An extended macroscopic transport model for rarefied gas flows in long capillaries with circular cross section
Bibliographic record
Abstract
Pressure-driven and thermally driven rarefied gas flows in long capillaries with circular cross sections are investigated. For both Poiseuille and thermal transpiration flows, a unified theoretical approach is presented based on the linear form of regularized 13-moment (R13) equations. The captured nonequilibrium effects in the processes are compared to available kinetic solutions, and the shortcomings of classical hydrodynamics, i.e., the Navier–Stokes–Fourier equations, are highlighted. Breakdown of Onsager’s symmetry is proposed as a criterion to determine the range of applicability of extended macroscopic models. Based on Onsager’s reciprocity relation it is shown that linearized R13 equations provide agreement with kinetic data for moderate Knudsen numbers, Kn≤0.25. Two-way flow pattern and thermomolecular pressure difference in simultaneous pressure-driven and temperature-driven flows are analyzed. Moreover, second-order boundary conditions for velocity slip and temperature jump are derived for the Navier–Stokes–Fourier system. The proposed boundary conditions effectively improve classical hydrodynamics in the transition flow regime.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 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".