Natural Convection of a Binary Fluid in a Slightly Inclined Shallow Cavity
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Bibliographic record
Abstract
ABSTRACT This article reports an analytical and numerical study of the natural convection in an inclined shallow cavity filled with a binary fluid. Newmann boundary conditions for temperature are applied to the long side walls of the enclosure, while the two short ones are assumed to be impermeable and insulated. The solutal buoyancy force are induced either by the imposition of constant fluxes of solute on the 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,RaT, the Lewis number Le, the buoyancy ratio ϕ, the inclination of the cavity Θ, the Prandtl numberPr, the aspect ratio of the cavity A, and the constant a. For convection in an infinite layer (A > > 1), an analytical solution of the steady form of the governing equations is obtained on the basis of the parallel flow approximation. The critical Rayleigh numbers for the onset of supercritical and subcritical convection are predicted by the present model. Also, it is demonstrated that, for small enough inclinations around the horizontal plane, multiple steady states exist, some of which are unstable. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. Good agreement is observed between the analytical prediction and the numerical simulations.
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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 | 0.001 |
| 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)
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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 it