This study investigates the complex heat transfer phenomena associated with the melting process in a ferromagnetic Carreau fluid, a topic that combines multiple nonlinear physical effects rarely addressed together. The Carreau fluid model effectively captures the non-Newtonian rheological behavior exhibited by various engineering and industrial materials, while the ferromagnetic property introduces additional control over the flow and thermal transport characteristics through externally applied magnetic fields. The combination of these effects gives rise to intricate patterns of motion, heat transfer, and mass transport that are of profound importance in advanced cooling systems, material processing, and magnetic field-assisted manufacturing technologies. The novelty of the present formulation lies in the simultaneous inclusion of melting and solute stratification phenomena within a ferromagnetic Carreau fluid framework, a coupling that has not been explored in previous studies. By incorporating both melting heat transfer and solute concentration gradients, this study introduces a new multi-physics model that captures phase change energy exchange, buoyancy modification, and mass diffusion effects simultaneously offering a more realistic representation of magnetized non-Newtonian systems. To analyze this highly coupled nonlinear system, the bvp4c solver, a robust numerical method for boundary value problems, is employed to obtain accurate and stable solutions for the velocity, temperature, and concentration fields. The investigation provides deep insight into the interplay among rheology, magnetization, melting, and solute stratification, revealing how these mechanisms collectively shape the heat and mass transfer characteristics of the flow. This integrated framework not only extends the theoretical understanding of ferromagnetic Carreau fluids but also advances the field beyond existing models by providing a foundation for designing thermo-magnetic systems that exploit controlled melting and stratification effects for enhanced performance.
Rehman et al. (Tue,) studied this question.