Design-oriented modeling of Ti?Al?V+TiO?/carboxymethyl cellulose-water based hybrid nanofluid: Backpropagation Bayesian Regularization neural network technique

Abstract

This study uses the Backpropagation Bayesian Regularization scheme neural network (BBRSNN) technique to study the influence of slip conditions on the Ti?Al?V+TiO?/Carboxymethyl Cellulose- water based hybrid nanofluid through an inclined rotating disc with Soret and Dufour effects. This model is useful for developing high-efficiency cooling systems, energy storage units, and chemical processing equipment because it helps precisely predict and optimize the behaviour of mass and heat transport in complicated fluid environments. While the Soret and Dufour effects are crucial for systems where coupled heat and mass diffusion occur, such as polymer processing, biomedical fluid transport, and membrane separation technologies, the inclusion of slip conditions enhances modeling accuracy in micro- and nano-scale flow devices, such as microchannel heat sinks. Engineers may create smarter, more effective industrial fluid-flow and thermal management systems thanks to the BR-NN optimization, which further improves model reliability. Following the validation of the approximate solution of multiple scenarios using the BBRSNN training and testing approach, the proposed model was given consideration for excellence. The proposed (BBRSNN) is confirmed using correlation analysis, mean squared error, and histogram of errors investigations. The accuracy level of the suggested technique ranges from 10?11 to 10?13. © 2026 The Authors.