Inertial Flow of Viscoelastic Second-Grade Fluid in a Ciliated Channel under a Magnetic Field and Darcy’s Resistance
Bibliographic record
Abstract
This paper proposes a mathematical analysis of the inertial flow of an MHD second-grade non-Newtonian fluid in a ciliated channel. The two-dimensional flow is modelled under the effect of inertial forces, magnetic field and Darcy’s resistance, which make the system of partial differential equations highly non-linear. To solve the complex system of partial differential equations, the Homotopy Perturbation Method (HPM) is preferred. The HPM solutions for the velocity profile, stream function and pressure gradient are obtained using the software MATHEMATICA. The significances of the Reynolds number (due to inertial forces), Hartmann number (due to magnetic field), porosity parameter (due to Darcy’s resistance) and fluid parameters (related to the second-grade fluid) on the pressure gradient, stream function and velocity profile are discussed in detail. The pertinent parameters show that the horizontal velocity decays in the presence of a magnetic field, whereas it rises under the effect of inertial forces, Darcy’s resistance and fluid viscosity in the centre of the channel. This research indicates that, for the ciliary flow of a second-grade fluid, a favourable pressure gradient (negative pressure gradient) in the horizontal direction increases when applying a magnetic field, whereas it decreases due to the porous medium. This mathematical model can be helpful to observe ciliary activity under magnetic resonance imaging, when ciliary activity is abnormal.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".