Analysis of nonlinear complex heat transfer MHD flow of Jeffrey nanofluid over an exponentially stretching sheet via three phase artificial intelligence and Machine Learning techniques

The aim of this study is to propose an innovative three-phase Artificial Intelligence (AI) and Machine Learning (ML) techniques for nonlinear dynamics for thermal analysis of magnetohydrodynamics Jeffrey nanofluid over an exponentially stretching sheet under radiation effects. An artificial intelligence-based scheme, namely Levenberg-Marquardt with back propagation Neural Network approach (LMS-BPNN), is used. Similarity transformations are used to convert nonlinear governing partial differential equations (PDEs) into ordinary differential equations (ODEs). The resulting ODEs are solved by computation software MATLAB with bvp4c solver. The accuracy of the proposed LMS-BPNN is compared with ML solution of boundary layer flow. Moreover, the effects of physical parameters on the momentum, thermal and concentration boundaries layers are examined under four scenarios. The validity and accuracy are examined with Mean Square Error (MSE), function fit, and correlation index. It is observed that the thickness of Momentum Boundary Layer (MBL) increases by increasing the order of stretching/shrinking parameter and magnetic field intensity. The temperature variation and skin fraction increase by increasing the values of Biot number and magnetic field respectively. The Artificial Neural Network (ANN) model demonstrated incredible accuracy, with an error range of ${10}^{-8}$ to ${10}^{-6}$. The regression values closer to 1 show that the predictions and the actual data match well, while the regression values nearer to 0 indicate that the model has difficulty in identifying the underlying patterns. It is also noted that, if the hidden layers are selected correctly, the model produces accurate results.