A Rigorous Formulation and Neural Network Prediction of Thermal Transport in Bingham-Papanastasiou Fluid Flow over Cylinders

Moving beyond the conventional locally similar framework, this study investigates coupled heat and mass transfer with thermophoresis in viscoplastic fluid flow over a stretching horizontal cylinder using the Bingham–Papanastasiou constitutive model. Existing studies on Bingham–Papanastasiou fluid boundary-layer flows are predominantly based on locally similar formulations, which restrict their validity to small axial distances. The only available study on Bingham–Papanastasiou fluid flow induced by a stretching cylinder also employs a locally similar framework; however, the transformations of the relevant conservation equations are not fully consistent in that formulation. The present study develops a correct formulation for flow over elongating cylinders and computes second–level locally non-similar solutions using suitable numerical techniques. To ensure reliability, the results obtained from two independent numerical approaches are cross verified, showing excellent agreement across all considered cases. The validated solutions are subsequently used to construct three-dimensional representations of the velocity, temperature and concentration fields as functions of both radial and axial coordinates under diverse parametric settings. Furthermore, thermophoretic transport effects are examined in the non-similar viscoplastic flow environment, a topic that has not been reported in the literature. In addition, a Bayesian neural network framework is developed to predict the solution profiles. The predictive capability of the framework is evaluated using multiple validation metrics, and the predicted results are shown to closely match the reference numerical solutions across a wide range of scenarios.