Conduction Shape Factor Models for Hollow Cylinders with Nonuniform Gap Spacing
Bibliographic record
Abstract
Ananalytical conduction shape factormodel is developed for the two-dimensional annular region formed between concentric isothermal cylinders in which the inner and outer boundaries have similar or different shapes. Themodel is based on the equivalent circular annulus with amodified independent parameter to account for local variations in the gap thickness. Validation of the model is performed using existing numerical data and analytical expressions from the literature for various geometries, includingpolygonal and rectangular cylinderswith a circular hole and the circular cylinder with a polygonal hole. The root-mean-square difference between the data and themodel is less than 5 % in all cases. Nomenclature A = cross-sectional area, m2 A? = dimensionless gap thickness, Ap =Pi A0 = modified dimensionless gap thickness d = diameter, m L = general characteristic length, m N = number of polygon sides n = combination parameter P = perimeter, m r = radius, m s = side length, m S = conduction shape factor (per unit length) S?L = dimensionless shape factor, SL=Pi = apothem, minimum radial dimension of a polygon, m = gap spacing, m Subscripts e = effective i = inner body o = outer body
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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) | 0.001 | 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 | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".