Both physical and mathematical models were developed to understand the heat transfer and fluid flow occuring in slag-cleaning furnaces. A one-tenth-scale model of two-dimensional flow, in which molten wax simulated the liquid slag, was used for the physical model experiments. The temperature field showed a strong thermal stratification in the main liquid body under natural convection conditions. The temperature and velocity fields in the wax tank were solved using a software package, microcompact. The computed results were compared with experimental results and showed satisfactory agreement.