A LUMP-INTEGRAL MODEL FOR FREEZING AND MELTING OF A BATH MATERIAL ONTO A PLATE SHAPED SOLID ADDITIVE IN AN AGITATED BATH

A lump integral model is developed for freezing and melting of the bath material onto the surface of a plate shaped additive immersed in an agitated melt bath. It exhibits the dependence of this occurrence on independent parameters-the initial temperature, θ ai of the additive, the bath temperature, θ b , the Biot number, B i the property ratio, B and the Stefan number, S t and yields closed-form solutions for time variant frozen layer thickness, ξ around the additive and heat penetration depth, η in the additive. In the solutions, B, B i , θ b and θ ai appear as a conduction factor, C of that ranges from 0 to ∞. The frozen layer thickness per unit S t with respect to C of takes time τ cmax =1/3 for its maximum growth whereas this maximum thickness ξ* cmax becomes (1- θ ai )/3. The total time of the growth of the maximum frozen layer thickness with its subsequent melting, τ ct is 4/3 when the heat penetration depth reaches the central axis of the plate additive, η=1. When C of →0 signifying highly agitated bath (h→∞) or additive preheated to the freezing temperature of the bath material, no freezing of the bath material occurs. For the bath at the freezing temperature of the bath material, the frozen thickness is also obtained. The model is validated by reducing the present problem to heating of the plate additive subjected to a constant temperature maintained at the freezing temperature of the bath material.