Laminar Free Convection from a Pair of Horizontal Cylinders: A Three-Temperature Problem
Bibliographic record
Abstract
The formulation of multi-temperature convection problems in terms of a single driving temperature difference and a single heat transfer coefficient does not properly reflect the physics of the problem. Paired heat transfer coefficients, which designate both the source and the sink of heat transfer, are a suitable alternative. A numerical technique, namely dQdT, is proposed to compute such paired heat transfer coefficients. The dQdT technique entails a numerical solution of the governing equations and consequent solutions of the energy equation with perturbed boundary conditions. In the present study, dQdT is applied to the three-temperature problem of steady-state laminar free convection from two horizontal cylinders, with equal diameters but different surface temperatures, aligned vertically at a center-to-center spacing of two diameters. A number of moderate Rayleigh numbers, 2×104<Ra<2×105, are considered. The baseline solutions are validated against experimental data from the literature. A grid convergence study is performed to assess the discretization error. The utility of dQdT in characterizing this three-temperature free convection problem, specifically in quantifying the interaction of the cylinders, is demonstrated. It has also been shown that the paired heat transfer coefficients obtained through dQdT provide detailed information about the local interaction of the cylinders, which are not available otherwise.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| 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".