Rate-type models of dissipative compressible fluids

Two models of dissipative compressible fluids are established within the general setting of Rational Thermodynamics. It is a common feature underlying the analysis of the thermodynamic consistency that the entropy production and the free energy potential are viewed as constitutive functions of the same set of physical variables and no internal variable is involved. Also in light of late experimental observations, hysteretic models are established for the dependence of pressure on the mass density. Next relaxation properties are modelled via rate equations with an objective derivative which combines the corotational rate with the divergence of the velocity.