Fractionalization in Prandtl fluid and machine learning

Abstract

Fractional calculus has played a vital role in complex dynamical systems in applied mathematical modeling with memory and anomalous diffusion in recent decades, while machine learning has revolutionized data-driven prediction. This study integrates these two powerful approaches to investigate a new problem: the fractional-order dynamics of a non-Newtonian Prandtl fluid in a stagnation point flow. We consider time-dependent, natural convection on an infinite plate, incorporating magnetic fields, chemical reactions, and cross-diffusion (Soret and Dufour) effects. The physical model is formulated using a system of coupled partial differential equations in the form of Caputo time-fractional derivatives. A finite difference method (FDM) provides numerical solutions, demonstrating that the fractional order parameter is a critical control variable for the flow, heat, and mass transfer processes. Finally, the relationship between thermal radiation and convective heat transfer is analyzed via multiple linear regression with testing and training models. The underlying model that is trained with linear regression (LR) with polynomial features is compared with the multi-layer perceptron (MLP) neural network model. Hence, the acquisition of both these trained models is drawn and shown in the illustration with FDM simulations. Moreover, the coefficient of determination (R2) and mean square error (MSE) are computed with LR and MLP, represented in tables. The objective of this study is to emphasize the impact of the Caputo fractional memory dependency, which has been uniquely captured by the machine learning algorithm.