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Ocean thermal energy conversion (OTEC) is a process in which the thermal gradient in ocean waters is used to evaporate and condense a working fluid and thereby extract useful work. Most studies of OTEC systems have focused on the economics and steady state behavior of this alternative energy conversion method. In this paper, one subsystem of the OTEC process is modelled in full transient, non-linear detail. Non-linearities occur due to the two-phase boiling process and the enthalpy-temperature thermophysics of the working fluid. The distributed nature of the system occurs due to the continuous change of percent gas in the boiler as the working fluid moves from the entrance (all liquid) to exit (all or nearly all gas). A numerical solution technique is proposed based on discretization. The evaporator considered is of the cross-flow type using propane as the working fluid, however the technique is valid for any channel configuration and working fluid provided that vertical flow exists in the working fluid. The model is used for transient studies in a wide range of working states.