Feed-forward neural network and Levenberg-Marquardt backpropagation algorithm for time-dependent squeezing dynamics prediction of polymer penta-hybrid nanofluid using machine learning

This study examines the unsteady squeezing flow and heat transfer behavior of a penta-hybrid nanofluid confined between two parallel plates. A time-dependent mathematical model is developed under the assumptions of incompressible, laminar flow, incorporating viscous dissipation and nanoparticle effects. A model, Artificial Neural Network (ANN) for behavior prediction, was integrated into this study. A two-layer feed-forward neural network with sigmoid activation in the hidden layer and linear neurons in the output layer was trained using the Levenberg-Marquardt backpropagation algorithm. The results show that increasing the squeezing parameter and the volume fraction of nanoparticles decreases the temperature profile, while increasing the Eckert number leads to an increase in the temperature profile. A slight increase in temperature is observed with an increase in the geometric ratio parameter, while the shape factor of nanoparticles causes a decrease in the temperature profile. Changing the shape factor from Spherical to Lamina for S < 0 and S > 0 resulted in a decrease of 18.09% and 7.39% in the temperature profile at the beginning (η = 0), respectively. The ANN model exhibits high performance, with rapid convergence of the mean squared error (MSE) and low error values across training, validation, and test datasets. The average MSE value in the ANN was on the order of 10 -10 , while the gradient value was approximately 10 -8 . The present model is applicable to confined electrochemical energy systems such as fuel cells, redox flow batteries, electrolyzers, and supercapacitors, where electrolyte transport and thermal regulation occur in narrow parallel-plate channels under dynamic operating conditions.