## 4 Conclusions  
Dynamic corrosion investigations of fine magnesia ceramics in silicate slag were conducted at 1450, 1500, and 1550 \({}^{\circ}\)C using CWTD with sample profile measurements at experimental temperatures. The dissolution quantities were calculated from the MCPs obtained using high-resolution laser measurements including the dimensions of the entire corroded sample surface. This enhanced the accurateness and trustworthiness of the results. The marginally declining slope or a nearly linear fashion of the dissolution quantities indicated quasi-steady dissolution. The Marangoni groove was present at all three experimental temperatures. The diffusivity of magnesia excluding the groove was successfully determined using the method based on Sherwood relations. The diffusivity of magnesia increased with the increasing temperature. At a given temperature, the increase in the diffusivity with the dissolution time was moderate, probably because of the decrease in the viscosity due to magnesia dissolution. The linear tendency in the Arrhenius plot confirmed the plausibility of the diffusivities, due to which, an accurate estimation of diffusivity at other temperatures can be obtained without performing the experiments. To evaluate the results for calculating effective binary diffusivities, the method that considers the deviations from the cylinder shape is recommended. Although these investigations were performed at 200 rpm, forced convection is expected to overrule the Marangoni convection at sufficiently high rotational speeds. This is the case when the critical Reynolds number (\(Re_{c}\)) is exceeded. The identification of a quantitative relation defining such \(Re_{c}\) is a potential future research direction. Conceptualization, B., H.H. and S.V. ; Investigation--Performing experiments and evaluation of results, B.; Methodology, B.; Formal analysis, B. and S.V. ; Validation, B.; Writing--original draft, B.; Visualization, B.; Writing--review & editing, H.H. and S.V. ; Supervision, H.H. and S.V. ; Resources, H.H. ; Funding acquisition, H.H. ; Project administration, S.V. All authors have read and agreed to the published version of the manuscript. The authors gratefully acknowledge the financial support under the scope of the COMET program within the K2 Center \"Integrated Computational Material, Process and Product Engineering (IC-MPPE)\" (Project No 859480). This program is supported by the Austrian Federal Ministries for Transport, Innovation, and Technology (BMVIT) and the Digital and Economic Affairs (BMDW), represented by the Austrian Research Funding Association (FFG), and the federal states of Styria, Upper Austria, and Tyrol. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{3}{*}{**Temperature**} & \multirow{3}{*}{**Corrosion Step, \(i\)**} & \multicolumn{2}{c}{**Diffusivity Using Sherwood**} & \multirow{3}{*}{**Effusivity Using Sherwood**} & \multirow{3}{*}{**Error (\%),**} \\  & & **Modified Tachibana and Fukui.** & & & \\  & & [15, 61] and Levich [63], \(D_{i,T}\) & & (\(\times 10^{-11}\) m\({}^{2}\)/s) & \\ \hline \multirow{6}{*}{1500 \({}^{\circ}\)C} & 1 & 21.68869 & 23.69462 & \(-\)8.47 \\ \cline{2-5}  & 2 & 25.55256 & 25.86278 & \(-\)1.20 \\ \cline{2-5}  & 3 & 40.66419 & 37.37829 & 8.79 \\ \cline{2-5}  & 4 & 26.83829 & 22.68239 & 18.32 \\ \cline{2-5}  & 5 & 33.96658 & 26.49371 & 28.21 \\ \cline{2-5}  & 6 & 34.35245 & 24.55846 & 39.88 \\ \cline{2-5}  & 7 & 37.68810 & 24.80654 & 51.93 \\ \hline \multirow{6}{*}{1550 \({}^{\circ}\)C} & 1 & 42.68372 & 42.94205 & \(-\)0.60 \\ \cline{2-5}  & 2 & 51.28981 & 46.86623 & 9.44 \\ \cline{1-1} \cline{2-5}  & 3 & 58.40322 & 48.03614 & 21.58 \\ \cline{1-1} \cline{2-5}  & 4 & 64.12555 & 47.33054 & 35.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
**Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data that support the findings of this study are available on reasonable request from the corresponding author.