Residual Strength Prediction of Chemically Reactive Two‐Phase Nanofluid Flow in a Bingham–Papanastasiou Rheological Theory Using a Morlet‐Based Wavelet Neural Network Approach

ABSTRACT

The behavior of nanofluid flow involving a zero‐mass flux condition has received considerable interest because of a realistic scenario. In reality, this condition confines the optimistic accumulation or disappearance of nanoparticles past a sheet, constructing a more physically realistic demonstration through several applications, such as heat exchangers or the cooling of electronics. Therefore, the current investigation explores the two‐phase magnetic flow of nanofluid by incorporating the Bingham–Papanastasiou fluid towards a moving cylinder with chemical reaction, first‐order velocity slip effect, and zero‐mass flux condition. In addition, the advanced machine learning models are also incorporated. The governing partial differential equations are transmuted into ordinary differential equations by making use of similarity variables. These transmuted equations are further solved to obtain a numerically single‐branch solution through the bvp4c solver. It has also developed wavelet neural network (WNN) surrogate models by using the Morlet wavelet as the activation function and compared two training strategies: the second‐order Levenberg–Marquardt algorithm and the first‐order Adam optimizer. The shear stress rises by approximately 22.18% as the Bingham number increases and decreases by up to 29.75% as the velocity‐slip parameter increases. In addition, the heat transfer rate escalates up to 1.86% due to the larger impacts of the curvature parameter. The Morlet‐WNN trained with Levenberg–Marquardt matches the bvp4c solutions almost exactly, with much smaller errors than the Adam‐trained WNN, which remains accurate but shows higher prediction errors and a larger generalization gap.