A numerical evaluation of the heat and mass transfer concerning a flat capillary evaporator provided by a bi-layered porous wick is presented. The wick has a shape of a flat disc and is assembled between the liquid feeding channel and the vapor chamber. An external heat input is applied into the upper surface of the bi-layered wick, where the working fluid evaporates. The mass and heat transfer are modeled using the mass and energy conservation equations. The model allows to verify the effect of design variables, such as working fluids, dimensions, permeability, average pore radius and thermal conductivity of the wick, in the performance of the capillary evaporator. It can be used as a predictive tool to design similar capillary pumping systems for thermal control of satellite or electronics systems in general.