Artificial neural network analysis of irreversibility in electroosmotic flow of Prandtl–Eyring fluid through an inclined peristaltic channel with ciliated walls

This study investigates the artificial neural network (ANN) analysis of electroosmotically driven flow of a Prandtl–Eyring fluid through a peristaltic inclined channel with ciliated walls, influenced by non-Darcy porous medium and motile microorganisms. The governing nonlinear partial differential equations are reduced into set of ordinary differential equations (ODEs) using lubrication approximations and Debye–Hückel transformations with suitable dimensionless variables. These ODEs are addressed analytically using the homotopy perturbation method, which linearizes them into subproblems and assumes a perturbed series solution for velocity, temperature, concentration, and bioconvection. The symbolic solutions for these subproblems are derived in the MATLAB environment using the dsolve command. Subsequently, expressions for concentration, velocity, bioconvection, and temperature are plotted as function of various parameters, including the Prandtl number, non-Newtonian fluid parameter, and magnetic parameter, to evaluate their effects. Data from these profiles are extracted to construct the ANN model, which is trained in a Python environment using TensorFlow version 2.17.0. The model includes a starting layer, couple of hidden layers having 64 neurons each, and an output layer, utilizing the rectified linear unit activation mechanism and Adam optimization algorithm. The performance of our ANN model is monitored by mean square error, root mean square error, regression (R2), gradients, validation, and error histograms, which demonstrate the model's high accuracy in predicting thermal, velocity, concentration, and bioconvection profiles. The results indicate significant impacts of the non-Darcy porous medium, magnetic field, electroosmotic parameter, and nonlinear fluid parameter on the momentum profile. The potential applications of this study include the development of microfluidic devices for targeted drug transport in biomedical engineering and the optimization of pollutant transport in environmental engineering.