Nano-fluid flow predictions in convergent/divergent channels using ANN-BLMT and physics-informed neural networks

This article investigates the impact of various nanoparticle and thermal transfer properties on the velocity and temperature profiles of magnetohydrodynamics (MHD)-influenced nano-fluid flow. A mathematical model based on physics-informed neural networks (PINNs) and the backpropagated Levenberg–Marquardt technique (ANN-BLMT) were used to solve this problem. To optimize the masses and biases of PINNs calculated using a hybrid technique combining the Archimedes optimization algorithm and the water cycle algorithm. Furthermore, the suggested method's efficacy is rigorously evaluated using multiple independent runs and compared to ANN-BLMT, NDsolve, fuzzy homotopy analysis, and collocation methods. When compared to other methodologies, unsupervised PINNs produce better results. Furthermore, this study employs a machine learning framework to investigate the effects of important factors such as Reynolds number, Eckert number, Prandtl number ( \({P}_{\text{r}}\) $P_{\text{r}}$ ), and angle variations on velocity and temperature values via both convergent and divergent channels. By focusing on these parameters, this study provides critical insights into the behavior of MHD nano-fluid flow, leading to a better understanding of the underlying mechanisms and paving the way for more accurate predictions and optimized designs in a variety of engineering applications that use machine learning algorithms. In the convergent channel, a rise in Hartmann numbers leads to a higher fluid velocity, but in the divergent channel, the fluid rate falls. The findings have practical applications in the era of artificial intelligence in engineering, medicine, and industry.