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Abstract: This paper presents a theoretical and numerical model to predict film condensation heat transfer in mini and micro-channels of different internal shapes. The model is based on a finite volume formulation of the Navier--Stokes and energy equations and it includes the contributions of the unsteady terms, surface tension, axial shear stresses, gravitational forces and wall conduction. Notably, interphase mass transfer and near-to-wall effects (disjoining pressure) are also included. Dimensional analysis and characteristic numbers of the process are proposed and simulation results are shown both in dimensionless and dimensional representations. Isothermal, iso-heat flux and variable heat flux external wall boundary conditions have been implemented and their effects on the distribution of the heat flux are shown and compared. The instantaneous local and perimeter-averaged heat transfer coefficients, the liquid condensate film thickness distribution, the cross sectional void fraction and the mean vapor quality can be obtained for different channel shapes. Results obtained for steady state conditions are presented for circular, elliptical (with different eccentricities), flattened (with different aspect ratios) and flower shape cross sections for R-134a and ammonia, for hydraulic diameters between 10μm and 3mm. A time dependent simulation with variable heat flux is presented for a copper channel having a length of 4cm and a rectangular cross section with a hydraulic diameter of 133μm and an aspect ratio of 2, showing the importance of axial conduction at this length scale. The model has been validated versus various benchmark cases and versus experimental data available in literature. [Copyright &y& Elsevier]