however, the problem is more difficult, and one gets [5g]:

(3.11)

The term involving the trace of the polymer contribution to the stress tensor arises in the equation of change for temperature for polymeric fluids, whereas there is no such term for Newtonian liquids.

Another difference between Newtonian fluids and polymeric liquids is in the heat conduction equation for a stationary fluid. According to the continuum mechanics for linear thermovisco-elasticity [14]

(3.12)

Here is the temperature at , and is a time-dependent thermal property corresponding to the heat capacity per unit volume. The general phase space kinetic theory for this situation gives [5h] Eq. 3.12 with:

(3.13)

Thus there is a contribution to the heat capacity that has a "fading memory." Insofar as we know, this effect has yet to be measured.

3c. Mass transport