The steady-state Hele–Shaw flow in the annulus in cylindrical coordinates is shown in Figure 1. The following arguments are assumed. The fluid is incompressible. The velocity of r -direction is zero; .
and
depends only on r . vθ andvz are the velocities of θ and thez -direction. The molten polymer acts as a non-Newtonian pure viscous fluid. The Hele–Shaw flow between the barrel and the screw in the (r , θ , z ) cylindrical coordinate system is formulated according to the assumptions mentioned above.
The equation of continuity is