Natural convection flows of Prabhakar-like fractional Maxwell fluids with generalized thermal transport
Natural convective flows of Prabhakar-like fractional viscoelastic fluids over an infinite vertical heated wall are studied by introducing the generalized fractional constitutive equations for the stress-shear rate and thermal flux density vector. The generalized memory effects are described by the...
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| Veröffentlicht in: | Journal of thermal analysis and calorimetry 2021-02, Vol.143 (3), p.2245-2258 |
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| container_title | Journal of thermal analysis and calorimetry |
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| creator | Shah, Nehad Ali Fetecau, Constantin Vieru, Dumitru |
| description | Natural convective flows of Prabhakar-like fractional viscoelastic fluids over an infinite vertical heated wall are studied by introducing the generalized fractional constitutive equations for the stress-shear rate and thermal flux density vector. The generalized memory effects are described by the time-fractional Prabhakar derivative. Closed-form solutions for the non-dimensional velocity and temperature fields are determined using the method of integral transform. The velocity and heat transfer of Prabhakar-like fractional Maxwell fluids with generalized thermal transport are compared with ordinary Maxwell fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Solutions of the generalized model are particularized into solutions corresponding to flows and heat transfer with Caputo memory, respectively, to flows of the ordinary fluids with ordinary heat transfer. The use of Prabhakar operators shows the possibility of a convenient choice of fractional parameters such that to have a very good fitting between theoretical and experimental data. |
| doi_str_mv | 10.1007/s10973-020-09835-0 |
| format | Article |
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The generalized memory effects are described by the time-fractional Prabhakar derivative. Closed-form solutions for the non-dimensional velocity and temperature fields are determined using the method of integral transform. The velocity and heat transfer of Prabhakar-like fractional Maxwell fluids with generalized thermal transport are compared with ordinary Maxwell fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Solutions of the generalized model are particularized into solutions corresponding to flows and heat transfer with Caputo memory, respectively, to flows of the ordinary fluids with ordinary heat transfer. 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The generalized memory effects are described by the time-fractional Prabhakar derivative. Closed-form solutions for the non-dimensional velocity and temperature fields are determined using the method of integral transform. The velocity and heat transfer of Prabhakar-like fractional Maxwell fluids with generalized thermal transport are compared with ordinary Maxwell fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Solutions of the generalized model are particularized into solutions corresponding to flows and heat transfer with Caputo memory, respectively, to flows of the ordinary fluids with ordinary heat transfer. The use of Prabhakar operators shows the possibility of a convenient choice of fractional parameters such that to have a very good fitting between theoretical and experimental data.</description><subject>Analytical Chemistry</subject><subject>Chemistry</subject><subject>Chemistry and Materials Science</subject><subject>Comparative analysis</subject><subject>Computational fluid dynamics</subject><subject>Constitutive equations</subject><subject>Constitutive relationships</subject><subject>Convective flow</subject><subject>Flux density</subject><subject>Free convection</subject><subject>Heat transfer</subject><subject>Heat transmission</subject><subject>Inorganic Chemistry</subject><subject>Integral transforms</subject><subject>Maxwell fluids</subject><subject>Measurement Science and Instrumentation</subject><subject>Operators (mathematics)</subject><subject>Physical Chemistry</subject><subject>Polymer Sciences</subject><subject>Shear rate</subject><subject>Thermoelectricity</subject><subject>Viscoelastic