**4. Conclusions**

A semi-analytical model of heat transfer between liquid and vapor has been proposed, using a single bubble approach, with the adaptation of the Fourier thermal equation to real cooling conditions and includes the effects of sensible and latent heat. The model appears to be physically consistent and interpretable trends have been obtained. The liquid surface tension, the injection depth and the thermal diffusivity of the vapor have been investigated, finding antagonistic behavior in the cooling process. Their effect results in the existence of an optimal injection depth that optimizes the heat transfer at given thermodynamic conditions of the vapor entering the desuperheater and at given bubble size.

The model can be proposed as a valid tool to help the design of multi-stage systems. Further theoretical and experimental investigations have been planned and will be performed in the future for a full validation of the model and for extension to the general area of multiple bubbles flow.

**Author Contributions:** Conceptualization, G.S.; data curation, L.C.; formal analysis, G.C.; investigation, G.S. and G.C.; methodology, G.S., L.C.; writing—original draft, G.C., L.C.; writing—review and editing, G.S. and G.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
