. (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