Resolving the controversy over tin and gallium melting in a rectangular cavity heated from the side

Is the flow monocellular or multicellular? This question was first raised by Dantzig 13 years ago. It was about the nature of the fluid flow for the gallium melting problem in a rectangular cavity heated from the side. Following Dantzig's work, several publications have appeared on the same problem, with fewer than a handfull reporting a multicellular structure. To date, all experimental results support the monocellular structure, yet some researchers claim that the monocellular solution is incorrect. A similar controversy was reported for the problem of tin melting, suggested in 1998 as a benchmark problem. Several arguments have been suggested to explain the discrepancies, but there does not seem to be a commonly accepted answer to the problem in the scientific community. In this work, we summarize earlier works and present a grid-refinement study for several discretization schemes with emphasis on tin melting and some results for gallium melting. Simulations are carried out with the enthalpy method. The flow cell structure is analyzed in detail, while some results are provided for the heat transfer and the melting rate. Our results show that the multicellular structure is the correct numerical solution and that the flow structure has a strong influence on other features of the solution. We also provide a detailed discussion of earlier results in order to clarify important issues and bring a final answer to the controversy.