Implementation of artificial neural network using Levenberg Marquardt algorithm for Casson–Carreau nanofluid flow over exponentially stretching curved surface

• Published in: Neural computing & applications Vol. 36; no. 31; pp. 19393 - 19415
• Main Authors: Almeida, F., Kumar, Pradeep, Ajaykumar, A. R., Nagaraja, B.
• Format: Journal Article
• Language: English
• Published: London Springer London 01.11.2024; Springer Nature B.V
• Subjects: Accuracy; Activation analysis; Activation energy; Algorithms; Artificial Intelligence; Artificial neural networks; Boundary conditions; Chemical reactions; Computational Biology/Bioinformatics; Computational Science and Engineering; Computer Science; Data Mining and Knowledge Discovery; Design engineering; Error analysis; Fluid flow; Image Processing and Computer Vision; Impact analysis; Machine learning; Nanofluids; Neural networks; Numerical methods; Original Article; Parameters; Predictions; Probability and Statistics in Computer Science; Regression models; Runge-Kutta method; Schmidt number; Thermal stratification; Artificial neural network; Casson–Carreau nanofluid; Activation energy; Exponential stretching sheet
• ISSN: 0941-0643; 1433-3058
• DOI: 10.1007/s00521-024-10193-3

A theoretical framework is constructed for the Casson–Carreau nanofluid flow over a curved surface that is stretched exponentially. Artificial intelligence and machine learning are in vogue as the technologies that involve them, have expanded exponentially. In the current analysis, the Levenberg–Marquardt algorithm is used to train a machine learning language made of artificial neural networks to train the mathematical model constructed by including chemical reaction, and an exponential heat source component. The activation energy effect is taken into account while analyzing the impact of fluid concentration. Double stratification and Stefan blowing boundary conditions are used. Runge–Kutta Fehlberg 4–5th order is a numerical method applied to form the solution. An artificial neural network is used to train, test, and validate numerical computations. The linear regression models, histograms, and mean squared errors are used to verify the model's accuracy. The accuracy of the training is predicted by the least error in the range of 10 −3 –10 −4 as per the absolute error analysis carried out individually for the six parameters under consideration. Results reveal that the velocity is augmented by Weissenberg number and the mixed convection parameter. The temperature enhances for increasing unsteadiness parameter and depletes for increasing thermal stratification parameter. The concentration increases with increasing activation energy parameter and decreasing Schmidt number. Consequently, this study reveals that artificial neural network can be used as an alternative for the prediction of prolonged calculations. Nevertheless, the flow structure designed for the fluid considered in the model can be a pathway to fabricate an optimized industrial design.