A new energy conservation scheme for the numeric study of the heat transfer in profile extrusion calibration

Abstract

Thermoplastic extrusion processes use a dry calibration/cooling system, composed by one or several calibrators in series. One of the major difficulties in the modelling is to prescribe adequate values for the heat transfer coefficients between the polymer and the cooler or the air. We present an optimization procedure coupled with a finite volume method to evaluate such coefficients from experimental data. The tecnhique is based in a new conservative second-order finite volume scheme using a cell-to-vertex interpolation to solve the thermal problem involving a specific method to take the discontinuities (temperature, velocity, and thermal conductivity) into account. We have also performed a sensitive analysis of the different parameters of the problem to evaluate the variation of the thermal transfer coefficient with respect to parameters such as velocity or inflow temperature.

High‐order accurate conjugate heat transfer solutions with a finite volume method in anisotropic meshes with application in polymer processing

“…Concerning the discretization methods for conjugate heat transfer problems (often referred to as elliptic interface problems), a comprehensive literature can be found including finite difference methods, 21,22 finite element methods, [23][24][25] discontinuous Galerkin methods, 26 finite volume methods, [27][28][29][30] lattice Boltzmann methods, 31,32 among others. Finite volume methods are particularly interesting in the context of heat and mass transfer problems, given the conservation property intrinsically preserved and the ease of handling general unstructured meshes.…”

A novel heat transfer coefficient identification methodology for the profile extrusion calibration stage

“…We provide a short description of the finite volume scheme based on the cell-to-vertex technology presented in [16], that closely follows the scheme proposed in [2]. We consider the energy equation on an open bounded polygonal domain Ω of R 2 with boundary Γ (we skip the index p for the sake of simplicity).…”

“…with β ki the interpolation coefficients for vertex k provides an expression of the temperature at the vertex v i in function of the temperature in the cell c i , i P µpkq. Special attention is required when dealing with the discontinuity at the contact interface and two distinct temperatures have to be evaluated at the same vertex (see [2] for a detailed description of the method). The numerical fluxes are then evaluated based on the two vectors T and Θ.…”

“…In the case of the interface between the polymer and the calibrator, we have to distinguish two cases regarding to the side where the flux comes from (see [2] for the details).…”