Newtonian Model of Calendering

In Gaskell s treatment, aNewtonian flow was assumed with a very small gap-to-radiusratio, h -C R. This assumption allows us to assume the well known lubrication approximation with only velocity components ux y). In addition, Gaskell s model assumes that a very large bank of melt exists in the feed side of the calender. The continuity equation and momentum balance reduce to 

This equation implies that the pressure gradient vanishes at x = x as well as at x = -x, at which point, as will be shown later, the pressure is at a maximum. 

With the above equations, the velocity distribution between the rolls becomes 

We will calculate the power consumption as well as predict the temperature rise within the material due to viscous heating. In order to compute the power consumption, we need 

Relation between the position of first contact, 2, and the position of sheet separation, 

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