Homogeneous-heterogeneous reactions on Darcy-Forchheimer nanofluid flow system

Abstract

The use of artificial neural networks (ANNs) to solve complex fluid dynamics problems has revolutionized computational approaches. This article explores novel ANN solutions for fluid problems. ANNs have demonstrated unmatched effectiveness in comprehending and forecasting fluidic behaviors, from mimicking complex fluid flow trends to optimizing structures for dynamics. This study emphasizes the significance of neural networks in revolutionizing our understanding and control of fluidic systems by using ANNs and Bayesian Regularization. This study examined the 3D Darcy-Forchheimer stretching flow (TDDFSF) of nanofluid under convective conditions along with homogeneous and heterogeneous reactions by employing the scheme of Bayesian Regularization with the procedure of backpropagation in neural networks (SBR-BNNs). The flow is influenced by Brownian diffusion, thermophoresis and zero nanoparticles mass flux condition. The PDEs given in this model are converted into nonlinear ODEs. Results from MSE, regression analysis, and error histogram are used to verify the performance of SBR-BNNs. The absolute errors lie in the ranges up to 10−9, which depict the worth of the solver SBR-BNNs. The absolute error measures the discrepancy between the values actually observed and those predicted by the SBR-BNNs model. SBR-BNNs' high precision in TDDFSF models can lead to more effective and reliable solutions.