Flow analysis of a power-law fluid confined in an extrusion die

The one-dimensional equations in cylindrical coordinates governing flow in an arbitrary cross-sectional shape of a cavity and the slot are derived by accounting of the order of magnitude of terms by using scaling arguments and asymptotic techniques. The derived equation is based on an average momentum and mass balance within the cavity. The one-dimensional equations governing flow in a single-cavity die which can be used to predict the geometry of the cavity and the film thickness deviations for given geometry and operating points and thus yield a design strategy for extrusion die optimized for specific applications. The derived one-dimensional governing equations with the exception of coordinates system for extrusion dies are found to be identical to that of Leonard [Polym. Eng. Sci. 25 (9) (1985) 570] and Weinstein and Ruschak [AIChE J. 42 (9) (1996) 2401] who used the shape factor in the different manner and can be reduced to Miller’s [Ind. Eng. Chem. Fundam. 11 (4) (1972) 524] simple model under the certain restrictions.