Paradigm predictive analysis of two-phase Eyring–Powell fluid flow over a vertical stretching sheet with temperature-dependent viscosity by multilayer neural networks - Zahoor Shah; Hamza Iqbal; Waqar Azeem Khan; Taseer Muhammad; Muhammad Shoaib (Case Studies in Thermal Engineering)
Recently, the accuracy and efficiency of solving complex fluid problems have benefited greatly from these latest advances in AI-integrated fluid mechanics. Deep-learning neural networks optimized with the Levenberg-Marquardt algorithm (DLNNs-LMA) is a supervised AI-based approach that is used to analyze the Eyring Powell fluid in a two-phase flow (EPFM-TPF) with dust particles and at temperature-dependent viscosity. PDEs are converted into nonlinear ODEs with similarity transformations, which are solved using the Adam method in Mathematica with varied physical parameters to generate a reference dataset. Finally, we examine graphically velocity and temperature profiles of both fluid and dust particles and for significant parameters. The novel DLNNs-LMA were used for the numerical computations on the reference data. The error analysis indicates a close correlation with the proposed databases and with reference datasets, having values between 10-3 and 10-9, which indicates a high accuracy of the proposed methodology. Its consistently low MSE (mean square error) values (at the scale of E-09 to E-10) make it a good approximation for most scenarios; there is very little deviation and strong predictability. The results obtained validate the robustness of the DLNNs-LMA approach to solve complex fluid dynamics problems. Further, there is variation in epochs (from 54 to 585) to account for the adaptability of the model, leading to the best convergence despite differences in scenarios. It is observed that the velocity profile gradually increases with the rising trend of M and β, and the absolute error was found in the range between E-04 to E-07 and E-02 to E-07, respectively.