A closed-form solution for laminar film condensation from downward pure vapour flow in vertical tubes

An analytical solution is derived for the film thickness for simplified steady-state governing equations of laminar film condensation from laminar pure vapours flowing downward in vertical tubes. This approach yields an accurate, approximate closed-form non-marching solution for the condensate film thickness. All other relevant quantities such as the heat transfer coefficient, the vapour and liquid velocity profiles, the vapour and liquid mass flow rates, the interfacial shear stress, and the pressure gradient can be easily computed in closed-form from this solution directly at any given axial location. The present solution compares very well to other analytical works that require more complicated iterative techniques with a marching solution approach.