Diffusion limited growth-up of channels of ICF and its influence on integral flow through the channel

Transit integral flow through the channel and the resulting temperature difference are extremely important in application of the induction channel furnace. Estimations showed that the force coming from the Boussinesq approximation is the leading force that drives the melt flow through the channel. The transit flow highly depends on the geometry of channels, power, heat losses, viscosity and other factors. One of the other factors is growth-up of channels during melting. The grown material is shown to be fractal- like, which occurs due to diffusion-limited accumulation of oxide particles to the surface. Therefore, the growth-up influences the cross-sectional area of the channel and conse- quently the transit flow and temperature difference in the channel. As a particular example, melting of steel is considered.