Numerical analysis of heat and mass transfer of polymer in extruder screw channel taking into account thermal conductivity of screw

A spatial mathematical model of heat and mass transfer processes in nonlinearly viscous polymer media under phase transition in the extruder screw channel taking into account the thermal conductivity of the screw is proposed. When solving the problem, the screw channel is unfolded on the plane, the principle of reverse motion is used, and physical variables (velocity-pressure) are expressed in terms of the vorticity-stream function. Boundary conditions for the longitudinal velocity component and the vorticity-stream functions are set on the assumption that liquid sticks to solid impermeable walls. Woods' formula of second order of accuracy is applied to determine the value of the vortex on the boundary. The thermophysical characteristics of the polymer are obtained as the continuous functions of temperature. The latent heat of phase transitions is taken into account via the temperature dependence of the heat capacity. The dependence of the effective viscosity of the polymer melt versus shear rate and temperature is described by a power law and the Reynolds equation, respectively. The resulting system of differential equations is solved by the finite difference method using a multilevel algorithm for iterative procedures. For implementation of the proposed mathematical model a software complex “Universal Screw 12” has been developed. Numerical studies have been performed to study heat and mass transfer of polymer in a screw taking into account the thermal conductivity of the screw. The fields of temperature and velocity vector components in the channel cross section, the diagrams showing changes in the average, minimum and maximum temperatures of the material with length, and the volume distribution of local overheating polymer melt in the extruder channel are constructed. It is shown that in mathematical modeling of extrusion processes in polymer materials it is necessary to consider heat and mass transfer in the extruder screw. This allows one to significantly improve the accuracy of qualitative and quantitative determination of the integral and differential characteristics of extrusion equipment.