My latest work has been published in the IMA Journal of Applied Mathematics. The full text PDF can be found here .

Abstract

A recent asymptotics-based thermomechanical model is adapted and applied to the mould region in the continuous casting of round steel billets, with a view to describing the complex interplay between air-gap formation, mould taper, cooling channel width and cooling water velocity. Although the situation is steady state, the analysis leads to what is mathematically a dual moving-boundary problem for the solid–melt and solid–air interfaces, where the distance from the top of the mould region is the time-like variable in the problem. Moreover, the two interfaces are initiated at different locations. In addition, the thermal and mechanical problems are found to decouple and it is possible to solve the first ahead of the second. The model equations are solved numerically using a finite-difference method, and the approach is subsequently successfully validated against a previous finite-element model and experimental data from temperature measurements taken within the mould.