A design of neuro-computational approach for double-diffusive natural convection nanofluid flow

Muhammad Shoaib; Rafia Tabassum; Kottakkaran Sooppy Nisar; Muhammad Asif Zahoor Raja; Nahid Fatima; Nuha Al-Harbi; Abdel-Haleem Abdel-Aty

doi:10.1016/j.heliyon.2023.e14303

A design of neuro-computational approach for double-diffusive natural convection nanofluid flow

Heliyon. 2023 Mar 6;9(3):e14303. doi: 10.1016/j.heliyon.2023.e14303. eCollection 2023 Mar.

Authors

Muhammad Shoaib^{1

2}, Rafia Tabassum¹, Kottakkaran Sooppy Nisar^{3

4}, Muhammad Asif Zahoor Raja⁵, Nahid Fatima⁶, Nuha Al-Harbi⁷, Abdel-Haleem Abdel-Aty^{8

9}

Affiliations

¹ Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan.
² Yuan Ze University, AI Center, Taoyuan, 320, Taiwan.
³ Department of Mathematics, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, 16278, Saudi Arabia.
⁴ School of Technology, Woxsen University, Hyderabad, 502345, Telangana State, India.
⁵ Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, ROC.
⁶ Department of Mathematics & Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia.
⁷ Department of Physics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia.
⁸ Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha, 61922, Saudi Arabia.
⁹ Physics Department, Faculty of Science, Al-Azhar University, Assiut, 71524, Egypt.

Abstract

The artificial intelligence based neural networking with Back Propagated Levenberg-Marquardt method (NN-BPLMM) is developed to explore the modeling of double-diffusive free convection nanofluid flow considering suction/injection, Brownian motion and thermophoresis effects past an inclined permeable sheet implanted in a porous medium. By applying suitable transformations, the PDEs presenting the proposed problem are transformed into ordinary ones. A reference dataset of NN-BPLMM is fabricated for multiple influential variants of the model representing scenarios by applying Lobatto III-A numerical technique. The reference data is trained through testing, training and validation operations to optimize and compare the approximated solution with desired (standard) results. The reliability, steadiness, capability and robustness of NN-BPLMM is authenticated through MSE based fitness curves, error through histograms, regression illustrations and absolute errors. The investigations suggest that the temperature enhances with the upsurge in thermophoresis impact during suction and decays for injection, whereas increasing Brownian effect decreases the temperature in the presence of wall suction and reverse behavior is seen for injection. The best measures of performance in form of mean square errors are attained as $7.1058 \times 10^{- 10}, 2.9262 \times 10^{- 10}, 1.1652 \times 10^{- 08}, 1.5657 \times 10^{- 10}$ and $5.5652 \times 10^{- 10}$ against 969, 824, 467, 277 and 650 iterations. The comparative study signifies the authenticity of proposed solver with the absolute errors about 10^-7 to 10^-3 for all influential parameters results.

Keywords: Artificial neural networks; Brownian motion; Double-diffusive convection; Intelligent computing; Levenberg-Marquardt method; Lobatto III-A technique; Nanofluid; Suction/injection; Thermophoresis effect.