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.

Theoretical investigation of a fluid model in calendering process involving slip at the upper roll surface

“…Stream function may be used to transform Equations (27,32,33,) and boundary conditions (25,26) into stream functions [27][28][29].…”

“…Equation ( 38) having order four we need two extra boundary condition therefore, we can use the definition of volumetric flow rate formula in terms of stream function as follows [28,29,30].…”

“…They investigated how material parameters influenced pressure distribution, pressure gradient, velocity profile, and other mechanical properties. Javed et al [28,29] evaluated the process of calendering using the Giesekus and Carreau fluid models. They carefully explored the influence of viscoelastic parameters on the final sheet thickness, as well as the velocity, pressure profile and mechanical properties.…”

Mathematical simulation of the calendering process for non-Newtonian polymers

“…As equation (26) states that pressure is simply a function of the "x" variable. We differentiate equation (62) with respect to y to eliminate the pressure gradient from equation (62).…”

“…Javed et al 25 studied the calender process numerically using the Giesekus model to compute pressure profile and observe the influence of engineering parameters on detaching sheet spread height. Javed et al 26 used the Carreau-Yasuda model to investigate the flow inside the fluid being calendered. How the Carreau-Yasuda model parameters affect the fluid velocity, pressure, and engineering quantities are discussed in detail.…”