KINETIC-THEORY AND TRANSPORT PHENOMENA FOR A DUMBBELL MODEL UNDER NONISOTHERMAL CONDITIONS

A Hookean dumbbell model for polymers in dilute solutions undergoing h omogeneous flow is generalized to include arbitrary imposed temperatur e profiles. In order to obtain the ''nonisothermal diffusion equation' ' for the probability density in polymer configuration space we genera lize the approach of Schieber and Ottinger [J. Chem. Phys. 89, 6972-69 81 (1988)] to Brownian motion out of equilibrium. In addition, we deri ve the polymer contributions to the mass-flux vector, stress tensor an d 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 equati ons for the mass, momentum and energy fluxes. For a simple steady shea r flow it is then possible to calculate the heat-flux vector explicitl y, at least for small temperature gradients and shear rates. We compar e our approach and results with previous works on this subject, and we finally discuss some extensions. (C) 1996 Society of Rheology.