Convection of a binary fluid saturating a shallow porous cavity subjected to cross heat fluxes
Bibliographic record
Abstract
In this work, natural convection in a differentially heated binary mixture is studied analytically and numerically. The fluid is subjected to the Soret effect and is contained in a shallow rectangular porous cavity. All four faces are exposed to uniform heat fluxes, opposite faces being heated and cooled, respectively. Analytical solutions for the stream function, temperature and concentration fields are obtained using a parallel flow assumption in the core region of the cavity and an integral form of the energy and constituent equations. Numerical confirmation of the analytical predictions is also obtained. Results are presented first in the presence of a vertical temperature gradient ( a = 0) for which the solution takes the form of a standard Bénard bifurcation. For this situation, steady bifurcations are either pitchfork or subcritical, depending on the separation parameter ϕ and Lewis number Le . The imperfection brought by a horizontal temperature gradient ( a ≠0) to the bifurcation is then investigated. Both the nonlinear analytical model and the numerical solution indicate that, depending on a , ϕ and Le , the onset of motion occurs through subcritical bifurcations. The existence of transcritical bifurcations is also demonstrated. The special case where the buoyancy forces induced by the thermal and solutal forces are opposing and of equal intensity (ϕ =-1) is also discussed. For this particular situation, the supercritical Rayleigh number for the onset of convection is predicted on the basis of a linear stability analysis. Multiple steady states near the threshold of convection are found.
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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 | 0.001 |
| 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".