Stability analysis of Cu–H<sub>2</sub>O nanofluid over a curved stretching–shrinking sheet: existence of dual solutions
Bibliographic record
Abstract
The effect of mass suction with temperature jump and velocity slip of viscous, unsteady nanofluid flow past a curved shrinking–stretching surface is analyzed in this work. Copper (Cu) and water are considered nanoparticles and base fluids, respectively. The complicated coupled system of differential equations is converted into non-dimensional form with some suitable similarity variables. The solution of the nonlinear problem is produced by use of numerical scheme available in the form of bvp4c package in MATLAB. In the case of shrinking towards the surface, a reverse flow situation is also developed and requires careful selection of solution by examining the stability of the solution. Detailed stability analysis is done and critical values are determined for the possible existence of dual solutions. Variation in parameters is analyzed by plotting graphs and tables. The numerical values are also calculated for the reduced Nusselt number and skin friction due to variation in values of different flow parameters. Results have shown that for the curved shrinking surfaces, one should expect multiple solutions for a set of parameter values such as mass suction, curvature, nanoparticles volume fraction, and unsteadiness.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".