Cooling a Solid Disc with Uniform Heat Generation Using Inserts of High Thermal Conductivity within the Constructal Design Platform
Bibliographic record
Abstract
In the present study, the problem of cooling a solid disc by way of placing inserts with high thermal conductivity was examined analytically and numerically within the platform of Constructal Theory. The work was accomplished using a fixed amount of a highly conductive material distributed in the form of incomplete inserts from the center (sink). Using Constructal Theory, the magnitudes of the heat resistances in the radial and the branching configurations were calculated analytically. Additionally, to validate the analytical solution, a numerical solution with the Finite Element Method was employed. The one-to-one comparison between the two distinct results reveals a good agreement. In the present case, the length of the inserts was different from the disc radius viz. a new degree of freedom was considered and the solution was remarkably different from the case involving a complete insert. The heat resistance was minimized with respect to the aspect ratio in order to determine the optimal number of inserts as well as the disc radius. It was demonstrated that within in a certain range of parameters, the heat conduction performance of incomplete inserts in the solid disc surpasses the heat conduction performance of standard complete inserts.
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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".