Bibliographic record
Abstract
Normal stress effects are investigated on tube flow of a single-component non-Newtonian fluid under a constant pressure gradient in a constant temperature field. The generalized hydrodynamic equations are employed, which are consistent with the laws of thermodynamics. In the cylindrical tube flow configuration, the solutions of generalized hydrodynamic equations are exactly solvable and the flow velocity is obtained in a simple one-dimensional integral quadrature. Unlike the case of flow in the absence of normal stresses, the flow develops an anomaly in that the flow in the boundary layer becomes stagnant and the thickness of such a stagnant velocity boundary layer depends on the pressure gradient, the aspect ratio of the radius to the length of the tube, and the pressure (or density and temperature) at the entrance of the tube. The volume flow rate formula through the tube is derived for the flow. It generalizes the Knudsen flow rate formula to the case of a non-Newtonian stress tensor in the presence of normal stress differences. It also reduces to the Navier–Stokes theory formula in the low shear rate limit near equilibrium.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".