Convective heat transfer in non-uniformly heated corrugated slots
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Bibliographic record
Abstract
An analysis of heat transfer in non-uniformly heated corrugated slots has been carried out. A sinusoidal corrugation is placed at the lower plate that is exposed to heating consisting of uniform and sinusoidal components, while the upper smooth plate is kept isothermal. The phase difference ΩTL describes the shift between the heating and geometric non-uniformities. The analysis is limited to heating conditions that do not give rise to secondary motions. Depending on ΩTL, the conductive heat flow is directed either upwards, or downwards, or is eliminated. Its magnitude is smallest for the long-wavelength systems and largest for the short-wavelength systems, and it increases proportionally to the corrugation amplitude and heating intensity. The same heating creates horizontal temperature gradients that give rise to convection whose form depends on ΩTL. Convection consists of counter-rotating rolls with the size dictated by the system wavelength when the hot spots (points of maximum temperature) overlap either with the corrugation tips or with the corrugation bottoms. Thermal drift forms for all other values of ΩTL. The convective heat flow is always directed upwards, and it is the largest in systems with wavelengths comparable to the slot height. The magnitude of the overall heat flow increases proportionally to the heating intensity when conductive effects dominate and proportionally to the second power of the heating intensity when convection dominates. It also increases proportionally to the corrugation amplitude. The system characteristics are dictated by convection when the relative position of the heating and corrugation patterns eliminates conduction. Addition of the uniform heating component amplifies the above processes, while uniform cooling reduces them. The processes described above are qualitatively similar for all Prandtl numbers of practical interest with the magnitude of the convective heat flow increasing with Pr.
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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 | 0.000 |
| 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 it