Analysis of Conduction-Controlled Rewetting of a Vertical Surface

The present paper presents a two-dimensional analysis of conduction-controlled rewetting of a vertical surface, whose initial temperature is greater than the rewetting temperature. The physical model consists of an infinitely extended vertical slab with the surface of the dry region adiabatic and the surface of the wet region associated with a constant heat transfer coefficient. The physical problem is characterized by three parameters: the Peclet number or the dimensionless wetting velocity, the Biot number, and a dimensionless temperature. Limiting solutions for large and small Peclet numbers obtained by utilizing the Wiener-Hopf technique and the kernel-substitution method exhibit simple functional relationships among the three dimensionless parameters. A semi- empirical relation has been established for the whole range of Peclet numbers. The solution for large Peclet numbers possesses a functional form different from existing approximate two-dimensional solutions, while the solution for small Peclet numbers reduces to existing one-dimensional solution for small Biot numbers. Discussion of the present findings has been made with respect to previous analyses and experimental observations.