The Soret-Dufour effects and non-uniform heat generation on gyrotactic and oxytactic microorganisms in stagnation point flow of CNTs-water based hybrid nanofluid flow via a rotating sphere with convective boundary conditions. Through the utilization of gyrotactic and oxytactic microorganisms, the system improves nutrient delivery and fluid mixing, which raises reaction rates and sensor sensitivity. Accurate biosensor performance depends on the hybrid nanofluid improved heat dissipation and stability, which are facilitated by the carbon nanotubes it contains. This approach is useful for applications in environmental monitoring, bioprocess engineering, and medical diagnostics since machine learning also facilitates real-time prediction, optimization, and control of sensor conditions. This research provides a novel numerical solution to this problem using back-propagation intelligent Bayesian regularization in the neural network domain (BIBR-NNs), which has convergent stability. Using a dataset for the proposed (BIBR–NNs) for many MHD-BNF-DSTR scenarios, the Bvp4c numerical technique. To determine the accuracy of the suggested model, the data is processed, appropriately tabulated, and its validity is tested. The BIBR-NNs training, testing, and validation procedures were utilized to assess the estimated solutions for specific occurrences and compare the proposed model for verification.
Abbas et al. (2026) studied this question.