Analytical Simulation of Natural Convection Between Two Concentric Horizontal Circular Cylinders: A Hybrid Fourier Transform-Homotopy Perturbation Approach
Bibliographic record
Abstract
In this study, a hybrid method combining the homotopy perturbation method (HPM) and Fourier transform (FT) is developed and denoted as FT-HPM.This novel algorithm leverages the properties of convolution theory to facilitate calculations and is applied to obtain approximate analytical solutions for the two-dimensional natural convection between two concentric horizontal circular cylinders maintained at various uniform temperatures.The effects of Rayleigh number, Prandtl number, and radius variation on the fluid flow (air) and heat transfer are investigated.Furthermore, velocity distributions are examined and discussed, while the Nusselt number is calculated to represent local and general heat transfer rates through the relevant Nusselt numbers.The convergence of the FT-HPM method is discussed theoretically, with the formulation of theorems that are applied to the results of the obtained solutions.Tables and graphs of the analytical solutions demonstrate the feasibility and potential usefulness of the proposed algorithm for addressing various nonlinear problems, particularly natural convection problems.This research contributes to the understanding of natural convection in complex geometries and provides a foundation for future studies in this field.
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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".