Compact Models for Transient Conduction or Viscous Transport in Non-Circular Geometries With a Uniform Source
Bibliographic record
Abstract
Transient heat conduction in solid prismatic bars of constant cross-sectional area having uniform heat generation and unsteady momentum transport in infinitely long ducts of arbitrary but constant cross-sectional area are examined. In both cases the solutions are mathematically modeled using a transient Poisson equation. By means of scaling analysis a general asymptotic model is developed for an arbitrary non-circular cross-section. Further, by means of a novel characteristic length scale, the solutions for a number of fundamental shapes are shown to be weak functions of geometry. The proposed models can be used to predict the dimensionless mean flux at the wall and the area averaged temperature or velocity for the tube, annulus, channel and rectangle for which exact series solutions exist. Due to the asymptotic nature of the proposed models, it is shown that they are also applicable to other shapes at short and long times for which no solutions or data exist. The root mean square (RMS) error based on comparisons with exact results is between 2.2–7.6 percent for all data considered.
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 | 0.000 |
| 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".