This paper presents a method to determine the mass transfer coefficients in the dissolution of dense ceramics in liquid slags. We use the rotating finger test for the experimental set-up, where a cylindrical sample is immersed in a slag bath and rotated with a constant angular speed. CFD simulations of the flow field are conducted using the volume of fluid method to incorporate both the slag and air phases. Owing to the very large Schmidt number of the arrangement and to avoid using extremely fine meshes, an asymptotic boundary layer approach is employed. This approach allows for the calculation of local, steady-state mass transfer coefficients along the sample in a postprocessing step without resorting to solving the species transport equation within the CFD calculations. The method is verified by comparing the results to those obtained via well-established equations. Resultant mass transfer coefficients are discussed with respect to values obtained from mass transfer equations in literature. The presented approach serves as an effective calculation method for the mass transfer coefficient and offers the opportunity to obtain the inverse calculation of diffusivities in systems where the Schmidt number reaches large values.