Heat transfer analysis of Walter’s-B flow over a vertical plate by using fractional operator
Bibliographic record
Abstract
The present study deals with the unsteady Walter’s-B fluid with hybrid fractional derivative namely constant proportional Caputo type with singular kernel. In this paper, we find new analytical solutions of a well-known problem of the fluid dynamics known as Stokes’ first problem. Using dimensional variables governing equations convert into dimensionless form. To solve the model analytically, one uses the Laplace transform approach. Analytical and numerical evaluations of the inverse Laplace transform have been conducted. The influence of several embedded flow properties, including the magnetic parameter, Grashof number, dimensionless time, Prandtl number, Schmidt number, and fractional parameter is analyzed graphically. More specifically, compared to the classical model, the fractional model provides a wider range of integral curves and better represents the flow behavior. The temperature and velocity of the fluid decrease with increasing fractional parameters during short intervals of time, but exhibit the reverse pattern over longer durations. Skin friction, the Sherwood number, and the Nusselt number are numerical quantities linked to engineering that are statistically computed and provided in tabular form.
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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 | 0.001 |
| 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".