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A mathematical model is developed for the description of the thermohydraulics of the two‐phase flow phenomenon in a vertical pipe. Using an additional momentum equation for the slip velocity, it is shown that the computation of slip and pressure drop from the model equations is possible without the use of any external correlations. The finite element method is used to solve the governing equations. The predictions for a steam‐water two‐phase flow in vertical upflow with constant wall heat flux agree well with experimental results and with widely used correlations.

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