Finite volume modeling of the non-isothermal flow of a non-Newtonian fluid in a rubber’s extrusion die

Abstract

Non-isothermal flow of a non-Newtonian fluid is the most complex and important problem in the rubber’s extrusion process. In this way, the aim of this work is to describe the computer modeling of the laminar flow through a nozzle by the finite volume method (FVM). The basis of the general mathematical treatment of flow processes are the balance equations for mass, momentum and energy. The flow can be fully described only when the velocity vector and the thermodynamic data as pressure, density and temperature are known at any time and at any point of the flow. To determine these quantities the conservation equations are combined with the constitutive equations which describe the correlations between parameters relating to motion and kinetics on the one hand and between the individual thermodynamic parameters on the other hand. Extrusion heads for the fabrication of rubber profiles are up to now designed on the basis of empirical knowledge of the non-linear inelastic flow behavior involving the heat transfer. The liquid rubber exhibits a shear rate and temperature-dependent viscosity, with ‘shear thinning’, that is, decreasing viscosity with increasing shear rate and temperature. We have taken the power-law model in order to simulate this rubber’s extrusion process. The mathematical model has the form $\mu \left(t\right)=K\left(T\right)I_2^{\left\{n\right(T)-1\}/2}$ where T, μ, I₂, n and K are termed the temperature, dynamic viscosity, the second invariant of the rate of deformation tensor, the power-law index and the consistency, respectively. These last two parameters were obtained at different temperatures from experimental tests and used in the computational simulation. Finally we have modeled the extrusion process for a type of nozzle, H810, in order to calculate the outlet velocity and temperature distribution of the rubber and conclusions are exposed.