Determination of Thermal Boundary Conditions Using Piecewise Hermite Polynomials During the Air Transfer Step of an Industrial Quenching Process
Bibliographic record
Abstract
Abstract The study herein presents the identification of the thermal boundary conditions during the air travel step before quenching by immersion under an industrial environment. The experimental characterization was done with quench probes instrumented with multiple in-body thermocouples and tested in situ to account for the uneven cooling during the air transfer. A fast-converging numerical approach using an exhaustive search algorithm was developed to solve the inverse heat transfer problem thus estimating the unknown thermal boundary conditions. The approach reconstructs the surface temperature based on the Hermite polynomials whose control points were determined as per the system movements and the underlying physics. The solver considers near-solution starting values obtained from converting the test data at subsurface locations into mathematical expressions, thereby bounding the solution domain. The proposed methodology minimizes the root mean square error (RMSE), it produces RMSE < 2 °C and peak max/min errors <3.5 °C confirming the accuracy of the procedure. Findings demonstrate the need to consider the heterogeneous conditions even for specimens that qualify for lumped capacitance analysis (Bi < 0.1). The irradiative effects can produce a difference in heat flux magnitude in the range of 10–35% between surfaces. This tendency has appeared for values of the Bi number between 0.05 and 0.08.
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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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".