An Improved Quasi-Steady Analysis for Solving Freezing Problems in a Plate, a Cylinder and a Sphere
Bibliographic record
Abstract
Abstract Freezing processes taking place in a plate, a cylinder and a sphere are investigated by using the improved quasi-steady analysis model developed in the present study. In the improved quasi-steady analysis, an additional term is added to the temperature profile to simulate the transient effect on the temperature distribution in the solid phase. This additional term is based on the ratio of the heat flux at the phase boundary to that at the cooling surface, and physically, presents the thermal capacity effect in the frozen region. The maximum relative error of the moving phase front location obtained from the improved quasi-steady analysis is about 3% in comparison with that obtained from the exact solution of the freezing process in a plate. Since there is no exact solution available for the freezing process taking place in a cylinder or a sphere, the results obtained from the improved quasi-steady analysis are compared with results from references. The maximum relative errors of the improved quasi-steady analysis for the cylindrical and spherical cases are less than 4% while the maximum relative errors of the quasi-steady approximation are higher than 42%. It is evident that the improved quasi-steady analysis developed in the present study maintains the simplicity of the quasi-steady approximation while greatly increasing its accuracy.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".