Theoretical analysis of the exiting thickness of sheets in the calendering of FENE-P fluid

• The calendering problem is modeled under lubrication approximation using the constitutive equation of FENE-P fluid.
• The closed form expressions of velocity and pressure gradient are obtained.
• The pressure is found numerically using fourth-order Runge–Kutta scheme.
• The engineering quantities of interest are analyzed over a wide range of Deborah number and extensibility parameter.

A theoretical model is presented to analyze the calendering process wherein, the material to be calendered, is represented by the constitutive equation of a FENE-P fluid. The continuity and momentum equations are used in conjunction with lubrication theory to derive the governing equation of the flow under consideration. Exact expressions for the velocity and pressure gradients are obtained. Numerical integration is performed to compute the pressure for a given dimensionless leave-off distance. The quantities of interest in the mechanical design of calendering system such as, the force separating the two rolls and total power input into both rolls are calculated and shown graphically over a wide range of Deborah number. It is found that rheological features of the material modify the pressure, flow characteristics and all other operating variables significantly. In fact, the present analysis highlights some interesting features of the pressure and other operating variables of the calendering problem which are not reported in the available literature.