A low‐dimensional description of transient shear‐thinning free‐surface flow in thin cavities, as applied to injection molding
Bibliographic record
Abstract
Abstract A spectral methodology is proposed to examine the influence of shear thinning on the transient free‐surface flow inside a three‐dimensional thin cavity. The problem is closely related to the filling stage during the injection molding process. The moving domain is mapped onto a rectangular domain at each time step of the computation. A modified pressure is introduced that is governed by the Laplace's equation. The flow field is expanded in Fourier series along the lateral direction in the mapped domain, and the Galerkin projection is used to derive the equations that govern the expansion coefficients, which are solved using a variable‐step finite‐difference scheme. This approach is valid for simple and complex cavities as illustrated for the cases of a flat plate with variable and constant thickness. It is shown that, even for highly non‐linear shear‐thinning flow, only a few modes are needed for convergence. Shear thinning generally influences the flow behaviour. However, shear thinning may enhance or prohibit the flow, depending whether the flow rate at the entrance of the cavity is fast or slow, respectively. Copyright © 2004 John Wiley & Sons, Ltd.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".