Effect of Subcooling on Cylindrical Melting

Abstract

An analysis is made of the melting of a subcooled solid surrounding a heated circular cylinder. The solution is facilitated by coordinate transformations which immobilized both the moving interface between the melt region and the solid and the moving temperature wave that diffuses into the solid. The actual solutions were carried out numerically via a finite-difference procedure which circumvents the nonlinearity associated with the moving interface. Results were obtained for a wide range of a subcooling parameter and of the Stefan number. It was found that the subcooling can have a marked effect on the melting characteristics. Depending on the degree of subcooling, the surface heat transfer can be several times greater than that for no subcooling. Furthermore, at high levels of subcooling and at long melting times, the liquid layer thickness may be only a small fraction of that without subcooling. Subcooling also sharpens the differences between cylindrical and plane melting. The ratio of the heat flux for cylindrical melting to that for plane melting increases substantially due to subcooling, while the thickness of the cylindrical melt layer is only a fraction of that of a corresponding plane melt layer.