Optimal Distribution of Heat Sources in Convergent Channels Cooled by Laminar Forced Convection
Bibliographic record
Abstract
The constructal theory is applied to the flow in a convergent channel. The primary goals of this work are to analyze the heat source distribution and generalize the formula concerning such configurations, to study the spacing between consecutive elements, and to verify the analysis by comparing the proposed configuration with numerical simulations. The results show that nonuniform distributions enhance the performance of the system by allowing the heat source element to work near its maximum condition. Furthermore, the optimal distribution occurs when the heat sources are placed closer to each other near the leading edge of the channel. While the literature shows that the spacing between any consecutive element increases as the sources move downstream from the leading edge, the present results proved that such conclusions are restricted, depending on the ratio of outlet to inlet freestream velocity. Accordingly, the spacing has a maximum value when the exit freestream velocity is more than twice that of the inlet. For design issues, the study also addresses the minimum heat required to achieve optimal system performance. The results show that the amount of heat needed by the system to work close to its optimal performance varies exponentially with the convergent angle and increases with the increase in the heating element’s width. The comparison of the present distribution of the heat source elements with a regular one (fixed spacing) is performed numerically to demonstrate the efficiency of the proposed configuration. The results show that the present model forces the system to work more efficiently than the uniform distribution.
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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".