The significance of radiative heat and mass transfer through a vertical sheet with chemical reaction: Designing by artificial approach Levenberg-Marquardt

Abstract

The present study examines the impact of incorporating soft computing algorithms during neural network training on the evaluation and prediction performance of artificial neural networks. The research centers on a magneto hydrodynamic flow model (RHMT-VSCR) that depicts the movement of rotating fluid along a vertical sheet in a permeable medium. Furthermore, the model considers the impact of heat source-sink interactions, thermal radiation, and reactive species in conjunction with the effects of Hall current on the enhancement of energy and solute profiles. Because the induced magnetic field has a negligible magnetic Reynolds number, it is disregarded. A set of governing nonlinear PDEs is converted to a system of ODEs by applying an appropriate postulate of similarity variables in order to analyze the system. The multilayer perceptron network utilizes a supervised Levenberg-Marquardt Backpropagation algorithm (LMLA-BPNN) to ascertain the ideal quantity of neurons to be included in the hidden layer of artificial neural networks intended for modeling purposes. The bvp4c numerical approach is utilized to establish a continuous neural network mapping, which produces datasets that are utilized for the purposes of authentication, training, and testing. The range i.e., 10-2 - 10-8 of absolute error of the reference and target data demonstrates the optimal accuracy performance of LMLA-BPNN networks. After acquiring knowledge of neural network mapping, it is applied to approximate solutions fora wide range of scenarios through the manipulation of physical constraints, including suction/injection quantities, magnetic parameter, and porosity parameter, which influence the characteristics of flow, energy, and concentration. To assess the precision of the proposed method, statistical graphs based on regression, mean squared error analysis graphs, and error histogram graphs are employed. The results of the research demonstrate that the Levenberg-Marquardt Backpropagation neural network mappings' derivation, convergence, authentication, and stability were effectively validated.