A closed-form solution for laminar film condensation from quiescent pure vapours on curved vertical walls

An analytical solution is derived for the governing equations of steady laminar film condensation from quiescent pure vapours on convex and concave curved vertical walls. The analysis is the equivalent in cylindrical coordinates of the Nusselt classical analysis for a vertical flat plate. An exact solution that uses the Lambert W-function is derived. An accurate simpler approximate closed-form solution is also obtained that can be easily used. Both solutions compute the axial variation of condensate film thickness, which can be used to compute local heat transfer coefficient. The deviation in the local heat transfer coefficient between the new approximate solution and the Nusselt solution would be about eight to ten percent for a film thickness that is ten percent of the curved wall radius.