Instability of gravity-driven flow of a heated power-law fluid with temperature dependent consistency
Bibliographic record
Abstract
In this paper we report on our investigation of the instability of a liquid layer flowing along a heated inclined plane. We develop and implement a theoretical model with a power-law constitutive relation which captures the temperature variation in the rheology of the fluid. We carry out a linear stability analysis and obtain Orr-Sommerfeld type equations for the evolution of infinitesimal perturbations imposed on the equilibrium flow. Numerical solutions were obtained, as well as asymptotic approximations based on the assumption of perturbations of long wavelength and small variation in the consistency of the fluid with respect to temperature. We investigate the critical conditions for the onset of instability and determine the effect of a non-Newtonian rheology and the dependence of the fluid properties on temperature. Nonlinear effects were considered by employing a reduced dimensionality model. Calculations of permanent waves arising from unstable uniform flows were made by carrying out numerical simulations of these equations.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 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".