ENTROPY PRODUCTION FOR DEVELOPING LAMINAR MIXED CONVECTION IN VERTICAL TUBES
Bibliographic record
Abstract
The problem of hydro-dynamically and thermally developing laminar mixed convection in a vertical tube with uniform wall heat flux has been studied numerically. The flow was assumed steady and axis-symmetrical and the fluid incompressible with constant thermo-physical properties except for its density in the gravity forces (Boussinesq's assumption). The system of non-linear, elliptic and coupled governing equations, subjected to appropriate boundary conditions, was successfully solved using the finite-control-volume method, a staggered non-uniform 34 (r) x 40 (φ) x 700 (z) grid and the power-law scheme for computing the heat and momentum fluxes. The modified SIMPLE procedure was used to treat the velocity-pressure coupling. Numerical results obtained for the developing velocity and temperature profiles of water were used to compute the rate of entropy production due to heat transfer and viscous effects. Some significant results showing profiles of these variables for various axial positions and different Grashof numbers are presented and discussed. The entropy profiles in the fully developed region are in excellent agreement with the corresponding analytical results. These results clearly show that the entropy production by both mechanisms is more important near the tube wall. In general, the entropy production due to heat transfer is several orders of magnitude larger than that due to viscous effects. It has also been found that the entropy generation increases considerably with an augmentation of the Grashof number.
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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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| 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".