Unsteady Internal Forced-Convective Flow Under Dynamic Time-Dependent Boundary Temperature
Bibliographic record
Abstract
A new all-time analytical model is developed to predict transient internal forced-convection heat transfer under arbitrary time-dependent wall temperature. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step wall temperature is generalized for arbitrary time variations in surface temperature using Duhamel’s theorem. A harmonic boundary temperature is considered, and new compact closed-form relationships are proposed to predic: 1) fluid temperature distribution; 2) fluid bulk temperature; 3) wall heat flux; and 4) the Nusselt number. An optimum value is found for the dimensionless angular frequency of the wall temperature to maximize the heat transfer rate of the studied unsteady forced-convective process. Such dimensionless parameter depends upon the imposed-temperature angular frequency, fluid thermophysical properties, and tube geometrical parameters. A general surface temperature is considered, and the temperature field inside the medium is obtained using a superposition technique. An independent numerical simulation is performed using ANSYS® Fluent. The comparison between the obtained numerical data and the present analytical model shows good agreement: a maximum relative difference less than 4.9%.
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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 | 0.001 |
| 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".