Optimizing Viscous Fluid Flow Embedded With Surface Constraints Based on Artificial Neural Networking Simulation

Abstract

In this investigation, the Levenberg–Marquardt algorithm with neural network (LMA-NN) model has been developed for the optimization of the viscous fluid. Suitable similarity transformations are applied to the set of partial differential equations for the transport of heat and concentration in two-dimensional convective flow. A formidable numerical technique is utilized to simulate flow dynamics conveying thermal energy and tiny substances on flat surfaces. In addition to this, high-fidelity reference data are cumulated via adaptive Runge–Kutta integration to determine the mean squared error (MSE). It is worth mentioning that the least margin of error of order ${10}^{-9}$–${10}^{-11}$ is obtained for all four separate surrogate ($S1$–$S4$) cases after application of the advanced Levenberg–Marquardt algorithm (LMA) neural network model. It is inferred that correlation coefficients tend to unity (i.e., $R\approx 1$) yielded by the MSE between the surrogate models approaching training (70%), validation (15%), and testing (15%). Neural computing explicitly confines the absolute deviations within the range of ${10}^{-6}$–${10}^{-5}$, which reveals that the higher the porosity, the greater the wall shear, which results in a thinner momentum boundary layer. Whereas strong coupling increases the concentration due to thermodiffusion. It is of great interest that LMA-NN model avoids the repetitive process of solving the equations time and again, while still giving accurate results. This inherent instinct of the methodolgy makes it useful for studying different practical cases of boundary-layer flow, such as cooling systems, filtration, catalytic processes, membrane systems, and other thermal applications in industry.