Analytical Modeling of Natural Convection in Concentric Spherical Enclosures
Bibliographic record
Abstract
A modeling procedure is developed for natural convec-tion heat transfer from an isothermal heated sphere lo-cated at the center of an isothermal, cooled, spherical-shaped enclosure. The model is based on the linear superposition of conduction and convection solutions, where the convective component is determined based on a combination of two limiting cases, laminar boundary layer convection and transition flow convection. The model is validated using experimental and numerical data from the literature, including data from an experi-mental test program performed by the authors in a pre-vious publication for four different enclosure configu-rations, 15 dodi 48, over the range of Rayleigh number 10 RaAi 1 10 7. The model accurately predicts the experimental data with an RMS difference of 2- 4 % and is in good agreement with the other data from the literature. Nomenclature A = area; m2 C = coefficient Ccs = Raithby and Hollands16 coefficient d = diameter; m FPr = Prandtl number function g = gravitational acceleration; ms2 GL = body gravity function k = thermal conductivity; WmK ke = effective thermal conductivity, kNuLSL; WmK L = general characteristic length; m
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| 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".