Transient pressure driven flow in an annulus partially filled with porous material: Azimuthal pressure gradient
Bibliographic record
Abstract
The transient flow formation due to sudden application of constant circumferential pressure gradient in an annulus partially filled with porous material has been considered. An exact solution of the governing equations has been obtained in Laplace domain using Laplace transform technique. Using suitable transformations, the equations are converted into standard Bessel equations whose solutions are available in the literature. The solutions to the Bessel equations are then inverted to the time domain using Riemann-sum approximation approach. The implicit finite difference scheme has also been employed in solving the governing equations in other to establish the accuracy of the Riemann-sum approximation approach for both transient and steady state solutions. The obtained solutions are then analysed for various dimensionless parameters entering the unified problem. There is a clear indication that large value of Da enhances the permeability of the porous region. Also, thin clear fluid region boosts 1 but has no significant influence on . While thin porous region enhances skin friction at both surfaces.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 | 0.001 |
| 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 source (direct Gemma or distilled Codex), 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".