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Numerical Analysis on the Freeze Coating of a Non-Isothermal Flat Plate with a Eutectic Binary Alloy

A numerical analysis on the freeze coating process is conducted to investigate the growth and decay behavior of freeze coat. A finite difference method is used to solve coordinate transformed governing equations. To account for the release of latent heat, and the heat flux from the liquid melt, proper phase change models and convective heat transfer coefficient are adopted. As results, the method of code validation is explained, followed by the presentation of results from numerical parametric study with various processing conditions. INTRODUCTION The freeze coating denotes a process by which a coating material at liquid state is deposited on a cooled, moving object by freezing, or more precisely by solidification. The object to be coated is cooled below the melting temperature of the coating material before entering liquid bath. Thus, as soon as the object enters the bath, a solid layer starts to grow on the surface of the object. The freeze coat grows according to the axial displacement of the object at first, but after the exhaustion of initial ‘coolness’ of the object it starts to decay and finally disappears by re-melting process. The analytic solutions of freeze coating with a pure material under simplifying assumptions, such as isothermal objects or no convection in the liquid bath, were published rather earlier[1~3]. But as real freeze coating processes can not satisfy the ideal constraint mentioned above, a numerical approach should be developed. Cheung[4] was the first who considered non-isothermal effects. In his study, asymptotic expressions for the evolution of freeze coat are obtained by way of a perturbation method. And the growth and decay behavior of freeze coat is also presented. The full treatment of thermal energy transport inside the object, except the axial diffusion, was done by Cheung and Cha[5]. They used a coordinate transform method to immobilize the continuously varying solid layer, and the effect of convection in the liquid bath was treated as a convective heat transfer boundary condition. Later, Cheung[6] proposed a procedure by which a convective heat transfer coefficient can be obtained when the liquid bath is not still. More recently Mohmaud[7] performed a transient analysis on the same process using finite element method. The freeze coating with a mushy material on an isothermal surface was studied by Rezaian and Poulikakos[8]. In the analysis, they proposed a process setup that the liquid melt is driven to flow parallel to the movement of the object, which is expected to minimize the flow-induced defects in freeze coat. Later, their study was extended to the semi-infinite plate cases by Stevens and Poulikakos[9]. Recently, Nam et al.[10] performed an analysis of the freeze coating of an infinitely small cylinder. The brief survey of the previous works shows that the researches on the growth and decay behavior of freeze coat are mainly concerned with the freeze coating with a pure material. Thus, the necessity of an analysis on the freeze coating with a mushy material, which also takes into account the effect of temperature variation in the object, is apparent and fully considered in the present study. PHYSICAL MODEL The freeze coating considered in this study is depicted in Fig.1. In the figure, a cooled plate is moving at a constant speed through the bath of a coating material that flows parallel to the plate. As the temperature of the plate is lowered below the melting temperature of the coating material before entering the bath, a solid layer and a mushy layer develop on the surface of the plate immediately after the plate entering. The configuration of freeze coat in Fig.1 shows the initial growth and subsequent decay behavior of the solid and the mushy layers. Mushy layer Solid layer Moving with U Plate x y