Non-isothermal Flow of Viscoelastic Elastomer Composites in a Converging Channel

Abstract

Highly filled polymer composites are very widely used in different processes of modern industry, and therefore the investigation of the flow of such media in different channels of processing equipment is being paid a great deal of attention. A mathematical model of the non-isothermal flow of a Newtonian fluid in a converging plane channel is presented. All the important factors that must be taken into account in the development of the model are noted. Many assumptions are made on the basis of the fact that flow occurs at low Reynolds numbers and high Peclet numbers. As the rheological model, the Maxwell higher convective model is used. The solution is sought using series, and all the stress components are expressed in the form of power series expansion. Thermal boundary conditions of the first kind, the temperature dependence of viscosity, and energy dissipation are taken into account. The problem of finding the temperature profiles is solved by an iteration scheme, at each step of which the collocation method is used. The results of calculations are given.