An analytical study of the early stages of unsteady free convective flow from a differentially heated rotating sphere at large Grashof numbers
Bibliographic record
Abstract
This research investigates the unsteady free convective flow of a viscous incompressible fluid from a differentially heated rotating sphere. The flow is assumed to remain laminar and to possess equatorial and azimuthal symmetry. The governing Navier-Stokes and energy equations are posed in terms of a scaled stream function -vorticity formulation and are solved subject to no-slip and specified surface temperature conditions. At t = 0 an impulsive heat flux is applied in the form of a jump in surface temperature. An asymptotic solution valid for large Grashof numbers and small times following the impulsive startup is constructed. Two small parameters have been identified and based on this the flow variables are expanded in a double series in powers of these parameters. The non-zero leading-order terms in the asymptotic expansions have been determined analytically and the corresponding heat transfer coefficient has been found. Future work will involve obtaining numerical solutions.
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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 | 0.000 | 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".