Extrusion Introduction An extruder is a common machine in industry ...

Figure 6. Standard cylindrical coordinate
Governing Equations
Under the assumptions ((a)~(d)), the governing equations, continuity equation and the r-
and z-directional momentum equation, for the flow in the draw-down region are as
follows:
1
r r ru
p
r
p
z
( ) + w
z = 0 (1)
1
2
u
ru
(2)
r
r r
1
r
2
z
2
w w
r
r r 2
z
(3)
As indicated in Figure 5, u and w are the r- and z-directional component of the velocity
vector u. R o (z) and R i (z) are the position of the outer and the inner surface of the tube
that should be also determined as the solution along with u, w and p for this free surface
problem.
The boundary conditions at the two free surfaces are follows,
At r = R o (z),
u
R o
z
w
0
(4)