Temperature rise in a verging annular die
Bibliographic record
Abstract
Abstract Plastic pipes, tubes or catheters are extruded by pressure-driven flows through annular dies. Whereas die lands are straight, the section connecting the die land to the extruder either converges or diverges, converging when the product is smaller than the extruder barrel, and diverging when larger. In this paper, we carefully consider the converging or diverging connecting flows, in spherical coordinates, for the most common configuration: the Newtonian pressure-driven flow through the annulus between two coapical coaxial cones. We derive the exact analytical solution for the velocity profile, and then use this to arrive at the exact analytical solution for the temperature rise caused by viscous heating. We care about this rise because it often governs maximum throughput, since pipe makers must protect the melt from thermal degradation. We find that both the velocity profile, and the temperature profile, peak over the same conical surface and this surface is nearer the inner die wall. We also provide analytical expressions for the nonlinear pressure profile and the die cooling requirement. We find that this cooling requirement is always higher on the inner cone.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 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 | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".