Magnetohydrodynamic formulations for the study of metal melting: Effect of magnetic field uniformity

Accurate prediction of magnetohydrodynamic flow in phase change processes is essential for advanced metallurgy and energy storage technologies. This study aims to identify optimal electromagnetic formulations and quantify the physical phenomena associated with assumptions of magnetic-field uniformity in melting processes. Gallium melting within a prismatic cavity was numerically investigated using ANSYS Fluent software by comparing the magnetic induction and electric scalar potential formulations against benchmark experimental data. Results show that both formulations predict consistent transport dynamics, with maximum pointwise differences of 0.08% in temperature, 8.20% in velocity, and 4.50% in peak Lorentz force intensity. However, the electric scalar potential formulation reduces computational time by 50%. For the magnetic field, assuming a uniform distribution rather than a more realistic non-uniform one underpredicts the time to reach a liquid fraction of 0.75 by 13.8% because it fails to replicate localized magnetic damping. This study establishes clear guidelines for balancing computational efficiency with physical accuracy in simulations involving melting under magnetic fields.