Artificial neural network for bioconvective Williamson nanofluid flow through a horizontal microchannel with waste discharge concentration

Artificial neural networks have greatly enhanced computational modelling, providing substantial improvements in accuracy, versatility, and predictive performance across a multitude of scientific disciplines. Discharging effluent is a critical concern for industrial plants and environmental treatment systems, as it may pollute water bodies, impacting both ecosystem health and compliance with environmental standards. The efficient monitoring and control of water pollution is crucial for preserving water resources and complying with environmental standards, both of which are vital for safeguarding ecosystems and providing sustainable industrial practices. Herein, we utilize an artificial neural network model to examine the heat transfer and irreversibility in axial bioconvective Williamson nanofluid flow inside a horizontal microchannel under variable thermal conductivity and external pollutant sources, as well as non-uniform heat generation/absorption with no-slip and wall boundary constraints. The analysis is further extended, based on the Buongiorno model, to capture transport mechanisms of nanoparticles that include both thermophoresis as well as Brownian motion. The governing nonlinear equations are converted into dimensionless ordinary differential equations, and we obtain a numerical solution using the shooting technique with Runge–Kutta–Fehlberg. A feedforward backpropagation artificial neural network is then trained on the resulting data. Results reveal that the nanofluid temperature rises in higher values of non-uniform heat generation/absorption and variable thermal conductivity parameters. Similarly, the concentration of motile microorganisms improves for both the bio-convection Lewis number as well as the Peclet number due to stronger thermal gradients. In general, the developed ANN model exhibits great predictability and authenticity toward characterizing complex nanofluid systems. The mean squared error values for all the cases with respect to the ANN model are in the range of e −10 to e −5 , which is suggesting good model performance. This scenario is where gradient descent optimization converges near e −8 . The correlation between training, testing, and validation data indicates a very strong linear relationship with an average absolute error of only R = 1, substantiating the accuracy and consistency of the proposed ANN-based model.