Thermal-hydraulic performance of flat-plate microchannel with fractal tree-like structure and self-affine rough wall
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Bibliographic record
Abstract
Inspired by the natural bifurcating structures, tree-like microchannels have been applied for microelectronics cooling. In order to understand the thermal-hydraulic performance of a flat-plat tree-like microchannel, successive branching ratios of tree-like structure are optimized based on minimization of flow resistance. It is shown that the optimal successive diameter ratio of symmetrical and dichotomous structures under volume constraint follows Murray’s law, while the optimal successive length ratio under the constraint of fixed channel area follows the power law 2−2/3. A mathematical model of convection in disc-shaped heat sink composed of a tree-like microchannel with self-affine rough surface is developed by the fractal geometry and finite element method. The flat-plate tree-like micro-channel with optimal successive diameter and length ratio shows enhanced thermal-hydraulic performance. The Nusselt number of the flat-plat tree-like micro-channel increases with the inlet Reynolds number and the self-affine fractal dimension of the rough wall. The present optimization method and mathematical model for the flat-plate tree-like microchannel shed light on the design of flat-plate micro-channel heat sinks and flow channel in fuel cell among other potential cooling applications.
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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 it