Numerical modelling of hyperbolic phase change problems: Application to continuous casting
Bibliographic record
Abstract
Heat diffusion processes are generally modeled based on Fourier’s law to estimate how the temperature propagates inside a body. This type of modeling leads to a parabolic partial differential equation, which predicts an infinite thermal wave speed of propagation. However, experimental evidence shows that diffusive processes occur with a finite velocity of thermal propagation in many applications. In this paper, we develop a mathematical formulation to predict the finite speed of heat propagation in multidimensional phase change problems. The model generalizes the enthalpy formulation by adding a hyperbolic term. The governing equations are simulated by the finite element method. The proposed model is first verified by comparing numerical and experimental results illustrating the difference between the infinite and finite propagation velocity for heat inside biological tissues. Then, the results of the two and three-dimensional numerical solution of the continuous steel casting process are presented. We will illustrate that the effects of the initial conditions vanish faster when using the parabolic equation, while they persist in the hyperbolic modeling approach. The results demonstrate significant differences in the initial thermal dynamics and at the solid-liquid interface position when adding the hyperbolic term. The changes are more noticeable in the regions of the steel beam where rapid heat loss and, consequently, faster phase change occur.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| 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".