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This work presents the design of a model-based nonlinear observer of an evaporator (a two-phase flow heat exchanger) for advanced dynamic control of air conditioning and refrigeration systems. A control-oriented, low-order model is derived for the evaporator. Based on sensor measurements of the evaporating temperature, the nonlinear observer can be used to estimate the heat transfer rate and the length of two-phase section that cannot be measured directly. The convergence of the observer is proved using contraction theory. The simulation results and experimental testing also demonstrate the convergence. In air conditioning and refrigeration applications, the nonlinear observer can be utilized to synthesize feedback linearization nonlinear control and provide accurate refrigerant charge inventory estimation and optimization.