Modelling Local Nusselt Numbers for Channels with Flow in Transition
Bibliographic record
Abstract
This work reports a study of heat transfer in turbulent flow entering into small channels, which causes a transition to laminar flow. Heat transfer in channels has been extensively studied, especially the Nusselt-Graetz problem, most commonly constant wall temperature or constant wall heat flux. Early works reported Nusselt values for circular pipes with laminar developed flows, including analytical solutions validated with experiments. Later, developing laminar flows were also studied, presenting correlations for Nusselt-Greatz along the entry region. Most of the engineering flows are turbulent, in such flows, convection increases significantly and laminar flow assumptions are not valid. Although that there are Nusselt numbers reported for the developed turbulent flows, describing the entry region is still a challenge. In literature, flows in circular channels are classified into three main categories: Laminar for Re < 2 300, turbulent for Re > 10 000, and transitional for the Re in between However, some cases, such as monolith type substrates, fit into none of those categories. Monolith based reactors are extensively used in the automotive industry, since they produce lower pressure drop than fixed beds; they are implemented in several other industrial processes as well. It creates a growing interest in its modelling Usually, the flow before a monolith is turbulent (Re ~ 10 4 ), however, its pass from an inlet pipe to channels that are one or two orders of magnitude smaller, decreases the Reynolds number dramatically. Although, there is a strong reduction of the Reynolds, to the order of 10 2 typically, turbulence is still strong in the entry region. In these cases, laminar flow does not apply, also, correlations for turbulent flow are not meant to work at such low Reynolds numbers, neither for decaying turbulence. Clearly the decaying turbulence will affect the mass and heat transfer coefficients in the entry region, which could have a significant impact on the performance of the entire reactor; hence, it must be described accurately.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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 teacher head, 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".