An integral model based freezing and melting of a melt material onto a solid additive

An integral model in nondimensional form is developed for freezing and melting of the melt material onto the surface of the additive that resembles a plate. It provides the governing equations coupled and nonlinear and indicates the dependence of this phenomenon on independent parameters-preheat temperatures θi, the Stefan number St, the Biot number Bi, the property ratio B, and the bath temperature θa. The solutions for the growth of the frozen layer and its melting along with instant equilibrium temperature of the surface of the additive and the heat penetration depth within the additive are obtained. Their graphical representation exhibits that with increase in each of θa, θi, Bi, and B, the total time of freezing and melting and the maximum thickness of the frozen layer developed onto the additive decrease. Increasing St does not alter such a total time. The validity of the model is checked.