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Fuzzy-based bee algorithm for machine learning and pattern recognition of computational data of nanofluid heat transfer

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Abstract

The CFD approach could waste a lot of time, effort, and cost for three-dimensional turbulent flow modeling. In the CFD method, any changes in the grid numbers in a specific region, the whole domain must be meshed and simulated again. More computational expenses are imposed when the mesh density must be increased. This study, for the first time, is aimed to develop a supplementary method using the artificial intelligence algorithm to reduce the post-processing calculations of the CFD approach. Eddy viscosity of alumina–water nanofluid turbulent flow inside a straight pipe is considered for prediction. The finite volume technique is used for solving the governing equations (i.e., mass, momentum, and energy) and the k–ɛ turbulence model of the CFD approach. Algorithms for artificial intelligence have shown promise for data learning and data patterning. In this study, the FVM solutions are learned by the artificial intelligence of the bee algorithm-based fuzzy inference system (BAFIS). The finite volume technique in the CFD modeling is integrated with the BAFIS to predict eddy viscosity in the nanofluid turbulent flow. Besides, the BAFIS performance and application are examined for meshing in the post-processing step of the CFD. In this way, the BAFIS learned the CFD-driven data for the existing nodes. Then the CFD data pattern is captured by the BAFIS. Finally, this CFD pattern is extended to more nodes. For achieving the intelligence, different input numbers (2 and 3), cluster numbers (5, 10, 15, and 20), as the fuzzy C-means clustering parameter, and neighborhood damping radius rates (0.85, 0.90, 0.95, and 0.99), as bee algorithm parameter, are investigated. The intelligence of the BAFIS was achieved for 3 inputs, the cluster number of 20, and the neighborhood damping radius rate of 0.99. The predictions of the eddy viscosity of BAFIS were the same as those of CFD. The BAFIS shows the ability for the accurate prediction of the eddy viscosity (regression number of 0.98). Comparing the time consumption of the methods, for the same number of nodes (i.e., 4,473) and the same computer specifications, the prediction time of the CFD (110 min) was around half of the learning time of BAFIS (52 min). It should be noted that after the data learning, the target variable, eddy viscosity in this study, could be predicted for any number of nodes (i.e., 774,771 nodes) within a negligible time (22 s). So, no significant time was consumed by BAFIS for the mesh increment. The BAFIS results covered the CFD results for additional nodes in the new dense mesh.

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Data availability

All data generated or analyzed during this study are included in this published article.

Abbreviations

C p :

Heat capacity (J/kg K)

d p :

Nanoparticle diameter (m)

k:

Thermal conductivity (W/m K)

k :

Turbulence kinetic energy (m2/s2)

Re:

Reynolds number (\(\frac{\rho VD}{\mu }\))

Pr:

Prandtl number (\(\frac{{\mu C}_{p}}{k}\))

T :

Temperature (K)

V :

Velocity (m/s)

ε :

Dissipation rate of turbulence kinetic energy (m2/s3)

µ :

Dynamic viscosity (kg/m s)

µ t :

Eddy viscosity (kg/m s)

ρ :

Density (kg/m3)

ϕ :

Particle volume fraction

BA:

Bee algorithm

eff:

Effective

FIS:

Fuzzy inference system

f :

Fluid

HTFs:

Heat transfer fluids

P :

Percentage of trained data

p :

Particle

StD:

Standard deviation

FCM:

Fuzzy C-means

ML:

Machine learning

NFs:

Nanofluids

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Author information

Authors and Affiliations

  1. Faculty of Infrastructure Engineering, School of Hydraulic Engineering, Dalian University of Technology, Dalian, 116024, China

    Aliasghar Azma & Yakun Liu

  2. Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran

    Iman Behroyan

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Meisam Babanezhad

  4. Faculty of Electrical–Electronic Engineering, Duy Tan University, Da Nang, 550000, Vietnam

    Meisam Babanezhad

  5. Department of Artificial Intelligence, Shunderman Industrial Strategy Co, Tehran, Iran

    Meisam Babanezhad

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  1. Aliasghar Azma
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  4. Yakun Liu
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Correspondence to Meisam Babanezhad.

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Azma, A., Behroyan, I., Babanezhad, M. et al. Fuzzy-based bee algorithm for machine learning and pattern recognition of computational data of nanofluid heat transfer. Neural Comput & Applic 35, 20087–20101 (2023). https://doi.org/10.1007/s00521-023-08851-z

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  • DOI: https://doi.org/10.1007/s00521-023-08851-z

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