Abstract
The instant interface equilibrium temperature at time τ=0+ in close form is obtained from a mathematical model which has been developed for a solid additive–melt bath system. It is a function of the Stefan number S t and the property ratio B as well as the initial temperature of the solid additive θ i. For B→∞ 0 ≤ S t ≤ ∞, or S t→0, 0 ≤ B ≤ ∞, the instant interface equilibrium temperature becomes the freezing temperature of the bath material, whereas it takes the temperature θ i of the additive before its immersion in the bath once B→0 for 0 ≤ S t ≤ ∞. In the case of S t→∞, 0 ≤ B ≤ ∞, it becomes θ e = [(24B)1/2 + 3θ i]/[(24B)1/2 + 3].