A method is proposed to determine the effective binary diffusivities in a dissolution of dense ceramics in liquid slags. This is achieved by combining computational fluid dynamics with a boundary layer approach to overcome the resolution problem that is associated with high Schmidt numbers. The rotating finger test experiment was performed with a dense alumina fine grain ceramic in a calcium aluminosilicate (CAS) slag. During the experiment, the sample dissolved, and the sample's shape deviated substantially from the initial cylindrical shape. The simulations were conducted in a middle step whereat the sample was already corroded, and the geometry was obtained from the laser measurements of the corroded surface. The diffusivities were evaluated via the average mass flux density and by fitting the experimental and simulation curves. Good agreement between the simulated and experimental corrosion profiles existed for the diffusivities evaluated by using the two methods.