Variable Viscosity Effects on Calendering Viscoplastic Fluids

Abstract

Non-isothermal flow of a variable viscosity non-Newtonian fluid between a pair of counter-rotating cylinders with equal speed and equal size rolls is analyzed to study theoretically the effect of viscous dissipation on the exiting sheet thickness for the power law plastic fluid model. A regular perturbation method based on the lubrication approximation theory is used to uncouple the momentum and the energy equations to provide numerical results of the effects of temperature profiles on the final sheet thickness. The heat transfer analysis of Calendering Non-Newtonian fluids is an important area on polymer processing. Here, we are interested in studying the heat transfer phenomena on calendering Non-Newtonian process using the power law model. This model, takes into account the effects of temperature on the consistency index, also the viscous dissipation. In this study the important parameters are the Nahme-Griffith number as a perturbation parameter, this one relates the temperature gradient generated by viscous dissipation to the temperature gradient necessary to modify the viscosity. In general form, the pressure distribution is determined from the momentum equation, and then we can calculate the velocity profile, finally the energy equation is solved to estimate the influence of variable viscosity and viscous dissipation on the final sheet thickness. The order of magnitude for the Graetz and Nahme-Griffith numbers were 10^(1) and 10^(-3), respectively. Finally the influence of power law index n and the flow rate on pressure and temperature are obtained.