The effect of the melt thermal gradient on the size of the constitutionally supercooled zone

Recent verification of the analytical Interdependence model by a numerical solidification model (μMatIC) confirmed the critical role of constitutional supercooling (CS) in achieving sufficient undercooling to trigger successful nucleation events. The location of the maximum amount of CS (ΔTCSmax) is some distance from the interface of the previously growing grain and this distance contributes to the final as-cast grain size. The effect of the thermal gradient, G, on the size of the CS zone (CSZ) was neglected in that work. However, G is expected to affect the size of the CSZ (i.e. the length of the CSZ, x'CSZ, and the location of ΔTCSmax, x'CSmax). This investigation assesses the effect of G on x'csz and x'CSmax. A range of G values is introduced into both the analytical and the numerical models to obtain a correlation between the value of G and the dimensions of the CSZ. The result of a test case from the analytical model shows that x'CSmax initially decreases rapidly and then decreases gradually approaching zero at very high values of G. Independent of the analytical model, the results from the numerical model replicate the trend obtained from the analytical model.