Nusselt Number Dependence on Aspect Ratio and Rayleigh Number: A Numerical Study of Rayleigh-Benard Instability
Bibliographic record
Abstract
Abstract In this paper, Rayleigh-Benard Convection (RBC) is investigated in a two-dimensional vertical cavity with the horizontal temperature gradient for Rayleigh numbers (Ra) up to 20000. The velocity and temperature fields along with the Nusselt number (Nu) are examined and discussed for various cases of aspect ratios (AR); 1 ≤ AR ≤ 100, along with examining the critical aspect ratio (ARcr). It is found that in the case of horizontal temperature gradient, convection starts at critical Rayleigh number ≈ 370. It is also observed that the fluid motion is initially restricted to wall proximity, but gradually as Ra increases, convection covers the whole cavity, including the core zone. Our numerical simulations show that as the AR increases beyond 13, for Ra = 6500 instabilities are observed in the cavity. Soon afterwards, secondary cells are formed and tend to decrease in number as Ra increases until the flow becomes fully turbulent. This computational study demonstrates that laminar and transition regimes get contracted with an increasing AR. Profiles of the averaged Nu for different AR are also provided on log Ra-log Nu map. The key finding of this research relates to the dependence of Nu on AR and Ra.
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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) | 0.000 | 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 | 0.001 | 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".