Free convection heat and mass transfer during pool penetration into a melting miscible substrate

A theoretical investigation is made of the process of free convection melting of a solid slab by an overlying hot liquid pool. The solid, when molten, is lighter than and miscible with the pool material. Systematic mathematical approximations to the Boussinesq equations of motion are performed to determine the behavior of the temperature and the concentration fields in two different flow regions. These are the boundary layer region at the melting interface and the turbulent core region in the bulk pool. The dependence of the melting rate on various controlling parameters, including the Grashof number based on the pool-to-substrate density ratio, the external Stefan number based on the pool-to-substrate temperature difference, and the internal Stefan number based on the freezing-point depression, is obtained by matching the boundary layer solution and the turbulent core solution in the region of overlap. Comparison of the present theory is made with existing experiments and found to be good.