Evaporative Cooling and Free-Cooling technologies have gained a growing interest in air-conditioning systems and they are suitable in different air conditioning applications: commercial, industrial, residential, and data centers. The Evaporative Cooling technologies are environmentally friendly and they have a very low global warming impact. Moreover, under the right applications, conditions, and operations, these technologies can provide excellent cooling and ventilation with minimal energy consumption. Since computing experiment based on mathematical modelling enables conduction of research in a shorter time and at smaller costs, in this paper first we develop a First-Principle Data-Driven model for an Indirect Evaporative Cooling system with Free Cooling and then we accordingly design a Matlab-based simulation environment. In particular, we model the key component, i.e. the evaporative heat exchanger, by means of a static Moving Boundary approach that segments the heat exchanger depending on the physical phenomena that occur inside it, providing a good balance between model complexity and accuracy. Simulation examples show how the model mimics properly some fundamental thermal aspects of the indirect evaporative cooling process.