Abstract

Significance: Casson fluid flow between parallel discs has significant applications in biomedical devices such as blood pumps, dialysis units, and artificial valves, in industrial processes involving inks, paints, and food pastes, and in engineering systems including lubrication, cooling and polymer processing. Artificial Neural Networks are increasingly applied in fluid dynamics for their ability to approximate nonlinear systems, reduce computational cost, and provide accurate predictions compared to traditional numerical schemes. Purpose: This work proposes a supervised learning approach using Artificial Neural Network Backpropagation trained with the Levenberg-Marquardt scheme (ANN-BLMS) to obtain numerical solutions of Casson fluid flow between two parallel discs with dissimilar in-plane motion (CFFPD). The method improves accuracy and stability, reduces computational cost, and predicts fluid flow behavior under varying physical parameters, with emphasis on the effects of the rotation parameter, Reynolds number, and Casson parameter on velocity profiles. Methodology: The system of governing partial differential equations is converted into dimensionless ordinary differential equations through similarity transformation and solved using the ANN-BLMS. The data for this study were obtained using NDSolve method and subsequently optimized with an artificial neural network. The data set for ANN-BLMS is computed by using 15% of the data for testing (TT), 15%for the training (TR), and 75% of the data, selected randomly, for validation (VL). Error histograms (EH) and regression (RG) measurements, together with strong agreement with known solutions, demonstrate the dependability of the developed algorithms, ANN-BLMS, on CFFPD, with an accuracy range from 10⁻³to 10⁻⁷. Findings: The radial velocity increases with the Casson parameter in the range 0 < η < 0.5, but decreases for 0.5 ≤ η ≤ 1, while the azimuthal velocity decreases for the Casson parameter grows. For both Reynolds number, and rotation parameter the radial velocity declines when 0 < η < 0.5, and rises for 0.5 ≤ η ≤ 1. The azimuthal velocity increases with the increase in both the Reynolds number and rotation parameter. The ANN-BLMS approach demonstrates strong agreement with existing solutions, offering higher accuracy, stability, and lower computational cost compared to traditional numerical methods.