The modelling of non-isothermal flow of viscoelastic materials using d
ifferential constitutive equations is investigated. The approach is ba
sed on the concept of a slip tensor describing the nonaffine motion of
the stress-carrying structure of the fluid. By specifying a slip tens
or and the elastic behaviour of the structure, the constitutive model
is determined. This slip tensor also appears in the energy equation an
d thus, for a given constitutive model, the form of the energy equatio
n is known. Besides the partitioning between dissipated and elasticall
y stored energy, also the difference between entropy and energy elasti
city is discussed. Numerical simulations are based on a stabilized Dis
continuous Galerkin method to solve the mass, momentum and constitutiv
e equations and a Streamline Upwind Petrov-Galerkin formulation to sol
ve the energy equation. Coupling is achieved by a fixed point iteratio
n. The flow around a confined cylinder is investigated, showing differ
ences between viscous and viscoelastic modelling, and between limiting
cases of viscoelastic modelling. (C) 1997 Elsevier Science B.V.