A numerical study of the calendering process is presented. The material to be calendered is modeled by using Giesekus constitutive equation. The flow equations are first presented in dimensionless forms and then simplified by incorporating the lubrication approximation theory. The resulting equations are analytically solved for the stream function. The pressure gradient, pressure, and other engineering parameters related to the calendering process, such as roll-separating force, power function, and entering sheet thickness, are numerically calculated by using Runge–Kutta algorithm. The influence of the Giesekus parameter and the Deborah number on the velocity profile, pressure gradient, pressure, power function, roll-separating force, and exiting sheet thickness are discussed in detail with the help of various graphs. The present analysis indicates that the pressure in the nip region decreases with increasing Giesekus parameter and Deborah number. The power function and the roll-separating force exhibit decreasing trends with increasing Deborah number. The exiting sheet thickness decreases up to a certain entering sheet thickness, as compared to the Newtonian case. Beyond this entering sheet thickness, the exiting sheet thickness increases with increasing entering sheet thickness.
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.
In this article, calendering analysis is presented using Johnson‐Segalman fluid model along with nonlinear slip condition introduced at the upper roll surface. The flow equations for the problem are developed and converted into dimensionless form with the help of dimensionless variables and then finally simplified by a well‐known lubrication approximation theory (LAT). To eliminate the pressure gradient from the governed equations, stream function is introduced. The final equations are solved numerically using Matlab built‐in procedure “bvp4c” to get the stream function and pressure gradient. The pressure and engineering quantities such as power input function and roll‐separating force are calculated by Runge‐Kutta fourth order method. The impact of the Johnson‐Segalman parameter and slip parameter on pressure, velocity and engineering quantities are presented with the help of various graphs. The Newtonian model predicts higher pressure in the nip zone than the Johnson‐Segalman fluid model, according to our findings. In the presence of the slip parameter, the force and power functions exhibit 37% and 61.71% decreases from Newtonian values, respectively. As the slip parameter is increased, the pressure distribution diminishes.
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