Development of Instant Interface Temperature at Time τ = 0⁺ of Low Melting Temperature Cylindrical Solid Additive-Bath System

A mathematical model in integral format is devised for the development of instant temperature at the interface between a low melting temperature solid cylindrical additive and the freezing layer of the bath material around the additive immediately after immersion of the additive in the bath. It indicates that this temperature is function of the phase change parameters, the Stefan number, S _ta of the additive, and S _tb of the bath material, the thermophysical property-ratio, γ and the melting temperature ratio, θ _ab of the additive-bath system and gives a close form expression for the instant interface temperature, θ _e. For given θ _ab < 1 and the Stefan number, S _ta, of the additive decreasing the Stefan number, S _tb of the bath material (∞ ≥ S _tb ≥ 0) or increasing γ (0 ≤ γ ≤ ∞) permits θ _e to increase from the initial temperature of the additive to the freezing temperature of the bath material. θ _e also gets increased by increasing any or both of S _tb and θ _ab. When the additive gets only heated after its immersion in the bath, the model of the present problem becomes exactly the same that was investigated recently validating the present problem.