Conduction Shape Factor Models for 3-D Enclosures
Bibliographic record
Abstract
Analytical models are presented for conduction shape factors for three-dimensional regions formed between an isothermal, arbitrarily-shaped body and its concentric, arbitrarily-shaped surrounding enclosure. The model is based on the exact solution for the concentric spheres and two methods are developed to predict the effective gap spacing. The models are validated using existing numeri-cal data from the literature and data from simulations per-formed using a commercial CFD software package. The models are shown to be in excellent agreement with the data for all enclosures with geometrically similar bound-ary shape, within 3 % RMS. For enclosures formed be-tween different boundary shapes, the models are shown to be accurate within 5%RMSwhen the minimum aspect ratio, i.e. the smallest outer boundary dimension over the largest inner dimension, is greater than 1.5. Nomenclature abc = cuboid side dimensions, m A = area, m2 d = diameter, m k = thermal conductivity,WmK L = general characteristic length, m m = combination parameter n = outward facing normal vector Q = total heat flow rate,W r = general radial coordinate R = thermal resistance, KW s = cube side length, m S = conduction shape factor, m
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".