One-dimensional equations governing single-cavity die design

The 1-D approximate equations governing flow in a single-cavity die have been examined in detail. Although the 1-D momentum equation in the slot and mass conservation equation used in previous studies are generally the same, various forms of the 1-D momentum equation governing flow in the cavity have been utilized. A rigorous accounting of the origin of the 1-D cavity equation is given, via asymptotic techniques, integral equations, and the use of approximate velocity fields. Additionally, these techniques are employed to place the slot flow and mass conservation equations utilized in previous studies, on a firmer theoretical ground. The derived cavity equation and differential equation system is found to be identical to that of Leonard (1985).