Bayesian regularization optimization technique for hybrid nanofluid with Cattaneo Christov flux model using wax and sand nanoparticles

Abstract The current study employs Bayesian-regularization optimizer technique with artificial neural networks (BROT-ANNs) to investigate the significance of local thermal non-equilibrium influences on wax + sand-based hybrid nanofluid flow across a disk with the Cattaneo–Christov flux model. Crystal growth, electron beam metal melting, convection or Bernard cells, welding, soap film stability, and other applications rely heavily on the Marangoni effect. This model enhances heat transfer prediction in enhanced oil recovery, drilling muds, and geothermal operations, where wax deposition and sand interaction have a significant impact on flow behaviour. It is also useful for designing thermal energy storage units, cooling technologies, and industrial heat exchangers that use hybrid nanofluid to create more stable, efficient, and controllable heat transmission. The use of Bayesian optimization ensures higher precision in parameter estimates, making the model applicable to real-world scenarios involving complex, non-Fourier heat transport. The proposed BROT-ANNs model outperforms other techniques and reference models with extraordinary accuracy levels ranging from $${10}^{-9}$$ to $${10}^{-12}$$ . Graphical abstract