Numerical and experimental modelling of two-dimensional unsteady heat transfer during inward solidification of square billets

Abstract

The development of air gaps between the solidifying shell and the mould is an inherent phenomenon in both continuous and static casting processes, and is one of the major factors affecting not only the microstructure formation but also the resulting properties and surface quality of castings. The heat flux transients at the casting/mould interface therefore attracted many attempts of mathematical modelling. In this study, an explicitly solved unsteady-state two-dimensional finite difference heat transfer model was used for the solution of the inverse heat conduction problem. The overall heat transfer coefficient between the casting surface and the cooling fluid (hg) – which is affected by a series of thermal resistances such as those from water, mould and air gap formed between the metal surface and the inner mould surface – is determined for the inward solidification of a hypoeutectic Al–Fe alloy casting in a water-cooled steel mould. Thermocouples were inserted into the casting with a view to continuously measure temperatures during solidification, which is necessary to furnish thermal information to be compared with simulations, and an automatic search selected the best theoretical–experimental fit from a range of transient heat transfer coefficient profiles. The microstructural cellular spacing was measured in order to permit correlations with the cooling rate (T˙) at different positions from the metal/mould interface to be established. It is shown by numerical heat transfer simulations that the cooling rate decreases from the casting surface, and after reaching a minimum value, starts to increase characterising a reversal trend towards the centre of the casting. It is also shown that the cellular spacing accompanies the trend in the cooling rate. The obtained results – transient (hg) profiles and growth laws relating the cellular spacing to (T˙) – can contribute to a better understanding of transport phenomena and microstructure evolution of more complex processes involving transient solidification.