Laminar Flow in Microchannels With Noncircular Cross Section
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Bibliographic record
Abstract
Analytical solutions are presented for laminar fully developed flow in micro-/minichannels of hyperelliptical and regular polygonal cross sections in the form of compact relationships. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rectangle-with-round-corners, rhombus, star-shape, equilateral triangle, square, pentagon, and hexagon. A point matching technique is used to calculate closed form solutions for the velocity distributions in the above-mentioned channel cross sections. The developed relationships for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including polygonal, rectangular, circular, elliptical, and rhombic cross sections. The present compact solutions provide a convenient and power tool for performing hydrodynamic analyses in a variety of fundamental and engineering applications such as in microfluidics, transport phenomena, and porous media.
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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 | 0.000 |
| 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 it