The two-phase flow region of a capillary tube-suction line heat exchanger was satisfactorily modeled rising the flash point as the start of an initial value, marching problem. Four governing differential equations and their implicit finite-difference approximations were derived from energy and momentum balances taken on heat exchanger differential control volumes. By assuming a linear quality profile in the heat exchanger, four working equations that are both decoupled and explicit were developed. The model was compared to a previous model that calculated the quality profile and to experimental data. The previous model showed fair agreement with experimental data only when the assumed flash point location resulted in a linear quality profile. Any other flash point location resulted in either no solution over the complete heat exchanger length or else significant errors. In contrast, the model proposed here showed fair agreement with experimental data, even when the flash point location was slightly in error. The new model is thus more satisfactory for design, because it allows realistic corrections to be made at the upstream boundary based on observing errors at the downstream boundary. It also reduced the number of computations since the working equations are decoupled and explicit.