MHD williamson nanofluid flow in the rheology of thermal radiation, joule heating, and chemical reaction using the Levenberg–Marquardt neural network algorithm

Abstract

Various studies have been conducted on the topic of predicting the thermal conductivity of nanofluids. Here, the thermal conductivity of nanofluids is determined using artificial neural networks since this approach is rapid and accurate, as well as cost-effective. To forecast the thermal conductivity of magnetohydrodynamic Williamson nanofluids flow through a vertical sheet, a feed-forward neural network with various numbers of neurons has been evaluated, and the best network based on the performance is selected. The fluid model incorporates the effects of Joule heating, heat generation absorption, thermal radiation, and a chemical reaction (MHD-WNF-HGA). A combination of heat radiation and reactive species improves the energy and solute profiles. The magnetic Reynolds number is assumed to be so small; therefore, the generated magnetic field has no effect. A postulate of similarity variables is used to convert the physical model in the form of nonlinear partial differential equations to an ordinary differential equation system. A supervised Levenberg–Marquardt backpropagation algorithm possesses a multilayer perceptron that is used for training the network, which is one of the top algorithms in machine learning. The bvp4c numerical technique is adopted to build the datasets for the construction of continuous neural network mapping. Flow, energy, and concentration profiles of the fluidic flow are constructed by adjusting several physical quantities such as the Williamson parameter, thermal radiation parameter, magnetic parameter, Eckert number, Darcy number, Brownian motion, and thermophoresis parameter. Analytical techniques such as error histogram graphs and regression-based statistical graphs are used to examine the accuracy of a suggested method. It has been found that the Levenberg–Marquardt backpropagation neural network mappings’ derivation, convergence, authentication, and consistency have been proven. Furthermore, thermal radiation assists the energy distribution to increase smoothly. Fluid velocity drops with the Williamson parameter, whereas thermophoresis impact enhances the strength of the nanofluid density.