Exact solutions for <i>n</i>-layer concentric flow of PTT fluids through a cylindrical pipe
Bibliographic record
Abstract
Flows of multiple layers of fluids are encountered in many industrial and manufacturing processes. This paper investigates the concentric n-layer flow for Phan–Thien–Tanner (PTT) fluids through a cylindrical pipe. Finitely many immiscible non-Newtonian fluids are considered to be flowing concentrically in a tube. The flow is modelled using the exponential PTT fluid model and exact solutions for velocity fields and volume flow rates are computed. It has been shown that the corresponding results for linear PTT fluid model as well as Newtonian fluids can be deduced from the obtained expressions, and that they match with the present literature. It has also been observed that for such layered flow, the non-Newtonian parameters significantly affect the flow of fluids in adjacent layers. The effects of involved parameters on the velocity profiles are also shown graphically. We show that a unique velocity maximum exists along the axis of the pipe. Moreover, it is observed with the help of an example that layer thickness can be adjusted to obtain maximal flow rate with a given pressure gradient.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".