Abstract
A Hookean dumbbell model for polymers in dilute solutions undergoing homogeneous flow is generalized to include arbitrary imposed temperature profiles. In order to obtain the ‘‘nonisothermal diffusion equation’’ for the probability density in polymer configuration space we generalize the approach of Schieber and Öttinger [J. Chem. Phys. 89, 6972–6981 (1988)] to Brownian motion out of equilibrium. In addition, we derive the polymer contributions to the mass‐flux vector, stress tensor and heat‐flux vector by means of the kinetic theory approach of Curtiss and Bird [Adv. Polym. Sci. 125, 1–101 (1996)] for the case of a slowly varying temperature gradient, and we find coupled constitutive equations for the mass, momentum and energy fluxes. For a simple steady shear flow it is then possible to calculate the heat‐flux vector explicitly, at least for small temperature gradients and shear rates. We compare our approach and results with previous works on this subject, and we finally discuss some extensions.
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