Marangoni convection. Part 1. A cavity with differentially heated sidewalls
Bibliographic record
Abstract
Marangoni convection in a cavity with differentially heated sidewalls has been investigated. The analysis includes the complete effects of interface deformation. The results determined for large Biot and zero Marangoni (zero Prandtl) numbers show that steady convection may exist for Reynolds numbers Re larger than, and for capillary numbers Ca and cavity lengths L smaller than, certain critical values. The main factor limiting the existence of steady convection involves the interface becoming tangential to the hot wall at the contact point (tangency condition). Unsteady analysis shows that the tangency condition defines the limit point for the system; its violation is most likely to lead to the formation of a dry spot at the hot wall. The critical values of Re, Ca, and L are mutually dependent and change with the heating rate (they reach a minimum for instantaneous heating). For a certain range of parameters, multiple (i.e. steady and oscillatory) states are possible. The oscillatory state has a form consisting of the steady mode with a simple harmonic sloshing motion superposed on it. A reduction in the heating rate permits heating of the liquid without triggering the oscillatory state. Transition between the steady and the oscillatory states involves a nonlinear instability process.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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".