Computational Modelling of Magnetized Casson-Williamson Nanofluid Flow with Thermophoretic Effects Using Hybrid ANN-BLMS and BVP4C: A Biomedical Perspective

This study investigates the nonlinear flow and heat transfer behaviour of Casson-Williamson nanofluids over a stretching surface, incorporating magnetic field, thermophoresis, and Brownian motion effects. A hybrid methodology combining MATLAB's BVP4C solver and Artificial Neural Network with Backpropagation Levenberg-Marquardt (ANN-BLMS) is developed to enhance solution accuracy and reduce computational cost. The ANN model is trained on high-fidelity numerical data and tested across multiple physical scenarios involving variations in Prandtl number, Weissenberg number, and nanoparticle effects. The hybrid model demonstrates excellent predictive capability with a minimum Mean Squared Error (MSE) of 4.8 × 10 -9 , achieving regression accuracy above 0.995 across all cases. Key performance trends such as thermal boundary layer thinning at high Prandtl numbers and nanoparticle redistribution via thermophoresis are accurately captured. The ANN-BLMS framework not only replicates the governing physics with high precision but also provides a robust, scalable alternative for simulating complex non-Newtonian nanofluid systems in biomedical and engineering applications. From a biomedical perspective, the computed transport trends are interpreted in the context of magnetically assisted nanofluid heat-mass transfer relevant to magnetic hyperthermia adjuncts and controlled delivery near stretching or membrane-like surfaces, using blood-analogue Casson-Williamson rheology as a modelling baseline. The ANN-BLMS component is employed as a surrogate of the bvp4c solution manifold within the sampled parameter space, complementing rather than replacing the governing boundary-layer model.