Analytical Modeling of Fluid Flow and Heat Transfer in Micro/Nano-Channel Heat Sinks
Bibliographic record
Abstract
Laminar forced convection in two-dimensional rectangular micro and nano-channels under hydrodynamically and thermally fully developed conditions is investigated analytically in the slip flow regime (0.001 < Kn < 0.1). Closed form solutions for fluid friction and Nusselt numbers are obtained by solving the continuum momentum and energy equations with the first-order velocity slip and temperature jump boundary conditions at the channel walls. Isoflux thermal boundary condition is applied on the heat sink base. Results of the present analysis are presented in terms of channel aspect ratio, hydraulic diameter, momentum and thermal accommodation coefficients, Knudsen number, slip velocity, Reynolds number and Prandtl number. It is found that fluid friction decreases and heat transfer increases, compared to no-slip flow conditions, depending on aspect ratios and Knudsen numbers that include effects of the channel size or rarefaction and the fluid/wall interaction.
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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".