The Heat Flux Vector(s) in a Two Component Fluid Mixture
Bulk kinematic properties of mixtures such as velocity are known to be the density weighed averages of the constituent velocities. No such paradigm exists for the heat flux of mixtures when the constituents have different temperatures. Using standard principles such as frame indifference, we address...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/5/2/77 |
| _version_ | 1797567430034194432 |
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| author | A. D. Kirwan Mehrdad Massoudi |
| author_facet | A. D. Kirwan Mehrdad Massoudi |
| author_sort | A. D. Kirwan |
| collection | DOAJ |
| description | Bulk kinematic properties of mixtures such as velocity are known to be the density weighed averages of the constituent velocities. No such paradigm exists for the heat flux of mixtures when the constituents have different temperatures. Using standard principles such as frame indifference, we address this topic by developing linear constitutive equations for the constituent heat fluxes, the interaction force between constituents, and the stresses for a mixture of two fluids. Although these equations contain 18 phenomenological coefficients, we are able to use the Clausius-Duhem inequality to obtain inequalities involving the principal and cross flux coefficients. The theory is applied to some special cases and shown to reduce to standard results when the constituents have the same temperature. |
| first_indexed | 2024-03-10T19:41:43Z |
| format | Article |
| id | doaj.art-5fd480b855ed4883944de94ae74a13d0 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T19:41:43Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-5fd480b855ed4883944de94ae74a13d02023-11-20T01:08:23ZengMDPI AGFluids2311-55212020-05-01527710.3390/fluids5020077The Heat Flux Vector(s) in a Two Component Fluid MixtureA. D. Kirwan0Mehrdad Massoudi1School of Marine Science and Policy, University of Delaware, 103 Robinson Hall, Newark, DE 19716, USAU.S. Department of Energy, National Energy Technology Laboratory (NETL), 626 Cochrans Mill Road, P.O. Box 10940, Pittsburgh, PA 15236, USABulk kinematic properties of mixtures such as velocity are known to be the density weighed averages of the constituent velocities. No such paradigm exists for the heat flux of mixtures when the constituents have different temperatures. Using standard principles such as frame indifference, we address this topic by developing linear constitutive equations for the constituent heat fluxes, the interaction force between constituents, and the stresses for a mixture of two fluids. Although these equations contain 18 phenomenological coefficients, we are able to use the Clausius-Duhem inequality to obtain inequalities involving the principal and cross flux coefficients. The theory is applied to some special cases and shown to reduce to standard results when the constituents have the same temperature.https://www.mdpi.com/2311-5521/5/2/77mixturesFourier’s heat conductionheat flux vectorcontinuum theoryClausius-Duhem inequality |
| spellingShingle | A. D. Kirwan Mehrdad Massoudi The Heat Flux Vector(s) in a Two Component Fluid Mixture Fluids mixtures Fourier’s heat conduction heat flux vector continuum theory Clausius-Duhem inequality |
| title | The Heat Flux Vector(s) in a Two Component Fluid Mixture |
| title_full | The Heat Flux Vector(s) in a Two Component Fluid Mixture |
| title_fullStr | The Heat Flux Vector(s) in a Two Component Fluid Mixture |
| title_full_unstemmed | The Heat Flux Vector(s) in a Two Component Fluid Mixture |
| title_short | The Heat Flux Vector(s) in a Two Component Fluid Mixture |
| title_sort | heat flux vector s in a two component fluid mixture |
| topic | mixtures Fourier’s heat conduction heat flux vector continuum theory Clausius-Duhem inequality |
| url | https://www.mdpi.com/2311-5521/5/2/77 |
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