Exact Solutions for the Incompressible Viscous Fluid of a Rotating Disk Flow
Bibliographic record
Abstract
The present paper is devoted to a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a disk rotating with a constant angular speed. In place of the traditional von Karman's axisymmetric evolution of the flow, the rotational non-axisymmetric stationary flow is taken into account here. As a consequence, the governing equations allow an exact solution to develop over the disk, which is influenced by a fixed point on the disk and also bounded everywhere in the normal direction to the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions, which differ from those of corresponding to the classical von Karman's flow. Making use of this solution, analytical formulas for the wall shear stresses are extracted. The critical peripheral locations at which extrema of the local skin friction occur are also determined. Analytic calculations show that for the specific flow the thicknesses take the same value. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. According to the Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, which is proportional to product of the thermal conduction, Reynolds number and temperature difference. Key Words: Exact Solution; Rotating-Disk Flow; Shear Stresses; Heat Transfer
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| 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) | 0.002 | 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".