Bibliographic record
Abstract
Axial flows in generalized ducts are studied for viscoelastic materials including a linear low-density polyethylene (LLDPE) melt. Viscoelasticity is described by an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times, which fits well experimental data for the shear and elongational viscosities and the normal stresses as measured in shear flow. The K-BKZ model can be reduced to the Newtonian and Maxwell models with appropriate choice of the parameters. A new technique is developed where the Finger and Cauchy-Green tensors are simplified for axial flows, since particle tracking is only required in the flow z-direction (not required in the x-y coordinate plane). Numerical solutions are presented in two-dimensional cross-sectional geometries, namely square, concave square, and eccentric annulus, for different flow rate and pressure drop changes. For the Maxwell model, the dimensionless pressure drop is independent of the Weissenberg number and a function only of the geometry. For the K-BKZ model representing the LLDPE melt, the dimensionless pressure drop is reduced with increasing flow rate, hence Weissenberg number. The present results are offered as benchmark solutions for the imposition of entry velocity and stress profiles in three-dimensional ducts, when secondary flows are not present.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".