Steady State Heat Transport by Microbubble Dispersions Mediating Convection With Phase Change Dynamics
Bibliographic record
Abstract
A new theory for additional heat transfer convected by a dispersed phase of microbubbles was posited recently. An additional convection term in the heat transport equation reflects the latent heat of vapor of the liquid carried by the microbubbles from hot zones that vaporize more liquid to cold zones where condensation releases the latent heat. This theory was shown to be consistent with analysis of observations of freezing times measured by in the original Mpemba effect study, by inferring heat transfer coefficients fitted by Newton’s law of cooling. In this paper, the scaling analysis, leading to the proposition that the additional heat flux is proportional to the phase fraction of microbubbles, is tested by steady state solutions of the canonical hot wall / cold wall buoyant convection problem. For phase fractions 0.02 and 0.1, the maximum ratio of additional Nusselt number emergent is five, occurring in the microfluidic regime. Increasing the characteristic length of the domain maintains the monotonicity of the increase in additional Nusselt number ratio over the case of no microbubbles present. The additional heat transfer due to the microbubble dispersion, ranging from 5-50%, is found to be nearly proportional to the microbubble phase fraction for the range of 0.02 to 0.2. However, larger characteristic lengths introduce insufficient heat flux from the hot wall to maintain a “driven cavity” flow structure, so that the steady state structure that emerges is a stable stratification with thin boundary layers near the hot and cold walls, with weak shear flow convection. The stable stratification resultant at higher characteristic lengths suppresses the additional heat flux due to microbubble mediation, but only moderately deviating from proportionality.
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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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".