Solving two-phase heat exchanger equations by using the finite element method

Heat exchangers (HEX) are widely used in a large number of industrial processes, as well as on-board auxiliary devices. One way to increase HEX thermal effectiveness, and therefore reduce weight, is to use phase-change processes in one or both working fluids. There are simplified models in the literature that provide HEX temperature fields, useful in the early design phases. However, these models assume single-phase fluids. This work generalizes the HEX equations for different arrangements (parallel, counter and cross flow configurations) considering vaporization (evaporation or boiling) or condensation processes. The application of the finite element method (FEM) is also described to obtain a numerical approximation of the solution in an efficient manner. The proposed method provides a general framework where the application of specific heat transfer coefficients correlations or fluid properties is straightforward. As a practical application, several operating conditions (number of transfer units until 5 and mass flow ratios between 0.1 and 1) and arrangements (parallelflow, counterflow and unmixed-unmixed crossflow) of a simplified HEX using coolant R123 and liquid water as working fluids are analyzed where the heat transfer coefficient depends on the vapor fraction. R123 coolant flows through 2 mm diameter pipes, in liquid phase at the HEX inlet and undergoing a complete or partial evaporation process depending on the operating point.