport</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear analysis</topic><topic>Partial Differential Equations</topic><topic>Soret coefficient</topic><topic>交叉扩散</topic><topic>偶应力</topic><topic>分岔现象</topic><topic>对流不稳定性</topic><topic>液体</topic><topic>组件</topic><topic>非线性分析</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ravi, R.</creatorcontrib><creatorcontrib>Kanchana, C.</creatorcontrib><creatorcontrib>Siddheshwar, P. G.</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Applied mathematics and mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ravi, R.</au><au>Kanchana, C.</au><au>Siddheshwar, P. G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Effects of second diffusing component and cross diffusion on primary and secondary thermoconvective instabilities in couple stress liquids</atitle><jtitle>Applied mathematics and mechanics</jtitle><stitle>Appl. Math. Mech.-Engl. Ed</stitle><addtitle>Applied Mathematics and Mechanics（English Edition）</addtitle><date>2017-11-01</date><risdate>2017</risdate><volume>38</volume><issue>11</issue><spage>1579</spage><epage>1600</epage><pages>1579-1600</pages><issn>0253-4827</issn><eissn>1573-2754</eissn><abstract>Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.</abstract><cop>Shanghai</cop><pub>Shanghai University</pub><doi>10.1007/s10483-017-2280-9</doi><tpages>22</tpages><edition>English ed.</edition></addata></record> |
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| subjects | Applications of Mathematics Classical Mechanics Convection Diffusion effects Fluid- and Aerodynamics Hopf bifurcation Hopf分岔 Liquids Mass transport Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Nonlinear analysis Partial Differential Equations Soret coefficient 交叉扩散 偶应力 分岔现象 对流不稳定性 液体 组件 非线性分析 |
| title | Effects of second diffusing component and cross diffusion on primary and secondary thermoconvective instabilities in couple stress liquids |
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