A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids
We revisit some classical models for dilute polymeric fluids, and we show that thermodynamically consistent models for non-isothermal flows of these fluids can be derived in a very elementary manner. Our approach is based on the identification of energy storage mechanisms and entropy production mech...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-08-01
|
| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/5/3/133 |
| _version_ | 1797558906286768128 |
|---|---|
| author | Mark Dostalík Josef Málek Vít Průša Endre Süli |
| author_facet | Mark Dostalík Josef Málek Vít Průša Endre Süli |
| author_sort | Mark Dostalík |
| collection | DOAJ |
| description | We revisit some classical models for dilute polymeric fluids, and we show that thermodynamically consistent models for non-isothermal flows of these fluids can be derived in a very elementary manner. Our approach is based on the identification of energy storage mechanisms and entropy production mechanisms in the fluid of interest, which, in turn, leads to explicit formulae for the Cauchy stress tensor and for all of the fluxes involved. Having identified these mechanisms and derived the governing equations, we document the potential use of the thermodynamic basis of the model in a rudimentary stability analysis. In particular, we focus on finite amplitude (nonlinear) stability of a stationary spatially homogeneous state in a thermodynamically isolated system. |
| first_indexed | 2024-03-10T17:38:01Z |
| format | Article |
| id | doaj.art-e1480760bd4c4f188697044cb00997c9 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T17:38:01Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-e1480760bd4c4f188697044cb00997c92023-11-20T09:48:28ZengMDPI AGFluids2311-55212020-08-015313310.3390/fluids5030133A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric FluidsMark Dostalík0Josef Málek1Vít Průša2Endre Süli3Faculty of Mathematics and Physics, Charles University, Sokolovská 83, CZ 186 75 Praha 8–Karlín, Czech RepublicFaculty of Mathematics and Physics, Charles University, Sokolovská 83, CZ 186 75 Praha 8–Karlín, Czech RepublicFaculty of Mathematics and Physics, Charles University, Sokolovská 83, CZ 186 75 Praha 8–Karlín, Czech RepublicMathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UKWe revisit some classical models for dilute polymeric fluids, and we show that thermodynamically consistent models for non-isothermal flows of these fluids can be derived in a very elementary manner. Our approach is based on the identification of energy storage mechanisms and entropy production mechanisms in the fluid of interest, which, in turn, leads to explicit formulae for the Cauchy stress tensor and for all of the fluxes involved. Having identified these mechanisms and derived the governing equations, we document the potential use of the thermodynamic basis of the model in a rudimentary stability analysis. In particular, we focus on finite amplitude (nonlinear) stability of a stationary spatially homogeneous state in a thermodynamically isolated system.https://www.mdpi.com/2311-5521/5/3/133thermodynamicscompressible dilute polymeric fluidsstability |
| spellingShingle | Mark Dostalík Josef Málek Vít Průša Endre Süli A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids Fluids thermodynamics compressible dilute polymeric fluids stability |
| title | A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids |
| title_full | A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids |
| title_fullStr | A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids |
| title_full_unstemmed | A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids |
| title_short | A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids |
| title_sort | simple construction of a thermodynamically consistent mathematical model for non isothermal flows of dilute compressible polymeric fluids |
| topic | thermodynamics compressible dilute polymeric fluids stability |
| url | https://www.mdpi.com/2311-5521/5/3/133 |
| work_keys_str_mv | AT markdostalik asimpleconstructionofathermodynamicallyconsistentmathematicalmodelfornonisothermalflowsofdilutecompressiblepolymericfluids AT josefmalek asimpleconstructionofathermodynamicallyconsistentmathematicalmodelfornonisothermalflowsofdilutecompressiblepolymericfluids AT vitprusa asimpleconstructionofathermodynamicallyconsistentmathematicalmodelfornonisothermalflowsofdilutecompressiblepolymericfluids AT endresuli asimpleconstructionofathermodynamicallyconsistentmathematicalmodelfornonisothermalflowsofdilutecompressiblepolymericfluids AT markdostalik simpleconstructionofathermodynamicallyconsistentmathematicalmodelfornonisothermalflowsofdilutecompressiblepolymericfluids AT josefmalek simpleconstructionofathermodynamicallyconsistentmathematicalmodelfornonisothermalflowsofdilutecompressiblepolymericfluids AT vitprusa simpleconstructionofathermodynamicallyconsistentmathematicalmodelfornonisothermalflowsofdilutecompressiblepolymericfluids AT endresuli simpleconstructionofathermodynamicallyconsistentmathematicalmodelfornonisothermalflowsofdilutecompressiblepolymericfluids |