In this chapter we will consider laminar flow of the condensate film of water vapor on the surface of a vertical plate. Condensation occurs if the water vapor is cooled below its saturation temperature. During condensation, latent heat of condensation is released and is assumed to be transferred from the water vapor–liquid condensate film interface to the cooler vertical plate surface only by conduction. The condensate film starts at zero thickness at the top of the vertical plate and starts to flow downwards under the action of gravity while the condensate film thickness grows. In the present analysis, we will assume a laminar flow of the condensate film, namely the Reynolds number will be less than 2000, and we will also assume that the condensate film is flowing downwards smoothly without any waviness. The heat transfer coefficient for a condensate film in a laminar flow was first developed by Nusselt in 1916.