Self-similarity in the problem of laminar film boiling on a vertical surface submerged in a large volume of a liquid

Using the methods of self-similarity for a laminar free-convective film boiling on a vertical finite-length surface submerged into a large volume of an arbitrarily subcooled liquid, we have derived expressions for the Nusselt criterion with a continuous transition from the film boiling in the saturated liquid to conditions of the strongly subcooled liquid for heat transfer between the heating surface and the interface, as well as for heat transfer from this interface to the bulk of the liquid while simultaneously taking radiative heat transfer into account. The existence of a hierarchy of different types of self-similarity in the given problem is demonstrated.