Bounded Pressure-Driven Flow of an Incompressible Electrically Conducting Fluid: Porous Medium and Lubrication Applications
Bibliographic record
Abstract
This work examines the effects of the interaction of a transversal and uniform magnetic field applied to a flow with an electrically conducting and incompressible fluid.This fluid is bounded by two fixed parallel walls in a channel.The bottom wall consists of a porous medium, where the jump of shear stress is given in terms of a suitable relative velocity by a semi-empirical boundary condition proposed by Beavers and Joseph.The formulation of the flow problem is based on the incompressible magnetohydrodynamic governing equations in terms of non-dimensional variables.The relevant physical parameter measuring the relative importance between magnetic and viscous forces is identified as the Hartmann number.The solution of the problem shows the existence of a flow deceleration strongly dependent upon the Hartmann number.In addition, another interesting result is the observed decrease in the magnitude of the longitudinal component of the magnetic flux density as Hartmann number increases.In conclusion, the application of a transverse magnetic field in the flow of an electrically conducting fluid in tiny pores can produce an effective effect like the flow deceleration produced as the porous medium permeability is decreased.Therefore, it seems to be possible to produce such an effect by just monitoring the magnetic field instead of changing the complex microstructure of the porous medium.Finally, the problem of lubrication with an MHD fluid was addressed.Exact solutions were obtained for the velocity and pressure field.Due to the braking effects caused by the Lorentz force, the pressure gradient is reduced and consequently the support force on the bearing is also reduced.Therefore, the MHD effects for this model undermine the lubrication effects of the purely hydrodynamic model.
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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".