Development and validation of a model for the temperature distribution in the extrusion calibration stage

• New model to calculate the temperature distribution in two phase systems.
• The approach is able to deal with temperature discontinuity at the phases interface.
• The methodology was implemented in OpenFOAM® computational library.
• The developed code is able to model the profiles extrusion cooling stage.

A new model to calculate the temperature discontinuity between two phases is derived in detail and implemented in the OpenFOAM® computational library. The derivation of the model is based on the local instantaneous conservation equation for energy. With the conditional volume averaging technique a single equation that governs the temperature distribution, valid in both phases, is obtained. The order of convergence of the solver is determined using the Method of Manufactured Solutions (MMS), which also allows to identify eventual coding bugs. To verify the developed code, 2D problems, namely the heat transfer between two slabs in contact and between two concentric hollow cylinders, are considered. For the same purpose, the solution for a complex two-dimensional layout, which consists of a polymeric sheet and a calibrator, is compared with benchmark solutions. Finally, the developed code is used to study the behavior of a complex 3D calibration system. All results show good agreement with benchmark ones or, in case of the realistic calibrators, are in line with our expectations.