Flux and the Continuous Casting of Steel

An equation is found for the temperature distribution in a steel casting, which satisfies the conditions on the interface with the liquid steel and predicts that the interface is parabolic. The heat flow from the casting across the flux into the mould gives the temperature distribution in the liquid flux, whose viscosity is temperature dependent. Lubrication theory determines the differential equation for the pressure field in the flux. No solution exists without mould oscillation, in agreement with observation. An approximate solution is found which predicts upper and lower bounds for the mould oscillation. The temperature distributions, casting thickness and pressure field are determined numerically in a particular case. The theory treats the region from the top of the casting to the horizontal section at which an air gap first forms. One parameter has to be estimated from experimental measurement of the depth of this region. 1