A Generalized Model for Gravity-Assisted Melting in Enclosures

Gravity-assisted melting in cylindrical and spherical capsules has been studied over the past decade. However, none of these earlier analyses are truly complete. All are based on a number of simplifying assumptions, and have been developed from the studies of Moore and Bayazitoglu (1981, 1982), Emmerman and Turcotte (1983), and Bareiss and Beer (1984). As a consequence, there is a notion that gravity-assisted melting is always dominated by conduction, with natural convection having a minor effect on the overall melting. In the absence of a generalized model for the melting process, there has also been a lack of proper scaling of the governing variables resulting in a proliferation of parameters, and ultimately unnecessary experimentation. In addition, correlations have been presented for different geometries often without any mention of the parameter ranges over which these are valid. In order to provide a stronger basis for the numerous analyses published previously, a more generalized model is presented in this paper. Since this model is based on fewer preliminary assumptions, it can be used to describe a wider variety of engineering problems than was possible with earlier models. Based on the observation that most of the heat transfer occurs through the liquid film,more » a scaling analysis is then done to derive the nondimensional equations and finally the nondimensional numbers governing the process.« less