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One‐dimensional equations governing single‐cavity die design
Author(s) -
Weinstein Steven J.,
Ruschak Kenneth J.
Publication year - 1996
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690420902
Subject(s) - partial differential equation , differential equation , flow (mathematics) , momentum (technical analysis) , integral equation , conservation of mass , conservation law , mathematics , mathematical analysis , physics , mechanics , economics , finance
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).