Mathematical model for instant interface equilibrium temperature at time τ=O + of solid additive–melt bath system

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].