We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.
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Thermodynamics of viscoelastic rate-type fluids with stress diffusion
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February 2018
Research Article|
February 02 2018
Thermodynamics of viscoelastic rate-type fluids with stress diffusion
Josef Málek
;
Josef Málek
a)
1
Faculty of Mathematics and Physics, Charles University in Prague
, Sokolovská 83, Praha 8, Karlín CZ 186 75, Czech Republic
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Vít Průša
;
Vít Průša
b)
1
Faculty of Mathematics and Physics, Charles University in Prague
, Sokolovská 83, Praha 8, Karlín CZ 186 75, Czech Republic
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Tomáš Skřivan;
Tomáš Skřivan
c)
1
Faculty of Mathematics and Physics, Charles University in Prague
, Sokolovská 83, Praha 8, Karlín CZ 186 75, Czech Republic
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Endre Süli
Endre Süli
d)
2
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter
, Woodstock Road, Oxford OX2 6GG, United Kingdom
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a)
E-mail: [email protected]
b)
E-mail: [email protected]
c)
E-mail: [email protected]
d)
E-mail: [email protected]
Physics of Fluids 30, 023101 (2018)
Article history
Received:
December 04 2017
Accepted:
January 08 2018
Citation
Josef Málek, Vít Průša, Tomáš Skřivan, Endre Süli; Thermodynamics of viscoelastic rate-type fluids with stress diffusion. Physics of Fluids 1 February 2018; 30 (2): 023101. https://doi.org/10.1063/1.5018172
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