Analytical Modeling of Outward Solidification With Convective Boundary in Cylindrical Coordinates
Bibliographic record
Abstract
Abstract Solidification consists of three stages at macroscale: subcooling, freezing and cooling. Classical two-phase Stefan problems describe freezing (or melting) phenomenon initially not at the fusion temperature. Since these problems only define subcooling and freezing stages, an extension to characterize the cooling stage is required to complete solidification. However, the moving boundary in solid-liquid interface is highly nonlinear, and thus exact solution is restricted to certain domains and boundary conditions. It is therefore vital to develop approximate analytical solutions based on physically tangible assumptions, like a small Stefan number. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder. By assuming a small Stefan number, three temporal regimes and four spatial layers are considered in the asymptotic analysis. The results are compared with numerical method. Further, effects of Biot numbers are also investigated regarding interface motion and temperature profile.
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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".