A BEM APPROACH TO MODEL HEAT-FLOW DURING CRYSTALLIZATION

In most polymer processing applications such as injection moulding, fibre spinning and extrusion, crystallization plays an important role. The energy flow at the solid liquid interface during crystallization controls the kinetics and subsequently influences the morphology of the transforming material. Our approach is based on the classical phase-change problem. The governing transient heat conduction equations in the liquid and the solid domains are solved using a boundary element method (BEM) with a time dependent fundamental solution to determine the temperature distribution. The boundary energy equation is used to predict the movement of the front. The crystallization kinetics are introduced through a mathematical model based on the cooling rate of a hypothetical control volume in the solid (crystalline) domain and the changes in the crystallinity are expressed in terms of the varying interface temperature. First, we verified the BEM formulation and implementation by comparing the results of two examples with an analytical and a finite difference method in one-dimension. Next, we investigated the effects of the crystallization kinetics by allowing the interface temperature to vary during the crystallization process. The results show that the crystallization front movement is slowed considerably when the kinetics are taken into account. Also, depending on the cooling rate and the parameters in the kinetics model, there may be undercooling during the process.