On thermodynamics, objectivity and the modeling of non-isothermal viscoelastic fluid behavior

The present paper is concerned with the modeling of non-isothermal viscoelastic fluid behavior. A general procedure, developed within the framework of thermodynamics of irreversible processes, is proposed to obtain constitutive relations that verify automatically the second law of thermodynamics and the principle of material objectivity. It is shown that the choice of the objective time derivative is important not only to assure a mathematically correct and physically realistic description of the viscoelastic behavior, but also to perform an adequate description of the thermomechanical coupling in the case of non-isothermal flows. Such a thermodynamic approach allows a rational identification of the terms responsible for the thermomechanical coupling in the heat equation, which is a first step to better understand their influence on the fluid behavior.