The first law of thermo is one equation you could try.
If you are interested in the heat transfer coefficient or the "critical heat flux" for boiling, the correlations by Kon'Kov and Doroshchuk are generally agreed upon for vertical smooth bore tubes. Refer to heat transfer texts that were edited by S. Kakac.
"Whom the gods would destroy, they first make mad "
Boiling or condensing inside vertical tube are not evaluated by any single equation today. Both directions of phase change go through 'flow regimes' in which the each phase may be turbulent, transition, or laminar by velocity or annular, bubble, sheer, flooded (ect.) by shape. These condition are determined and analyzed in increments that are weighted over the length of the tube. Short of the data and tools, you might estimate from text (Kern) or web resources.
