Numerical nonlinear analysis of subcritical Rayleigh-Bénard convection in a horizontal confined enclosure filled with non-Newtonian fluids
Bibliographic record
Abstract
Non-Newtonian subcritical convection in a Rayleigh-Bénard configuration was investigated numerically, using rigid boundary conditions. The flow configuration consisted of a finite aspect ratio enclosure subject to a vertical temperature gradient, which was established by heating and cooling the lower and the upper walls by either a constant heat flux or by applying constant temperatures. The non-Newtonian fluid viscosity was modeled using the Carreau-Yasuda model. The convective flow was governed by the conservation equations, which were solved numerically using a finite difference method with a time-accurate scheme. For a shallow enclosure, when the walls were subject to constant heat fluxes, an asymptotic solution was derived assuming a parallel flow behavior. A comparison between the numerical and asymptotic solutions was performed. The effects of the controlling parameters, namely, the Rayleigh and the Prandtl numbers, and the fluid rheological parameters on the onset of subcritical convective flow were investigated. The threshold for the onset of subcritical convection was found to be well below the threshold of stationary convection and decreased considerably (with the fluid rheological parameters variation) as the fluid became more and more shear thinning. Depending on the governing parameters, steady and unsteady-periodic flow solutions were possible. Within a square enclosure with slip or no-slip vertical walls, maintaining the active walls at a constant heat flux or at constant temperature, the rheological subcritical flow behavior remained qualitatively the same, but led to different subcritical convection thresholds.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 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".