Extended thermodynamics of a non-Newtonian fluid

Thermodynamics restrictions are calculated upon the constitutive equations of a non-Newtonian fluid. The fluid is of the rate type and the proper thermodynamic theory for such materials is seen to be extended thermodynamics. Thermodynamic stability conditions lead to the proper sign of the normal-stress coefficient, i.e. the sign that is compatible with experiment. Wave speeds for shear waves are calculated and the treatment of incompressible fluids is discussed.