fluids</subject><subject>Viscoelasticity</subject><issn>1388-6150</issn><issn>1588-2926</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kUFP3DAQhSNUpNKFP9BTJE49BMZOnNjH1aoFpIUiWs6WccZZQzZebIfd9tdjNpUQl2oOM7K-9_Tkl2VfCZwRgOY8EBBNWQCFAgQvWQEH2RFhnBdU0PpTust014TB5-xLCI8AIASQo6y7UXH0qs-1G15QR-uG3PRuG3Jn8luvHlbqSfmit0-YG6_2QKKv1W6LfZ_Q0bYh39q4yjscMDnZv9jmcYV-nbjo1RA2zsfj7NCoPuDJvz3L7n98_724LJY_L64W82WhKypigaSF2rQlowQ0NUbUdWMYaVqmFeNaNBXVTY36gaIhVasa5KphAmoNXCvg5Sw7nXw33j2PGKJ8dKNPkYOklagEAS6qRJ1NVKd6lHYwLgXVaVpc2_QTaGx6n9esZCXh4s322wdBYiLuYqfGEOTVr7uPLJ1Y7V0IHo3ceLtW_o8kIN_aklNbMrUl921JSKJyEoUEDx3699z_Ub0CC8SYaA</recordid><startdate>20210201</startdate><enddate>20210201</enddate><creator>Shah, Nehad Ali</creator><creator>Fetecau, Constantin</creator><creator>Vieru, Dumitru</creator><general>Springer International Publishing</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope><orcidid>https://orcid.org/0000-0001-9989-8452</orcidid></search><sort><creationdate>20210201</creationdate><title>Natural convection flows of Prabhakar-like fractional Maxwell fluids with generalized thermal transport</title><author>Shah, Nehad Ali ; Fetecau, Constantin ; Vieru, Dumitru</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c429t-e1d06fd35210c2ff9667f517d5ca58c9742c76ecb2ef14da7e8a75906c08ca083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Analytical Chemistry</topic><topic>Chemistry</topic><topic>Chemistry and Materials Science</topic><topic>Comparative analysis</topic><topic>Computational fluid dynamics</topic><topic>Constitutive equations</topic><topic>Constitutive relationships</topic><topic>Convective flow</topic><topic>Flux density</topic><topic>Free convection</topic><topic>Heat transfer</topic><topic>Heat transmission</topic><topic>Inorganic Chemistry</topic><topic>Integral transforms</topic><topic>Maxwell fluids</topic><topic>Measurement Science and Instrumentation</topic><topic>Operators (mathematics)</topic><topic>Physical Chemistry</topic><topic>Polymer Sciences</topic><topic>Shear rate</topic><topic>Thermoelectricity</topic><topic>Viscoelastic fluids</topic><topic>Viscoelasticity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shah, Nehad Ali</creatorcontrib><creatorcontrib>Fetecau, Constantin</creatorcontrib><creatorcontrib>Vieru, Dumitru</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><jtitle>Journal of thermal analysis and calorimetry</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shah, Nehad Ali</au><au>Fetecau, Constantin</au><au>Vieru, Dumitru</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Natural convection flows of Prabhakar-like fractional Maxwell fluids with generalized thermal transport</atitle><jtitle>Journal of thermal analysis and calorimetry</jtitle><stitle>J Therm Anal Calorim</stitle><date>2021-02-01</date><risdate>2021</risdate><volume>143</volume><issue>3</issue><spage>2245</spage><epage>2258</epage><pages>2245-2258</pages><issn>1388-6150</issn><eissn>1588-2926</eissn><abstract>Natural convective flows of Prabhakar-like fractional viscoelastic fluids over an infinite vertical heated wall are studied by introducing the generalized fractional constitutive equations for the stress-shear rate and thermal flux density vector. The generalized memory effects are described by the time-fractional Prabhakar derivative. Closed-form solutions for the non-dimensional velocity and temperature fields are determined using the method of integral transform. The velocity and heat transfer of Prabhakar-like fractional Maxwell fluids with generalized thermal transport are compared with ordinary Maxwell fluids with generalized thermal transport and with the ordinary viscoelastic fluids with classical Fourier thermal flux. Solutions of the generalized model are particularized into solutions corresponding to flows and heat transfer with Caputo memory, respectively, to flows of the ordinary fluids with ordinary heat transfer. 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| subjects | Analytical Chemistry Chemistry Chemistry and Materials Science Comparative analysis Computational fluid dynamics Constitutive equations Constitutive relationships Convective flow Flux density Free convection Heat transfer Heat transmission Inorganic Chemistry Integral transforms Maxwell fluids Measurement Science and Instrumentation Operators (mathematics) Physical Chemistry Polymer Sciences Shear rate Thermoelectricity Viscoelastic fluids Viscoelasticity |
| title | Natural convection flows of Prabhakar-like fractional Maxwell fluids with generalized thermal transport |
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