Analysis and Simulation of Heat Transfer in a Superhydrophobic Microchannel
Bibliographic record
Abstract
The transport behavior of a superhydrophobic Hele-Shaw channel subject to arbitrary velocity slip, temperature slip, and constant heat flux boundary conditions is analyzed, resulting in a general expression for the Nusselt number. The results of a scaling analysis and numerical simulation are then presented characterizing the thermal behavior of an idealized pillar-structured superhydrophobic surface in the low pillar concentration limit that treats the trapped gas phase as adiabatic. When thermal behavior is uncoupled from the flow, the temperature slip length is shown to follow the same φs−1/2 dependency on pillar solid fraction as the velocity slip length. Further analysis and simulation including the effects of Marangoni stress, so that the thermal and flow fields are no longer decoupled, yields a further geometric scaling parameter. It is demonstrated that the apparent slip length may be increased against an adverse channel temperature gradient due to the local non-equilibrium of temperature in the vicinity of each pillar.
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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 | 0.001 | 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) | 0.006 | 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".