This paper presents numerical simulations of annular laminar film condensation heat transfer in microchannels of different internal shapes. The model, which is based on a finite volume formulation of the Navier-Stokes and energy equations for the liquid phase only, importantly accounts for the effects of axial and peripheral wall conduction and nonuniform heat flux not included in other models so far in the literature. The contributions of the surface tension, axial shear stresses, and gravitational forces are included. This model has so far been validated versus various benchmark cases and versus experimental data available in literature, predicting microchannel heat transfer data with an average error of 20% or better. It is well known that the thinning of the condensate film induced by surface tension due to gravity forces and shape of the surface, also known as the "Gregorig" effect, has a strong consequence on the local heat transfer coefficient in condensation. Thus, the present model accounts for these effects on the heat transfer and pressure drop for a wide variety of geometrical shapes, sizes, wall materials, and working fluid properties. In this paper, the conjugate heat transfer problem arising from the coupling between the thin film fluid dynamics, the heat transfer in the condensing fluid, and the heat conduction in the channel wall has been studied. In particular, the work has focused on three external channel wall boundary conditions: a uniform wall temperature, a nonuniform wall heat flux, and single-phase convective cooling are presented. As the scale of the problem is reduced, i.e., when moving from mini- to microchannels, the results show that the axial conduction effects can become very important in the prediction of the wall temperature profile and the magnitude of the heat transfer coefficient and its distribution along the channel. [DOI: 10.1115/1.4005712]