This study analyzes the impact of local thermal non-equilibrium on the bioconvection flow of hybrid nanofluid across a slender extending sheet containing gyrotactic bacteria using artificial neural networks trained using a Bayesian regularization backpropagation approach (ANN-BRS). The effects of magnetic fields, thermal radiation, and Hall current are all things related to fluid flow. The suggested model has particular applicability in microscale drug delivery systems, where gyrotactic microorganisms and hybrid nanofluid can be employed to control nutrition and medication dispersion under non-equilibrium temperature circumstances. It can be used in lab-on-chip and organ-on-chip technologies to improve bio-mixing and accurate heat control. The model also applies to micro-solar collectors and porous micro-heat exchangers, which use hybrid nanoparticles to boost thermal efficiency. It can also be used in bioreactors and biomedical cooling systems, where local thermal non-equilibrium effects and ANN-based prediction allow for precise control of heat, mass, and microbe transfer, resulting in optimal performance. Similarity transformations are used to convert the original nonlinear PDEs into non-dimensional ODEs and the bvp4c program is applied to numerically resolve the resulting boundary-value problem. The training, testing, and validation processes yield the expected outcomes for every scenario based on the chosen data points. Regression analysis, histograms of error, and mean square error (MSE) metrics are employed to assess the ANN-BRS model's outcome. The liquid phase heat thermal profile increases as the interphase heat transfer parameter values rise, while the solid phase thermal profile decreases.

This study examines the outcome of heat generation on thermophoretic particle deposition in Co3O4/HFE-7100 nanofluid flowing past a vertical cylinder in a permeable media under local thermal non-equilibrium conditions employing an ANN coupled with a Bayesian-regularized back-propagation algorithm. For contrast, a simplified mathematical formulation is also used to examine the thermal behavior without local thermal equilibrium assumptions, that is, without LTNE limitations. The solid matrix and fluid phase are treated as distinct temperature fields in the LTNE framework, necessitating unique thermal gradients for each phase. Optimizing heat transfer performance using ANN-based regression modeling is the main goal of this work. Well-structured training and testing datasets are used to guarantee numerical stability and prediction resilience, and the Bayesian-regularization back-propagation technique is applied to enhance generalization capacity. The impact of dominating governing factors is illustrated graphically, and an error evaluation is provided to gauge model correctness. The ANN model was trained using the obtained dataset and then tested against numerical values of important engineering variables. Tables and graphs are utilized to show how new factors affect the flow’s dynamics. The rate of liquid phase heat transmission declines as the inter-phase heat transport values increase.