A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids

Abstract

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.

Incompressible limit of a compressible Oldroyd-B model

“…Although the mathematical study of Oldroyd-B models attracts a lot of attention, there are few results about the system (1.1). In [6], we notice that the compressible Oldroyd-B model (1.1) and some related non-isothermal models can be derived in the thermodynamic framework. This idea can be traced back to [24] and has been widely used in [4,12,22,23,27].…”