Natural Convective Heat Transfer From a Narrow Isothermal Vertical Flat Plate With a Uniform Heat Flux at the Surface
Bibliographic record
Abstract
Natural convective flow over a vertical plate with a uniform heat flux over its surface has been numerically studied. When the plate is wide compared to its height the flow can be adequately modeled by assuming two-dimensional flow. However, when the width of the plate is relatively small compared to its height, the heat transfer coefficient can be considerably greater than that predicted by these two-dimensional flow results. The Nusselt number distribution over a narrow vertical plate, with a uniform heat flux at the plate surface, has been numerically determined. This heated plate is embedded in a plane adiabatic surface, the surface of the adiabatic surface being in the same plane as the heated plate. It has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in dimensionless form. The solution has the Rayleigh number, the dimensionless plate width and the Prandtl number as parameters. Results have been numerically determined for a relatively wide range of Rayleigh numbers and dimensionless plate widths for a Prandtl number of 0.7. The dimensionless plate width has been found to have a significant influence on the mean Nusselt number for the plate when the plate is narrow and the Rayleigh number is low. The conditions under which three dimensional flow effects can be neglected have been deduced and an empirical equation for the mean Nusselt number for narrow plates with a uniform surface heat flux has been derived from the numerical results.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.002 | 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 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".