Temperature profile within a plane channel of an experimental extrusion die under polymer processing conditions

Abstract

The flow of melted polyethylene (Dowlex 2042 E ) through an extrusion die is investigated both experimentally and numerically. This article deals with the reconstruction of thermal history of the melted polymer in the channel die and the influence of the extrusion parameters on the inlet temperature profile. The inverse heat transfer problem is formulated as an optimization problem by considering both the heat transfer and Navier-Stokes equations. It is solved by using the classical conjugate gradient algorithm. Experimental results are presented and the article focuses on the importance of checking the adequacy of the modelling equations in experimental data processing in order to avoid convergence of the inverse algorithm toward solutions which have no physical significance. The effects of the pressure drop combined with the viscous dissipation effect along the channel die are then discussed. Nomenclature C p heat capacity (J kg À1 C À1 ) F source term of energy (Pa s À3 ) J functional to be minimized ( C 2 ) l c length of the die connector (m) l b width of the zone (m) l p perimeter (m) L hp length of the heating-plate (m)axial and radial velocities (m s À1 ) Y measure temperatures ( C) Subscripts and Superscripts c connector m, p sensor locations 0 inlet extrusion die hp heating plate melt melted polymer n iteration number n vector normal p polymer s outlet extrusion die w die wall Greek symbols " shear rate (s À2 ) dynamic viscosity (Pa s) conductivity (W m À1 C À1 ) density (kg m À3 ) adjoint variable sensitivity variable Dirac delta function O spatial domain IntroductionDuring polymer extrusion, even after the melting zone, heat transfer takes an important place at the outlet of the extruder [1,2]. Due to high viscous dissipation and very low heat conductivity, the temperature profile within the channel die can be quite sharp. Overheated areas can be generated and degradation of the polymer could occur. For such creeping flow the temperature field is affected far downstream from the entrance of the die, so to predict accurately and to control the temperature rise, the inlet temperature profile has to be taken into account. However, due to the history in the extruder, the material temperature at the die entrance is rarely uniform. Hence, the determination of this temperature profile is referred to as a boundary inverse heat convection-conduction problem. There are numerous works on the initial temperature profile restoration, for example, in [3] the inlet temperature profile is estimated in the laminar duct flow and subsequent investigations [4-6] examine various aspects of this problem. Recently, Hsu et al. [7] presented a two-dimensional inverse least squares method to estimate both inlet temperature and wall heat flux in a steady laminar flow in a circular duct. Huang and Chen [8] have solved a non-stationary Navier-Stokes equation, to provide coefficients for energy equation, but the velocity field does not depend on temperature. Gejadze and Jarny [9] have presented a detailed analysis of IHCP coupled ...