Numerical computation of Cross nanofluid model using neural network and Adaptive Neuro-Fuzzy Inference system with statistical insights for enhanced flow optimization

In this study, we present a novel integration of numerical methodologies and advanced computational intelligence to elucidate the dynamics of cross nanofluid flow over a Riga plate through a Darcy-Forchheimer porous medium. Brownian motion and thermophoretic phenomena are considered, along with the impacts of activation energy. Slip velocities, convective, and zero-flux boundary conditions are taken into account in the 3D cross nanofluid flow model in the presence of gyrotactic microorganisms. The non-linear PDE model is transformed into a highly non-linear ODE system using von Ka<acute accent>rma<acute accent>n similarity variables. Taking advantage of Python-derived numerical data as a foundational dataset from the system of non-linear ODEs, we employ neural network algorithms to refine and predict flow behaviors under varying conditions. The research progresses by contrasting these predictions with empirical observations, providing a rigorous validation framework. Furthermore, we incorporate the Adaptive Neuro-Fuzzy Inference System (ANFIS) alongside statistical analyses to examine the impacts of physical parameters, offering unparalleled insight into nanofluid mechanics. This multifaceted approach not only bridges theoretical and practical aspects of fluid dynamics but also proposes a robust model for predicting nanofluid behavior, poised to catalyze advancements in thermal engineering and nanotechnology applications. The precision and adaptability of our methodology underscore its potential as a cornerstone in future fluid dynamics research, inviting scrutiny and discussion from esteemed peers in the field. We have validated our model by finding various sets of error estimations. Furthermore, the velocity profile increases with the enhancement of the Hartmann number or magnetic parameter while decreasing with higher values of the Weissenberg number. The temperature profile decreases with increasing estimates of thermal stratification and the Biot number. The concentration profile amplifies with the Brownian motion parameter while decreasing against the thermophoresis parameter.