Multi-objective Optimization of Staggered Tube Banks in Cross-flow Using Machine Learning and Genetic Algorithm
Bibliographic record
Abstract
This paper presents the numerical multi-objective optimization of staggered tube banks in cross-flow using neural networks and genetic algorithm. The objective is to determine the optimal dimensionless transverse and longitudinal pitches that establish a proper compromise between heat transfer enhancement and pressure drop minimization across a wide range of inlet Reynolds numbers (1,000–50,000). Tube banks simulations are performed for randomly selected pairs of design points to generate data on Nusselt number and friction factor. This dataset is used to train neural networks, which predict heat transfer and pressure drop characteristics as functions of dimensionless pitches. Appropriate objective functions are defined using trained neural networks and integrated into Genetic Algorithm to efficiently identify Pareto-optimal solutions. Results indicate that Reynolds number has a negligible effect on the Pareto front, as the optimal trade-offs between heat transfer and pressure drop remain consistent across different flow regimes. The best point on the Pareto front, defined as the solution with the minimum distance to the utopia point, exhibits dimensionless longitudinal and transverse pitches of approximately 0.90 and 1.30, respectively, regardless of the Reynolds number. Additionally, the study confirms that compact tube banks with dimensionless longitudinal pitches smaller than 1.0, often excluded in experimental and numerical studies, can be successfully simulated and optimized using the proposed framework. The findings provide practical guidelines for designing high-efficiency staggered tube banks and demonstrate a computationally efficient approach to optimize heat exchanger configurations without relying on empirical correlations.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| 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".