Onset of thermal convection of a weakly rarefied Maxwellian gas: A continuum-slip approach
Bibliographic record
Abstract
The onset of the Rayleigh–Bénard convection for a monatomic rarefied gas of Maxwellian type is investigated at small Knudsen numbers. Density variations due to compressibility have been considered without any restriction imposed on the magnitude of temperature difference. The steady-state conduction problem has been solved both analytically and numerically using a continuum approach with velocity-slip and temperature-jump conditions at the solid boundaries. The influence of the Froude number and the Knudsen number is comprehensively studied. To examine the onset of thermal convection, a linear temporal stability analysis is performed for the conduction state and the dispersion relation is calculated by a Chebyshev collocation method. The neutral stability curve obtained in the Froude–Knudsen number plane marks transition to convection from a pure conduction state. The critical wave number for the onset of convection is found to be close to 3.14, agreeing well with the existing findings. The convection only occurs for Knudsen numbers smaller than 0.027. A comparison between the Maxwellian model and the hard-sphere model is given and discussed. The encouraging results suggest the use of more realistic gas models in future studies.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| 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".