Constitutive equations of non-isothermal polymer melt

Constitutive equations of non-isothermal polymer melt are presented by the analysis of entropic free energy contribution of the macromolecular chains, which are treated as elastic dumbbell models. With describing non-isothermal dumbbell spring, as the function of temperature, the non-linear elastic coefficient expression causes the appearance of temperature gradient in stress constitutive equations. Following the constitutive equation of Hookean dumbbell model, non-isothermal stress constitutive equations of FENE and FENE-P models are derived. In deriving process of constitutive equations, the second moment approximation is used to closure FENE model. Using the non-isothermal constitutive equations, numerical simulations of polymer flow through shear cavity and planar contraction cavity are presented. And the distributions of correlative stress functions and the effects of different temperatures on stress functions are discussed. The present results are shown to explore the non-isothermal constitutive equations of elastic dumbbell models, and to search more accurately describing way of non-isothermal polymer melt.