Double-diffusive and Soret-induced convection in a shallow horizontal porous layer
Bibliographic record
Abstract
This paper reports an analytical and numerical study of the natural convection in a horizontal porous layer filled with a binary fluid. A uniform heat flux is applied to the horizontal walls while the vertical walls are impermeable and adiabatic. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the horizontal walls (double-diffusive convection, $a\,{=}\,0$ ) or by temperature gradients (Soret effects, $a\,{=}\,1$ ). The governing parameters for the problem are the thermal Rayleigh number, $R_T$ , the Lewis number, $Le$ , the solutal Rayleigh number, $R_S$ , the aspect ratio of the cavity, $A$ , the normalized porosity of the porous medium, $\varepsilon$ , and the constant $a$ . The onset of convection in the layer is studied using a linear stability analysis. The thresholds for finite-amplitude, oscillatory and monotonic convection instabilities are determined in terms of the governing parameters. For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained by assuming parallel flow in the core of the cavity. The critical Rayleigh numbers for the onset of supercritical, $R_{\hbox{\scriptsize\it TC}}^{\hbox{\scriptsize\it sup}}$ , or subcritical, $R_{\hbox{\scriptsize\it TC}}^{\hbox{\scriptsize\it sub}}$ , convection are predicted by the present theory. A linear stability analysis of the parallel flow pattern is conducted in order to predict the thresholds for Hopf bifurcation. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical prediction and the numerical simulations.
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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 | 0.000 |
| 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".