Sensitivity of calendered thickness to temperature variations for Newtonian fluids

In this work we treat theoretically the calendering process of Newtonian fluids with finite sheet initial thickness, taking into account that the viscosity of the fluid is a well-defined function of the temperature. We predict that the inclusion of temperature-dependent viscosity influences significantly on the exiting sheet thickness in the calendering process. The mass, momentum and energy balance equations, based on the lubrication theory, were nondimensionalized and solved for the velocity, pressure and temperature fields by using perturbation and numerical techniques, where the exiting sheet thickness represents an eigenvalue of the mathematical problem. When the above variables were obtained, the exiting sheet thickness in the calendering process was determined, considering the influence of the temperature variations in the process. The mentioned governing equations contain basically two dimensionless parameters: the well-known Graetz number, GzGz; and a parameter that takes into account the effect of the variable viscosity as a function of the temperature, ϵϵ, defined as the ratio of the Nahme–Griffith number, NaNa, to the Graetz number, GzGz. Using the limit of ϵ≪1ϵ≪1, the dimensionless exiting sheet thickness of the calendering process has been obtained as a function of the involved dimensionless parameters. The numerical results show that the inclusion of temperature-dependent viscosity effect reduces about 5.89% the dimensionless exiting sheet thickness or 20.1% the leave-off distance in comparison with the case of temperature-independent viscosity.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Calender with a sheet of Newtonian fluid is studied. ► Temperature-dependent viscosity effects were taken into account. ► A semi-analytical solution, based on the lubrication theory, was obtained. ► The exiting sheet thickness decreases due to temperature-dependent viscosity effects.