Soret effect inducing subcritical and Hopf bifurcations in a shallow enclosure filled with a clear binary fluid or a saturated porous medium: A comparative study
Bibliographic record
Abstract
Soret-driven thermosolutal convection within a shallow porous or fluid layer subject to a vertical gradient of temperature is investigated analytically and numerically. The bridging between a clear fluid and Darcy porous media problems is conducted using the Brinkman–Hazen–Darcy model in its transient form. The analytical solution is derived on the basis of the parallel flow approximation, and validated numerically using a finite difference method by solving the full governing equations. The study is focused on the thermal diffusion effects on the flow intensity, and on the heat and mass transfer rates. In particular, a comparative study is made for the two limiting cases that emerge from the present investigation, namely the low porosity Darcy porous medium and the clear fluid medium. The flow behavior for both cases is qualitatively similar. The critical Rayleigh numbers for the onset of subcritical, oscillatory and stationary convection are determined explicitly as functions of the governing parameters for infinite and finite layers. At the onset of instabilities, the wavenumber is equal to zero and the oscillation frequency vanishes at the onset of Hopf bifurcation. For a finite aspect ratio enclosure, the frequency is finite and decreases as the aspect ratio increases. The codimension-2 point exists and different flow regimes are delineated. For constant heat flux boundaries, only standing oscillatory and steady waves are found to exist. The analytical and numerical results are found to be in good agreement, within the range of the governing parameters considered in the present study. The thermal diffusion effect on the flow intensity and on the heat and mass transfer is more enhanced for Darcy medium compared to the clear fluid, for which the viscous effects are significant.
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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 | 0.000 |
| 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 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".