Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning
The current research offers credible mathematical models solely for estimating mono-nanofluids' density (ρnf), which can be useful for thermal engineering calculations required by various industries and applications. Accordingly, a comprehensive data bank encompassing 4004 experimental data-poi...
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Elsevier
2025-06-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379725001421 |
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| author | Omid Deymi Fahimeh Hadavimoghaddam Saeid Atashrouz Saptarshi Kar Ali Abedi Ahmad Mohaddespour Mehdi Ostadhassan Abdolhossein Hemmati-Sarapardeh |
| author_facet | Omid Deymi Fahimeh Hadavimoghaddam Saeid Atashrouz Saptarshi Kar Ali Abedi Ahmad Mohaddespour Mehdi Ostadhassan Abdolhossein Hemmati-Sarapardeh |
| author_sort | Omid Deymi |
| collection | DOAJ |
| description | The current research offers credible mathematical models solely for estimating mono-nanofluids' density (ρnf), which can be useful for thermal engineering calculations required by various industries and applications. Accordingly, a comprehensive data bank encompassing 4004 experimental data-points was utilized to execute two rigorous machine-learning techniques: Group Method of Data Handling (GMDH) and Gene Expression Programming (GEP). Subsequently, two high-accuracy correlations were fine-tuned based on the four independent variables: average nanoparticle diameter (dnp), nanoparticle mass concentration (ϕm), nanoparticle density (ρnp), and base-fluid density (ρbf). Two variables pressure (P) and temperature (T), with rather minor impacts on the density of the mono-nanofluids under investigation, were excluded in the final correlations as a result of the modeling process and the intelligent operation of the machine-learning techniques. By performing multiple statistical and graphical analyses, comparative evaluations highlighted the superior performance and outstanding accuracy of the GEP-based correlation (with AAPRE=0.6614% and R2=0.9671). Moreover, sensitivity analysis and parametric trend assessments revealed that ϕm and ρbf were the most crucial variables affecting ρnf values, with relevancy factors of approximately 0.72 and 0.71, respectively. By considering the GEP-based correlation's outputs and applying the leverage statistical approach, a considerable portion (96.33%) of the total data-points was identified as valid data. |
| format | Article |
| id | doaj-art-dc8f145ece1c40c39b419ac5313cabfd |
| institution | OA Journals |
| issn | 2211-3797 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj-art-dc8f145ece1c40c39b419ac5313cabfd2025-08-20T02:28:11ZengElsevierResults in Physics2211-37972025-06-017310824810.1016/j.rinp.2025.108248Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learningOmid Deymi0Fahimeh Hadavimoghaddam1Saeid Atashrouz2Saptarshi Kar3Ali Abedi4Ahmad Mohaddespour5Mehdi Ostadhassan6Abdolhossein Hemmati-Sarapardeh7Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, IranInstitute of Unconventional Oil & Gas, Northeast Petroleum University, Heilongjiang, Daqing 163318, PR China; Ufa State Petroleum Technological University, Ufa 450064, RussiaDepartment of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran; Corresponding authors.College of Engineering and Technology, American University of the Middle East, KuwaitCollege of Engineering and Technology, American University of the Middle East, KuwaitDepartment of Chemical Engineering, McGill University, Montreal, QC H3A 0C5, CanadaState Key Laboratory of Continental Shale Oil, Northeast Petroleum University, Daqing, 163318, China; Institute of Geosciences, Marine and Land Geomechanics and Geotectonics, Christian-Albrechts-Universität, Kiel 24118, Germany; Corresponding authors.Department of Petroleum Engineering, Shahid Bahonar University of Kerman, Kerman, Iran; State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing, PR China; Corresponding authors.The current research offers credible mathematical models solely for estimating mono-nanofluids' density (ρnf), which can be useful for thermal engineering calculations required by various industries and applications. Accordingly, a comprehensive data bank encompassing 4004 experimental data-points was utilized to execute two rigorous machine-learning techniques: Group Method of Data Handling (GMDH) and Gene Expression Programming (GEP). Subsequently, two high-accuracy correlations were fine-tuned based on the four independent variables: average nanoparticle diameter (dnp), nanoparticle mass concentration (ϕm), nanoparticle density (ρnp), and base-fluid density (ρbf). Two variables pressure (P) and temperature (T), with rather minor impacts on the density of the mono-nanofluids under investigation, were excluded in the final correlations as a result of the modeling process and the intelligent operation of the machine-learning techniques. By performing multiple statistical and graphical analyses, comparative evaluations highlighted the superior performance and outstanding accuracy of the GEP-based correlation (with AAPRE=0.6614% and R2=0.9671). Moreover, sensitivity analysis and parametric trend assessments revealed that ϕm and ρbf were the most crucial variables affecting ρnf values, with relevancy factors of approximately 0.72 and 0.71, respectively. By considering the GEP-based correlation's outputs and applying the leverage statistical approach, a considerable portion (96.33%) of the total data-points was identified as valid data.http://www.sciencedirect.com/science/article/pii/S2211379725001421Mono-nanofluidsDensityMathematical correlationsStatistical and graphical analysesSensitivity analysis |
| spellingShingle | Omid Deymi Fahimeh Hadavimoghaddam Saeid Atashrouz Saptarshi Kar Ali Abedi Ahmad Mohaddespour Mehdi Ostadhassan Abdolhossein Hemmati-Sarapardeh Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning Results in Physics Mono-nanofluids Density Mathematical correlations Statistical and graphical analyses Sensitivity analysis |
| title | Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning |
| title_full | Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning |
| title_fullStr | Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning |
| title_full_unstemmed | Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning |
| title_short | Innovative mathematical correlations for estimating mono-nanofluids' density: Insights from white-box machine learning |
| title_sort | innovative mathematical correlations for estimating mono nanofluids density insights from white box machine learning |
| topic | Mono-nanofluids Density Mathematical correlations Statistical and graphical analyses Sensitivity analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2211379725001421 |
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