Internal flows of pure vapor experiencing film condensation on the bottom wall of an inclined (horizontal to vertical) channel and the inside wall of a vertical cylinder are studied. The annular flow regime considered here has turbulent (or laminar) vapor in the core and thin laminar condensate on the wall. Both smooth and wavy interfaces are considered. We propose a theory which yields a new general asymptotic form of interfacial shear, addresses solvability of the governing equations, gives the solution of the equations near the point of onset of condensation and facilitates implementation of one- or two-dimensional numerical schemes for the entire flow. The results, in a suitable limit, are shown to be in excellent agreement with a classical exact solution. We implement a one-dimensional numerical solution scheme to assess popular interfacial shear models and heat transfer correlations. These assessments, based on comparison of computational predictions with data from well-known experiments, identify two potentially good interfacial shear models which can be further developed for greater reliability.