The Nusselt number of a hot sphere levitated by a volatile pool

The duration of the inverse Leidenfrost phenomenon depends on the Nusselt number Nu of the sphere, itself determined by the equations of motion and heat flow governing the thin film of vapour which are themselves coupled to the elliptic Laplace relation determining the shape of the entire liquid-vapour interface. In this talk, it is shown that in the limit as the ratio h/b of film thickness to sphere radius vanishes, all properties of the phenomenon, including the Nusselt number relation, can be calculated numerically using only the Laplace relation and the boundary layer equations describing the thin film; it is not necessary to introduce equations of motion and heat flow governing the outer thick region. In Morris (2024), this method is demonstrated by using it to determine Nu for a sphere sufficiently small that the acceleration g due to gravity is negligible thoughout the governing equations, except where multiplied by the density of the sphere. In addition to those results, in this talk, numerical results for Nu obtained by applying the method to larger spheres will also be described.