Numerical approach for the calendering process using Carreau-Yasuda fluid model

Abstract

This paper presents a numerical study of the calendering mechanism. The calendered material is represented using the Carreau-Yasuda fluid model. The governing flow equations in the calendering process are made first dimensionless then the lubrication approximation theory (LAT) is used to simplify them. The simplified flow equations are transformed into stream function and then are numerically solved. A numerical method is constructed with Matlab’s built-in-bvp4c routine to find the stream function and pressure gradient. We use the Runge-Kutta algorithm to calculate the pressure and mechanical quantities related to the calendering process. In this analysis the pressure distribution increases with increasing Weissenberg number, however the pressure domain length decreases as the Weissenberg number increases. The pressure inside the nip region decreases from its Newtonian value when the power law index is less than one (shear thinning), and the pressure profile increases from its Newtonian pressure when the power law index is greater than one(shear thickening). How the Carreau-Yasuda fluid model parameters influence the velocity and related calendering process quantities are also discussed via graphs.