Flow with evaporation in parallel lines with common inlet and outlet headers may result in an uneven flow distribution among the parallel pipes. The prediction of the flow rate distribution in steady state as well as under transient conditions was based on simplified models. In this paper a more accurate time dependent model based on the temporal-local flow pattern in the pipe is presented. The pipe is subdivided into numerical sections and the calculation of the pressure drop in each cell is based on mechanistic models that are specific for the flow pattern in the cell. The analysis is used to calculate the steady state solutions for the flow rate distribution among the pipes and the temperature, holdup, mass concentration and quality along each pipe. A linear stability analysis is performed to demarcate between stable and unstable steady state solutions. In addition transient simulations are carried out to predict the system response to finite disturbances and to calculate the system behavior due to variations in the operating conditions such as inlet flow rate and heating power input. (C) 2011 Elsevier Ltd. All rights reserved.