Transient pressure driven flow in an annulus partially filled with porous material: Azimuthal pressure gradient
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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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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.
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