Physically based closed-form solutions for film condensation of pure vapors in vertical tubes

Abstract

This work analytically solves the governing equations of the laminar film condensation from pure vapors in vertical tubes to find the condensate film thickness. The solution is then extended to turbulent flow conditions for steam. All other relevant quantities are derived from the film thickness solution. For laminar film condensation of quiescent vapors, an exact explicit solution and an approximate closed-form solution were found by using a new definition of the dimensionless film thickness, the Lambert W-function, and a logarithmic function approximation. For laminar mixed-convection film condensation with interfacial shear stress, an approximate closed-form solution was found by using a new definition of the pressure gradient. For turbulent film condensation of steam, correlations of the turbulent vapor and liquid viscosities were formed by asymptotically comparing this approximate laminar closed-form solution to a turbulent flow numerical solution. The present solutions compared very well to published numerical and experimental data.