.
(12)
When a nonlinear viscosity is adopted for practical problems, line
integrals concerning the r -direction, as shown in Eq. (12), are
performed.
Equations (6)–(11) express the flow velocity, strain rate, and flow
rate, which are determined by the pressure gradient. In a typical 3D
analysis such as 3D FEM, the three components of the flow velocity and
pressure (a total of four variables) are unknown variables to be
determined for an element. However, only pressure is unknown in the
Hele–Shaw formulation mentioned above. Reducing the number of unknown
quantities from four to one contributes to a considerable improvement in
the calculation efficiency (i.e., the calculation time as well as memory
usage).
The steady-state heat transfer for the resin, barrel, and screw is
formulated by the heat conduction equation in the cylindrical
coordinates system. The thermal conductivity, density, and heat capacity
are assumed to be constant. Thermal diffusion along the thickness
direction (r -direction) is considered to be