Prediction of Thermal Behavior in Ferromagnetic Carreau Fluids Using Neural Networks Algorithm

Abstract

This study investigates the melting heat transfer characteristics of a ferromagnetic Carreau fluid (FCF) influenced by an external magnetic dipole. The Carreau model captures the non-Newtonian shear-thinning and shear-thickening nature of the fluid, while ferromagnetic effects introduce magnetically induced forces that modify flow and heat transport. The gov-
erning nonlinear ordinary differential equations are solved using MATLAB’s bvp4c solver. The resulting reference data are used to train an Artificial Neural Network (ANN) optimized via the Levenberg–Marquardt Technique (LMT). The proposed ANN–LMT  framework demonstrates high predictive accuracy with low Mean Squared Error (MSE) values, showing excellent agreement with numerical results. A specific set of physical parameters including the melting parameter (B), ferro-magnetic interaction parameter (β), Eckert number (Ec), Prandtl number (P r), Schmidt number (Sc), dimensionless Curie temperature (ε) and Weissenberg number (W e) was used to simulate the ferromagnetic Carreau fluid flow. Physically, increasing W e and β reduces the velocity, while higher P r and B suppress temperature and concentration due to diffusion and melting effects. Conversely, greater Ec enhances thermal gradients, Sc weakens solute diffusion, and rising ε increases concentration. Overall, the ANN–LMT model provides an efficient and accurate computational alternative for analyzing complex magnetothermal flow systems, with potential extensions to unsteady and three-dimensional configurations.