Theoretical investigations of electromagnetic control of glass melt flow

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The electromagnetic flow control of high-conductivity fluids like liquid metals is well established, while the application of Lorentz forces in low-conductivity fluids such as glass melts is relatively new. This work explores the generation of Lorentz forces in glass melts through the interaction of electrical currents and external magnetic fields, focusing on regulating mass flow rates and enhancing mixing. The first part examines one-dimensional analytical models of glass melt pipe flow, influenced by Lorentz forces, gravity, and temperature variations due to heat loss, electrical heating, advection, and diffusion. It identifies a new flow regime where, without heat loss, mean velocity is proportional to the square root of the driving force, while wall heat loss leads to non-unique solutions and bifurcations due to the interplay of velocity, temperature, and material properties. These findings are validated by two-dimensional numerical simulations. The second part presents three-dimensional simulations of glass melt in a crucible heated by rod electrodes, showing that Lorentz forces increase kinetic energy and mean velocity in a nearly linear relationship. A hysteresis characterizes the transition between buoyancy and Lorentz force-dominated flow regimes, resulting in multiple steady solutions based on initial conditions. The three-dimensional problem is simplified to one-dimensional algebraic equations, revealing the impact