Thermodynamics of viscoelastic rate-type fluids with stress diffusion

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. Different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate type fluids with stress diffusion