External-cooling indirect evaporative coolers with different configurations and working air sources are incomprehensively analyzed and compared so far. This paper investigates the mechanism and theory of operation of indirect flat-panel evaporative coolers based on X-analysis. Then, based on the second law of thermodynamics analysis, the entropy production rate of the flat-plate heat exchanger of the cooler is calculated. As a result of this analysis, the optimal energy efficiency-evaporation efficiency and cooling capacity values are presented in terms of effective parameters in the design.