A Numerical Study of Unsteady Natural Convection from Two-Sided Thin Horizontal Isothermal Plates
Bibliographic record
Abstract
Unsteady natural convective heat transfer following sudden heating of two-sided, thin isothermal horizontal plates with complex shapes has been numerically studied.The plates were isothermal and exposed to air at ambient conditions.Three different plate shapes were considered.Variations of the heat transfer rates, expressed in terms of the Nusselt number with dimensionless time for various Rayleigh numbers were first obtained with the square root of the plates' surface area being used as the length scale.Then, the heat transfer rates for steady state were obtained with the same length scale being used.The transient heat transfer rate results showed that depending on the value of the Rayleigh number, the Nusselt number either gradually decreased to a steady state value or first decreased to a minimum and then increased to the steady state value.Similar Nusselt number variation with time were obtained for all plate shapes considered.Now, in studies of steady state natural convective heat transfer rates from horizontal plates with different shapes, it has been found that if 4*Area/Perimeter is used as the length scale in presenting the results, the variation of Nusselt number with Rayleigh number were essentially the same for all shapes considered.Therefore, the unsteady state results obtained in the present study were re-expressed using 4*Area/Perimeter as the length scale and it was found that the variations of Nusselt number with dimensionless time for various Rayleigh numbers for the plate shapes considered, were much closer to each other when 4*area/perimeter was used as the length scale than when the square root of the plate area was used as the length scale.
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How this classification was reachedexpand
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 | 0.000 |
| 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 teacher head, 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".