Comparative analysis of a novel Lobatto IIIA data-driven intelligent Morlet-based wavelet neural network optimization for dissipative flow in a two-phase non-Newtonian nanofluid model with thermal radiation and Joule heating effects

The inspection of the zero-mass flux condition by incorporating radiative nanofluid flow has received significant attention due to its realistic scenario. In fact, this condition restricts the idealistic accumulation or vanishing of nanoparticles towards the surface, making the physical model a more realistic representation of applications such as electronic cooling or heat exchangers. In this study, the two-phase nanofluid flow of the Bingham-Papanastasiou model across a movable cylinder with zero mass flux condition, chemical reaction, viscous dissipation, Joule heating, and radiation effects is examined. The leading partial differential equations are transformed into ordinary differential equations through the similarity factors, and then we use bvp4c to find the single-branch solutions. To reduce the computational cost of repeated bvp4c evaluations in parametric studies, we develop wavelet neural network (WNN) surrogate models employing the Morlet wavelet as the activation function and compare two training strategies: the second-order Levenberg-Marquardt algorithm and the first-order Adam optimizer. The numerical solutions confirm that the zero-mass flux constraint yields physically consistent nanoparticle transport, while thermal radiation significantly modifies the wall heat transfer rate. The surrogate-model results show that the Morlet-WNN trained with the Levenberg-Marquardt optimizer achieves high agreement with small but nonzero errors with bvp4c outputs ( R 2 = 1 with extremely small errors). The LM model showed close agreement with bvp4c outputs, with small but nonzero errors, whereas Adam produced larger errors and lower R 2 values. Overall, the proposed Morlet-WNN-LM surrogate provides a reliable and surrogate-based alternative to repeated bvp4c simulations, enabling rapid thermo-fluidic evaluation for design and optimization.