The presented work describes a mathematical model for the simulation of the heat transfer in a horizontal falling film evaporator for sea water desalination in the context of a multi-effect distillation process. The simultaneous evaporation and condensation of falling films on the inside and outside of a horizontal tube is mathematically described and solved numerically. For the description of radial heat transfer, the pipe circumference is divided into an impingement zone and a zone of laminar flow. Different model equations are implemented for both zones. Moreover, the accumulation of condensate at the bottom of the pipe, as well as liquid motion in axial direction is described. The inside pressure drop along the tube, as well as the temperature changes were calculated. The model of outer heat transfer is validated for a limited range of Reynolds numbers. It is compared to experimental data and numerical results from literature and it is shown how the application of the model may be extended to a larger range of outside-Reynolds numbers. Regarding the phenomena inside the tube, the calculated results indicate a significant relevance of the pressure drop on the heat transfer for increased pipe lengths. The reducing influence of accumulating condensate on the overall heat transfer is identified as comparably low. Finally, various combinations of pipe diameters and lengths are analyzed and the associated transmitted heat flows are graphically summarized.