Transient Hyperbolic Heat Conduction in a Functionally Graded Hollow Cylinder
Bibliographic record
Abstract
DOI: 10.2514/1.41368 Hyperbolic heat conduction in a functionally graded hollow cylinder is investigated in this paper. Except for uniform thermal relaxation time, all other material properties of the cylinder are assumed to vary along the radial direction following a power-law form with arbitrary exponents known as the nonhomogeneity indices. When the cylinder is infinitely long, end effects can be ignored, and the one-dimensional heat conduction problem in the radial directionissolvedanalyticallyintheLaplacedomain.The finaltransientsolutionoftheprobleminthetimedomainis obtained by numerical inversion of the Laplace transformed temperature and heat flux. The exact speed of the thermalwave in the nonhomogeneous cylinder isalso obtained.Moreover, the effects of the nonhomogeneity indices and thermal relaxation time on the results are shown graphically by some illustrative examples. The current results are corroborated by the steady-state results for the homogeneous cylinder in the literature.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| 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".