On thermodynamics of viscoelastic rate type fluids with temperature dependent material coefficients
Abstract
We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type models for viscoelastic fluids. In particular, we study the models that allow one to consider temperature dependent material coefficients. This naturally calls for the formulation of a temperature evolution equation that would accompany the evolution equations for the mechanical quantities. The evolution equation for the temperature is explicitly formulated, and it is shown to be consistent with the laws of thermodynamics and the evolution equations for the mechanical quantities. The temperature evolution equation contains terms that are ignored or even not thought of in most of the works dealing with this class of fluids. The impact of the additional terms in the temperature evolution equation on the flow dynamics is documented by the solution of simple initial/boundary value problems.
Keywords
Cite
@article{arxiv.1612.01724,
title = {On thermodynamics of viscoelastic rate type fluids with temperature dependent material coefficients},
author = {Jaroslav Hron and Vojtěch Miloš and Vít Průša and Ondřej Souček and Karel Tůma},
journal= {arXiv preprint arXiv:1612.01724},
year = {2017}
}
Comments
Introduction, Page 2 and Page 3: We have been referred to relevant papers by I. J. Rao, K. Kannan and K. R. Rajagopal, who have considered viscoelastic rate type fluids with temperature dependent material coefficients. The comment on the relation between their work and our work has been added to the introduction