### Peter Wapperom and Martien A. Hulsen

### Thermodynamics of viscoelastic fluids: the temperature equation

#### Journal of Rheology **42**, 1998, p. 999-1019

#### Abstract

From the thermodynamics with internal variables we will derive the
temperature equation for viscoelastic fluids.
We consider the type of storage of mechanical
energy, the dissipation of mechanical energy, the compressibility of the fluid,
the non-equilibrium heat capacity and thermal expansion,
and deformation induced anisotropy
of the heat conduction. The well-known stress differential models that
fit into the thermodynamic theory will be treated as an example.
Adapting a power-law scaling of the shear moduli on temperature and density,
as is usual in rubber elasticity, we will derive an approximation of the
temperature equation in measurable
quantities. This equation will be compared with experimental results.
#### Keywords

temperature equation; differential stress models;
thermodynamics; (positive) dissipation; energy and entropy elasticity;
compressibility; non-equilibrium heat capacity and thermal expansion